Dynamics and Stability of Rolling Viscoelastic Tires

DOE Office of Scientific and Technical Information (OSTI.GOV)

Potter, Trevor

2013-04-30

Current steady state rolling tire calculations often do not include treads because treads destroy the rotational symmetry of the tire. We describe two methodologies to compute time periodic solutions of a two-dimensional viscoelastic tire with treads: solving a minimization problem and solving a system of equations. We also expand on work by Oden and Lin on free spinning rolling elastic tires in which they disovered a hierachy of N-peak steady state standing wave solutions. In addition to discovering a two-dimensional hierarchy of standing wave solutions that includes their N-peak hiearchy, we consider the eects of viscoelasticity on the standing wavemore » solutions. Finally, a commonplace model of viscoelasticity used in our numerical experiments led to non-physical elastic energy growth for large tire speeds. We show that a viscoelastic model of Govindjee and Reese remedies the problem.« less

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

PubMed

Guo, Xiao; Wei, Peijun

2016-03-01

The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

Magnetorheological elastomer vibration isolation of tunable three-dimensional locally resonant acoustic metamaterial

NASA Astrophysics Data System (ADS)

Xu, Zhenlong; Tong, Jie; Wu, Fugen

2018-03-01

Magnetorheological elastomers (MREs) are used as cladding in three-dimensional locally resonant acoustic metamaterial (LRAM) cores. The metamaterial units are combined into a vibration isolator. Two types of LRAMs, namely, cubic and spherical kernels, are constructed. The finite element method is used to analyze the elastic band structures, transmittances, and vibration modes of the incident elastic waves. Results show that the central position and width of the LRAM elastic bandgap can be controlled by the application of an external magnetic field; furthermore, they can be adjusted by changing the MRE cladding thickness. These methods contribute to the design of metamaterial MRE vibration isolators.

Interaction of Lamb Waves with Fatigue Cracks in Aluminum

DTIC Science & Technology

2011-09-01

Interaction of Lamb Waves with Fatigue Cracks in Aluminum E. D. SWENSON, C. T. OWENS and C. ALLEN ABSTRACT Elastic waves can travel across...the interaction of Lamb waves with both open and closed low-cycle fatigue cracks in aluminum plates using a three-dimensional laser Doppler vibrometer...and antisymmetric Lamb wave modes differ upon encountering fatigue cracks. INTRODUCTION The use of guided elastic waves (Lamb waves) has shown

Band transition and topological interface modes in 1D elastic phononic crystals.

PubMed

Yin, Jianfei; Ruzzene, Massimo; Wen, Jihong; Yu, Dianlong; Cai, Li; Yue, Linfeng

2018-05-01

In this report, we design a one-dimensional elastic phononic crystal (PC) comprised of an Aluminum beam with periodically arranged cross-sections to study the inversion of bulk bands due to the change of topological phases. As the geometric parameters of the unit cell varies, the second bulk band closes and reopens forming a topological transition point. This phenomenon is confirmed for both longitudinal waves and bending waves. By constructing a structural system formed by two PCs with different topological phases, for the first time, we experimentally demonstrate the existence of interface mode within the bulk band gap as a result of topological transition for both longitudinal and bending modes in elastic systems, although for bending modes, additional conditions have to be met in order to have the interface mode due to the dispersive nature of the bending waves in uniform media compared to the longitudinal waves.

Solitons interaction and integrability for a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Guo, Yong-Jiang; Li, Hui-Min

2018-03-01

Under investigation in this paper is a (2+1)-dimensional variable-coefficient Broer-Kaup system in water waves. Via the symbolic computation, Bell polynomials and Hirota method, the Bäcklund transformation, Lax pair, bilinear forms, one- and two-soliton solutions are derived. Propagation and interaction for the solitons are illustrated: Amplitudes and shapes of the one soliton keep invariant during the propagation, which implies that the transport of the energy is stable for the (2+1)-dimensional water waves; and inelastic interactions between the two solitons are discussed. Elastic interactions between the two parabolic-, cubic- and periodic-type solitons are displayed, where the solitonic amplitudes and shapes remain unchanged except for certain phase shifts. However, inelastically, amplitudes of the two solitons have a linear superposition after each interaction which is called as a soliton resonance phenomenon.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Davey-Stewartson system on surface waves of finite depth

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Xie, Xi-Yang; Wu, Xiao-Yu; Sun, Yan; Guo, Yong-Jiang

2018-04-01

Under investigation in this paper is a (2+1)-dimensional Davey-Stewartson system, which describes the transformation of a wave-packet on water of finite depth. By virtue of the bell polynomials, bilinear form, Bäcklund transformation and Lax pair are got. One- and two-soliton solutions are obtained via the symbolic computation and Hirota method. Velocity and amplitude of the one-soliton solutions are relevant with the wave number. Graphical analysis indicates that soliton shapes keep unchanged and maintain their original directions and amplitudes during the propagation. Elastic overtaking and head-on interactions between the two solitons are described.

A third-order moving mesh cell-centered scheme for one-dimensional elastic-plastic flows

NASA Astrophysics Data System (ADS)

Cheng, Jun-Bo; Huang, Weizhang; Jiang, Song; Tian, Baolin

2017-11-01

A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Grüneisen equation of state, the Wilkins constitutive model, and the von Mises yielding criterion. The scheme combines the Lagrangian method with the MMPDE moving mesh method and adaptively moves the mesh to better resolve shock and other types of waves while preventing the mesh from crossing and tangling. It can be viewed as a direct arbitrarily Lagrangian-Eulerian method but can also be degenerated to a purely Lagrangian scheme. It treats the relative velocity of the fluid with respect to the mesh as constant in time between time steps, which allows high-order approximation of free boundaries. A time dependent scaling is used in the monitor function to avoid possible sudden movement of the mesh points due to the creation or diminishing of shock and rarefaction waves or the steepening of those waves. A two-rarefaction Riemann solver with elastic waves is employed to compute the Godunov values of the density, pressure, velocity, and deviatoric stress at cell interfaces. Numerical results are presented for three examples. The third-order convergence of the scheme and its ability to concentrate mesh points around shock and elastic rarefaction waves are demonstrated. The obtained numerical results are in good agreement with those in literature. The new scheme is also shown to be more accurate in resolving shock and rarefaction waves than an existing third-order cell-centered Lagrangian scheme.

Liquid-assisted tunable metasurface for simultaneous manipulation of surface elastic and acoustic waves

NASA Astrophysics Data System (ADS)

Yuan, Si-Min; Ma, Tian-Xue; Chen, A.-Li; Wang, Yue-Sheng

2018-03-01

A tunable and multi-functional one-dimensional metasurface, which is formed by engraving periodic semi-ellipse grooves on the surface of an aluminum half-space, is proposed in this paper. One characteristic of the metasurface is the manipulation of multi-physical fields, i.e. it could be utilized to manipulate surface elastic and acoustic waves simultaneously. The dispersion curves of the elastic and acoustic waves can be effectively tuned by adding liquids into the grooves. Based on the tunability different applications can be realized by adding different volumes of different liquids into the grooves. As an example, simultaneous rainbow trapping of the surface elastic and acoustic waves is demonstrated in the metasurface. Moreover, a resonant cavity where the elastic and acoustic waves are highly confined is reported. The proposed metasurface paves the way to the design of multi-functional devices for simultaneous control of elastic and acoustic waves.

Elastic guided waves in a layered plate with rectangular cross section.

PubMed

Mukdadi, O M; Desai, Y M; Datta, S K; Shah, A H; Niklasson, A J

2002-11-01

Guided waves in a layered elastic plate of rectangular cross section (finite width and thickness) has been studied in this paper. A semianalytical finite element method in which the deformation of the cross section is modeled by two-dimensional finite elements and analytical representation of propagating waves along the length of the plate has been used. The method is applicable to arbitrary number of layers and general anisotropic material properties of each layer, and is similar to the stiffness method used earlier to study guided waves in a laminated composite plate of infinite width. Numerical results showing the effect of varying the width of the plate on the dispersion of guided waves are presented and are compared with those for an infinite plate. In addition, effect of thin anisotropic coating or interface layers on the guided waves is investigated.

Problems of interaction longitudinal shear waves with V-shape tunnels defect

NASA Astrophysics Data System (ADS)

Popov, V. G.

2018-04-01

The problem of determining the two-dimensional dynamic stress state near a tunnel defect of V-shaped cross-section is solved. The defect is located in an infinite elastic medium, where harmonic longitudinal shear waves are propagating. The initial problem is reduced to a system of two singular integral or integro-differential equations with fixed singularities. A numerical method for solving these systems with regard to the true asymptotics of the unknown functions is developed.

A discontinuous Galerkin method for poroelastic wave propagation: The two-dimensional case

NASA Astrophysics Data System (ADS)

Dudley Ward, N. F.; Lähivaara, T.; Eveson, S.

2017-12-01

In this paper, we consider a high-order discontinuous Galerkin (DG) method for modelling wave propagation in coupled poroelastic-elastic media. The upwind numerical flux is derived as an exact solution for the Riemann problem including the poroelastic-elastic interface. Attenuation mechanisms in both Biot's low- and high-frequency regimes are considered. The current implementation supports non-uniform basis orders which can be used to control the numerical accuracy element by element. In the numerical examples, we study the convergence properties of the proposed DG scheme and provide experiments where the numerical accuracy of the scheme under consideration is compared to analytic and other numerical solutions.

Reflection and transmission of elastic waves through a couple-stress elastic slab sandwiched between two half-spaces

NASA Astrophysics Data System (ADS)

Wang, Changda; Chen, Xuejun; Wei, Peijun; Li, Yueqiu

2017-12-01

The reflection and transmission of elastic waves through a couple-stress elastic slab that is sandwiched between two couple-stress elastic half-spaces are studied in this paper. Because of the couple-stress effects, there are three types of elastic waves in the couple-stress elastic solid, two of which are dispersive. The interface conditions between two couple-stress solids involve the surface couple and rotation apart from the surface traction and displacement. The nontraditional interface conditions between the slab and two solid half-spaces are used to obtain the linear algebraic equation sets from which the amplitude ratios of reflection and transmission waves to the incident wave can be determined. Then, the energy fluxes carried by the various reflection and transmission waves are calculated numerically and the normal energy flux conservation is used to validate the numerical results. The special case, couple-stress elastic slab sandwiched by the classical elastic half-spaces, is also studied and compared with the situation that the classical elastic slab sandwiched by the classical elastic half-spaces. Incident longitudinal wave (P wave) and incident transverse wave (SV wave) are both considered. The influences of the couple-stress are mainly discussed based on the numerical results. It is found that the couple-stress mainly influences the transverse modes of elastic waves.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

Topology optimization of two-dimensional elastic wave barriers

NASA Astrophysics Data System (ADS)

Van hoorickx, C.; Sigmund, O.; Schevenels, M.; Lazarov, B. S.; Lombaert, G.

2016-08-01

Topology optimization is a method that optimally distributes material in a given design domain. In this paper, topology optimization is used to design two-dimensional wave barriers embedded in an elastic halfspace. First, harmonic vibration sources are considered, and stiffened material is inserted into a design domain situated between the source and the receiver to minimize wave transmission. At low frequencies, the stiffened material reflects and guides waves away from the surface. At high frequencies, destructive interference is obtained that leads to high values of the insertion loss. To handle harmonic sources at a frequency in a given range, a uniform reduction of the response over a frequency range is pursued. The minimal insertion loss over the frequency range of interest is maximized. The resulting design contains features at depth leading to a reduction of the insertion loss at the lowest frequencies and features close to the surface leading to a reduction at the highest frequencies. For broadband sources, the average insertion loss in a frequency range is optimized. This leads to designs that especially reduce the response at high frequencies. The designs optimized for the frequency averaged insertion loss are found to be sensitive to geometric imperfections. In order to obtain a robust design, a worst case approach is followed.

Hamiltonian structures for systems of hyperbolic conservation laws

NASA Astrophysics Data System (ADS)

Olver, Peter J.; Nutku, Yavuz

1988-07-01

The bi-Hamiltonian structure for a large class of one-dimensional hyberbolic systems of conservation laws in two field variables, including the equations of gas dynamics, shallow water waves, one-dimensional elastic media, and the Born-Infeld equation from nonlinear electrodynamics, is exhibited. For polytropic gas dynamics, these results lead to a quadri-Hamiltonian structure. New higher-order entropy-flux pairs (conservation laws) and higher-order symmetries are exhibited.

Nonlinear elasticity in rocks: A comprehensive three-dimensional description

DOE PAGES

Lott, Martin; Remillieux, Marcel; Garnier, Vincent; ...

2017-07-17

Here we study theoretically and experimentally the mechanisms of nonlinear and nonequilibrium dynamics in geomaterials through dynamic acoustoelasticity testing. In the proposed theoretical formulation, the classical theory of nonlinear elasticity is extended to include the effects of conditioning. This formulation is adapted to the context of dynamic acoustoelasticity testing in which a low-frequency “pump” wave induces a strain field in the sample and modulates the propagation of a high-frequency “probe” wave. Experiments are conducted to validate the formulation in a long thin bar of Berea sandstone. Several configurations of the pump and probe are examined: the pump successively consists ofmore » the first longitudinal and first torsional mode of vibration of the sample while the probe is successively based on (pressure) $P$ and (shear) $S$ waves. The theoretical predictions reproduce many features of the elastic response observed experimentally, in particular, the coupling between nonlinear and nonequilibrium dynamics and the three-dimensional effects resulting from the tensorial nature of elasticity.« less

Scattering of surface water waves involving semi-infinite floating elastic plates on water of finite depth

NASA Astrophysics Data System (ADS)

Chakrabarti, Aloknath; Mohapatra, Smrutiranjan

2013-09-01

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

Wave excitations of drifting two-dimensional electron gas under strong inelastic scattering

NASA Astrophysics Data System (ADS)

Korotyeyev, V. V.; Kochelap, V. A.; Varani, L.

2012-10-01

We have analyzed low-temperature behavior of two-dimensional electron gas in polar heterostructures subjected to a high electric field. When the optical phonon emission is the fastest relaxation process, we have found existence of collective wave-like excitations of the electrons. These wave-like excitations are periodic in time oscillations of the electrons in both real and momentum spaces. The excitation spectra are of multi-branch character with considerable spatial dispersion. There are one acoustic-type and a number of optical-type branches of the spectra. Their small damping is caused by quasi-elastic scattering of the electrons and formation of relevant space charge. Also there exist waves with zero frequency and finite spatial periods—the standing waves. The found excitations of the electron gas can be interpreted as synchronous in time and real space manifestation of well-known optical-phonon-transient-time-resonance. Estimates of parameters of the excitations for two polar heterostructures, GaN/AlGaN and ZnO/MgZnO, have shown that excitation frequencies are in THz-frequency range, while standing wave periods are in sub-micrometer region.

External Vibration Multi-directional Ultrasound Shearwave Elastography (EVMUSE): Application in Liver Fibrosis Staging

PubMed Central

Zhao, Heng; Song, Pengfei; Meixner, Duane D.; Kinnick, Randall R.; Callstrom, Matthew R.; Sanchez, William; Urban, Matthew W.; Manduca, Armando; Greenleaf, James F.

2014-01-01

Shear wave speed can be used to assess tissue elasticity, which is associated with tissue health. Ultrasound shear wave elastography techniques based on measuring the propagation speed of the shear waves induced by acoustic radiation force are becoming promising alternatives to biopsy in liver fibrosis staging. However, shear waves generated by such methods are typically very weak. Therefore, the penetration may become problematic, especially for overweight or obese patients. In this study, we developed a new method called External Vibration Multi-directional Ultrasound Shearwave Elastography (EVMUSE), in which external vibration from a loudspeaker was used to generate a multi-directional shear wave field. A directional filter was then applied to separate the complex shear wave field into several shear wave fields propagating in different directions. A two-dimensional (2D) shear wave speed map was reconstructed from each individual shear wave field, and a final 2D shear wave speed map was constructed by compounding these individual wave speed maps. The method was validated using two homogeneous phantoms and one multi-purpose tissue-mimicking phantom. Ten patients undergoing liver Magnetic Resonance Elastography (MRE) were also studied with EVMUSE to compare results between the two methods. Phantom results showed EVMUSE was able to quantify tissue elasticity accurately with good penetration. In vivo EVMUSE results were well correlated with MRE results, indicating the promise of using EVMUSE for liver fibrosis staging. PMID:25020066

Thermal stress effects on the flexural wave bandgap of a two-dimensional locally resonant acoustic metamaterial

NASA Astrophysics Data System (ADS)

Li, Zhen; Zhu, Yun; Li, Yueming

2018-05-01

The elastic wave bandgap is obviously affected by heat while considering thermal stress. Nevertheless, the flat band, occurring in the lowest flexural branch, has not yet been explained clearly. This study investigates the influence of thermal stress on a flexural wave bandgap in a two-dimensional three-component acoustic metamaterial. Simulation results demonstrate that the band structure shifts to a lower frequency range, and the vibration response appears at a larger amplitude due to the bending stiffness being softened by the compressive membrane force. In addition, the first flexural band reduces to zero frequency in the central Brillouin zone. By viewing the vibration modes of the proposed unit cell, it is found that the out-of-plane mode shape attenuates with increasing temperature, while the in-plane vibration modes are unaffected by thermal stress.

Two-zone elastic-plastic single shock waves in solids.

PubMed

Zhakhovsky, Vasily V; Budzevich, Mikalai M; Inogamov, Nail A; Oleynik, Ivan I; White, Carter T

2011-09-23

By decoupling time and length scales in moving window molecular dynamics shock-wave simulations, a new regime of shock-wave propagation is uncovered characterized by a two-zone elastic-plastic shock-wave structure consisting of a leading elastic front followed by a plastic front, both moving with the same average speed and having a fixed net thickness that can extend to microns. The material in the elastic zone is in a metastable state that supports a pressure that can substantially exceed the critical pressure characteristic of the onset of the well-known split-elastic-plastic, two-wave propagation. The two-zone elastic-plastic wave is a general phenomenon observed in simulations of a broad class of crystalline materials and is within the reach of current experimental techniques.

Dynamics of film. [two dimensional continua theory

NASA Technical Reports Server (NTRS)

Zak, M.

1979-01-01

The general theory of films as two-dimensional continua are elaborated upon. As physical realizations of such a model this paper examines: inextensible films, elastic films, and nets. The suggested dynamic equations have enabled us to find out the characteristic speeds of wave propagation of the invariants of external and internal geometry and formulate the criteria of instability of their shape. Also included herein is a detailed account of the equation describing the film motions beyond the limits of the shape stability accompanied by the formation of wrinkles. The theory is illustrated by examples.

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media.

PubMed

Voinovich, Peter; Merlen, Alain

2005-12-01

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.

Two-dimensional numerical simulation of acoustic wave phase conjugation in magnetostrictive elastic media

NASA Astrophysics Data System (ADS)

Voinovich, Peter; Merlen, Alain

2005-12-01

The effect of parametric wave phase conjugation (WPC) in application to ultrasound or acoustic waves in magnetostrictive solids has been addressed numerically by Ben Khelil et al. [J. Acoust. Soc. Am. 109, 75-83 (2001)] using 1-D unsteady formulation. Here the numerical method presented by Voinovich et al. [Shock waves 13(3), 221-230 (2003)] extends the analysis to the 2-D effects. The employed model describes universally elastic solids and liquids. A source term similar to Ben Khelil et al.'s accounts for the coupling between deformation and magnetostriction due to external periodic magnetic field. The compatibility between the isotropic constitutive law of the medium and the model of magnetostriction has been considered. Supplementary to the 1-D simulations, the present model involves longitudinal/transversal mode conversion at the sample boundaries and separate magnetic field coupling with dilatation and shear stress. The influence of those factors in a 2-D geometry on the potential output of a magneto-elastic wave phase conjugator is analyzed in this paper. The process under study includes propagation of a wave burst of a given frequency from a point source in a liquid into the active solid, amplification of the waves due to parametric resonance, and formation of time-reversed waves, their radiation into liquid, and focusing. The considered subject is particularly important for ultrasonic applications in acoustic imaging, nondestructive testing, or medical diagnostics and therapy.

Breathers, quasi-periodic and travelling waves for a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation in fluids

NASA Astrophysics Data System (ADS)

Hu, Wen-Qiang; Gao, Yi-Tian; Zhao, Chen; Jia, Shu-Liang; Lan, Zhong-Zhou

2017-07-01

Under investigation in this paper is a generalized ?-dimensional Yu-Toda-Sasa-Fukayama equation for the interfacial wave in a two-layer fluid or the elastic quasi-plane wave in a liquid lattice. By virtue of the binary Bell polynomials, bilinear form of this equation is obtained. With the help of the bilinear form, N-soliton solutions are obtained via the Hirota method, and a bilinear Bäcklund transformation is derived to verify the integrability. Homoclinic breather waves are obtained according to the homoclinic test approach, which is not only the space-periodic breather but also the time-periodic breather via the graphic analysis. Via the Riemann theta function, quasi one-periodic waves are constructed, which can be viewed as a superposition of the overlapping solitary waves, placed one period apart. Finally, soliton-like, periodical triangle-type, rational-type and solitary bell-type travelling waves are obtained by means of the polynomial expansion method.

Wavelet-based multiscale adjoint waveform-difference tomography using body and surface waves

NASA Astrophysics Data System (ADS)

Yuan, Y. O.; Simons, F. J.; Bozdag, E.

2014-12-01

We present a multi-scale scheme for full elastic waveform-difference inversion. Using a wavelet transform proves to be a key factor to mitigate cycle-skipping effects. We start with coarse representations of the seismogram to correct a large-scale background model, and subsequently explain the residuals in the fine scales of the seismogram to map the heterogeneities with great complexity. We have previously applied the multi-scale approach successfully to body waves generated in a standard model from the exploration industry: a modified two-dimensional elastic Marmousi model. With this model we explored the optimal choice of wavelet family, number of vanishing moments and decomposition depth. For this presentation we explore the sensitivity of surface waves in waveform-difference tomography. The incorporation of surface waves is rife with cycle-skipping problems compared to the inversions considering body waves only. We implemented an envelope-based objective function probed via a multi-scale wavelet analysis to measure the distance between predicted and target surface-wave waveforms in a synthetic model of heterogeneous near-surface structure. Our proposed method successfully purges the local minima present in the waveform-difference misfit surface. An elastic shallow model with 100~m in depth is used to test the surface-wave inversion scheme. We also analyzed the sensitivities of surface waves and body waves in full waveform inversions, as well as the effects of incorrect density information on elastic parameter inversions. Based on those numerical experiments, we ultimately formalized a flexible scheme to consider both body and surface waves in adjoint tomography. While our early examples are constructed from exploration-style settings, our procedure will be very valuable for the study of global network data.

System and method to create three-dimensional images of non-linear acoustic properties in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T.; Schmitt, Denis P.; Skelt, Christopher; Johnson, Paul A.; Guyer, Robert; TenCate, James A.; Le Bas, Pierre-Yves

2013-01-01

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

Experimental evidence of coherent transport.

PubMed

Flores-Olmedo, E; Martínez-Argüello, A M; Martínez-Mares, M; Báez, G; Franco-Villafañe, J A; Méndez-Sánchez, R A

2016-04-28

Coherent transport phenomena are difficult to observe due to several sources of decoherence. For instance, in the electronic transport through quantum devices the thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities, destroy phase coherence. In other wave systems, the temperature and dephasing may not destroy the coherence and can then be used to observe the underlying wave behaviour of the coherent phenomena. Here, we observe coherent transmission of mechanical waves through a two-dimensional elastic Sinai billiard with two waveguides. The flexural-wave transmission, performed by non-contact means, shows the quantization when a new mode becomes open. These measurements agree with the theoretical predictions of the simplest model highlighting the universal character of the transmission fluctuations.

Experimental evidence of coherent transport

PubMed Central

Flores-Olmedo, E.; Martínez-Argüello, A. M.; Martínez-Mares, M.; Báez, G.; Franco-Villafañe, J. A.; Méndez-Sánchez, R. A.

2016-01-01

Coherent transport phenomena are difficult to observe due to several sources of decoherence. For instance, in the electronic transport through quantum devices the thermal smearing and dephasing, the latter induced by inelastic scattering by phonons or impurities, destroy phase coherence. In other wave systems, the temperature and dephasing may not destroy the coherence and can then be used to observe the underlying wave behaviour of the coherent phenomena. Here, we observe coherent transmission of mechanical waves through a two-dimensional elastic Sinai billiard with two waveguides. The flexural-wave transmission, performed by non-contact means, shows the quantization when a new mode becomes open. These measurements agree with the theoretical predictions of the simplest model highlighting the universal character of the transmission fluctuations. PMID:27121226

Computer simulation of the Farley-Buneman instability and anomalous electron heating in the auroral ionosphere

DOE Office of Scientific and Technical Information (OSTI.GOV)

Machida, S.; Goertz, C.K.

1988-09-01

We study the nonlinear saturation of the Farley-Buneman instability in a collisional plasma by a 2 1/2 dimensional electrostatic particle simulation which includes inelastic and elastic collisions of electrons and elastic collision of ions with neutrals. In our simulation, a uniform convection electric field is applied externally so that the relative velocity between the electrons and ions is greater than the ion sound speed and destabilizes the instability. We find a nonlinear frequency shift from higher to lower frequencies and diffusion of the wave spectrum in two dimensional wave number space. We are especially interested in finding whether the saturatedmore » wave turbulence can account for the anomalous heating rates observed in the polar ionosphere by Schlegel and St.-Maurice (1981). We find that the dominant mechanism for electron heating is due to an enhanced effective electron collision frequency and hence enhanced resistive heating as suggested by Primdahl (1986) and Robinson (1986) and not due to the heating of electrons by the electric field of the waves parallel to the magnetic field. For the ionospheric conditions discussed by Schlegel and St.-Maurice (1981) we find an anomalous heating rate of about 4 x 10/sup -7/ W/m/sup 3/. copyright American Geophysical Union 1988« less

Conical Refraction of Elastic Waves by Anisotropic Metamaterials and Application for Parallel Translation of Elastic Waves.

PubMed

Ahn, Young Kwan; Lee, Hyung Jin; Kim, Yoon Young

2017-08-30

Conical refraction, which is quite well-known in electromagnetic waves, has not been explored well in elastic waves due to the lack of proper natural elastic media. Here, we propose and design a unique anisotropic elastic metamaterial slab that realizes conical refraction for horizontally incident longitudinal or transverse waves; the single-mode wave is split into two oblique coupled longitudinal-shear waves. As an interesting application, we carried out an experiment of parallel translation of an incident elastic wave system through the anisotropic metamaterial slab. The parallel translation can be useful for ultrasonic non-destructive testing of a system hidden by obstacles. While the parallel translation resembles light refraction through a parallel plate without angle deviation between entry and exit beams, this wave behavior cannot be achieved without the engineered metamaterial because an elastic wave incident upon a dissimilar medium is always split at different refraction angles into two different modes, longitudinal and shear.

Metamaterials: supra-classical dynamic homogenization

NASA Astrophysics Data System (ADS)

Caleap, Mihai; Drinkwater, Bruce W.

2015-12-01

Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material parameters that can be electronic, magnetic, acoustic, or elastic, and must adequately represent the wave interaction behavior in the composite within desired frequency ranges. In some cases—for example, the low frequency regime—there exist various efficient ways by which effective material parameters for wave propagation in metamaterials may be found. However, the general problem of predicting frequency-dependent dynamic effective constants has remained unsolved. Here, we obtain novel mathematical expressions for the effective parameters of two-dimensional metamaterial systems valid at higher frequencies and wavelengths than previously possible. By way of an example, random configurations of cylindrical scatterers are considered, in various physical contexts: sound waves in a compressible fluid, anti-plane elastic waves, and electromagnetic waves. Our results point towards a paradigm shift in our understanding of these effective properties, and metamaterial designs with functionalities beyond the low-frequency regime are now open for innovation. Dedicated with gratitude to the memory of Prof Yves C Angel.

Static and dynamic properties of incommensurate smectic-A(IC) liquid crystals

NASA Technical Reports Server (NTRS)

Lubensky, T. C.; Ramaswamy, Sriram; Toner, John

1988-01-01

The elasticity, topological defects, and hydrodynamics of the incommensurate smectic A(IC) phase liquid crystals are studied. The phase is characterized by two colinear mass density waves of incommensurate spatial frequency. The elastic free energy is formulated in terms of a displacement field and a phason field. It is found that the topological defects of the system are dislocations with a nonzero phason field and phason field components. A two-dimensional Burgers lattice for these dislocations is introduced. It is shown that the hydrodynamic modes of the phase include first- and second-sound modes whose direction-dependent velocities are identical to those in ordinary smectics.

Thickness Measurement of Surface Attachment on Plate with Lamb Wave

NASA Astrophysics Data System (ADS)

Ma, Xianglong; Zhang, Yinghong; Wen, Lichao; He, Yehu

2017-12-01

Aiming at the thickness detection of the plate surface attachment, a nondestructive testing method based on the Lamb wave is presented. This method utilizes Lamb wave propagation characteristics of signals in a bi-layer medium to measure the surface attachment plate thickness. Propagation of Lamb wave in bi-layer elastic is modeled and analyzed. The two-dimensional simulation model of electromagnetic ultrasonic plate - scale is established. The simulation is conducted by software COMSOL for simulation analysis under different boiler scale thickness wave form curve. Through this study, the thickness of the attached material can be judged by analyzing the characteristics of the received signal when the thickness of the surface of the plate is measured.

Soliton interactions and Bäcklund transformation for a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili equation in fluid dynamics

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Sun, Yan

2018-01-01

In this paper, we investigate a (2+1)-dimensional variable-coefficient modified Kadomtsev-Petviashvili (mKP) equation in fluid dynamics. With the binary Bell-polynomial and an auxiliary function, bilinear forms for the equation are constructed. Based on the bilinear forms, multi-soliton solutions and Bell-polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton interactions are presented. Based on the graphic analysis, Parametric conditions for the existence of the shock waves, elevation solitons and depression solitons are given, and it is shown that under the condition of keeping the wave vectors invariable, the change of α(t) and β(t) can lead to the change of the solitonic velocities, but the shape of each soliton remains unchanged, where α(t) and β(t) are the variable coefficients in the equation. Oblique elastic interactions can exist between the (i) two shock waves, (ii) two elevation solitons, and (iii) elevation and depression solitons. However, oblique interactions between (i) shock waves and elevation solitons, (ii) shock waves and depression solitons are inelastic.

Shear Elasticity and Shear Viscosity Imaging in Soft Tissue

NASA Astrophysics Data System (ADS)

Yang, Yiqun

In this thesis, a new approach is introduced that provides estimates of shear elasticity and shear viscosity using time-domain measurements of shear waves in viscoelastic media. Simulations of shear wave particle displacements induced by an acoustic radiation force are accelerated significantly by a GPU. The acoustic radiation force is first calculated using the fast near field method (FNM) and the angular spectrum approach (ASA). The shear waves induced by the acoustic radiation force are then simulated in elastic and viscoelastic media using Green's functions. A parallel algorithm is developed to perform these calculations on a GPU, where the shear wave particle displacements at different observation points are calculated in parallel. The resulting speed increase enables rapid evaluation of shear waves at discrete points, in 2D planes, and for push beams with different spatial samplings and for different values of the f-number (f/#). The results of these simulations show that push beams with smaller f/# require a higher spatial sampling rate. The significant amount of acceleration achieved by this approach suggests that shear wave simulations with the Green's function approach are ideally suited for high-performance GPUs. Shear wave elasticity imaging determines the mechanical parameters of soft tissue by analyzing measured shear waves induced by an acoustic radiation force. To estimate the shear elasticity value, the widely used time-of-flight method calculates the correlation between shear wave particle velocities at adjacent lateral observation points. Although this method provides accurate estimates of the shear elasticity in purely elastic media, our experience suggests that the time-of-flight (TOF) method consistently overestimates the shear elasticity values in viscoelastic media because the combined effects of diffraction, attenuation, and dispersion are not considered. To address this problem, we have developed an approach that directly accounts for all of these effects when estimating the shear elasticity. This new approach simulates shear wave particle velocities using a Green's function-based approach for the Voigt model, where the shear elasticity and viscosity values are estimated using an optimization-based approach that compares measured shear wave particle velocities with simulated shear wave particle velocities in the time-domain. The results are evaluated on a point-by-point basis to generate images. There is good agreement between the simulated and measured shear wave particle velocities, where the new approach yields much better images of the shear elasticity and shear viscosity than the TOF method. The new estimation approach is accelerated with an approximate viscoelastic Green's function model that is evaluated with shear wave data obtained from in vivo human livers. Instead of calculating shear waves with combinations of different shear elasticities and shear viscosities, shear waves are calculated with different shear elasticities on the GPU and then convolved with a viscous loss model, which accelerates the calculation dramatically. The shear elasticity and shear viscosity values are then estimated using an optimization-based approach by minimizing the difference between measured and simulated shear wave particle velocities. Shear elasticity and shear viscosity images are generated at every spatial point in a two-dimensional (2D) field-of-view (FOV). The new approach is applied to measured shear wave data obtained from in vivo human livers, and the results show that this new approach successfully generates shear elasticity and shear viscosity images from this data. The results also indicate that the shear elasticity values estimated with this approach are significantly smaller than the values estimated with the conventional TOF method and that the new approach demonstrates more consistent values for these estimates compared with the TOF method. This experience suggests that the new method is an effective approach for estimating the shear elasticity and the shear viscosity in liver and in other soft tissue.

Comment on "Anomalous wave propagation in a one-dimensional acoustic metamaterial having simultaneously negative mass density and Young's modulus" [J. Acoust. Soc. Am. 132, 2887-2895 (2012)].

PubMed

Marston, Philip L

2014-03-01

The phase and group velocities of elastic guided waves are important in the physical interpretation of high frequency scattering by fluid-loaded elastic shells. Outside the context of scattering, those properties are also important for understanding the energy flow in acoustic metamaterials. In a recent investigation of acoustic metamaterials exhibiting anomalous wave propagation [J. Acoust. Soc. Am. 132, 2887-2895 (2012)] criticism of negative group velocity terminology was generalized to elastic waves guided on ordinary materials. Some context and justification for retaining the identification of negative group velocities associated with a type of backscattering enhancement for shells are explained here. The phase evolution direction is determined by the boundary conditions.

Bandgaps and directional properties of two-dimensional square beam-like zigzag lattices

NASA Astrophysics Data System (ADS)

Wang, Yan-Feng; Wang, Yue-Sheng; Zhang, Chuanzeng

2014-12-01

In this paper we propose four kinds of two-dimensional square beam-like zigzag lattice structures and study their bandgaps and directional propagation of elastic waves. The band structures are calculated by using the finite element method. Both the in-plane and out-of-plane waves are investigated simultaneously via the three-dimensional Euler beam elements. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. The effects of the geometry parameters of the xy- and z-zigzag lattices on the bandgaps are investigated and discussed. Multiple complete bandgaps are found owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the periodic systems. The deformed displacement fields of the harmonic responses of a finite lattice structure subjected to harmonic loads at different positions are illustrated to show the directional wave propagation. An extension of the proposed concept to the hexagonal lattices is also presented. The research work in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

A Novel Approach to Constrain Near-Surface Seismic Wave Speed Based on Polarization Analysis

NASA Astrophysics Data System (ADS)

Park, S.; Ishii, M.

2016-12-01

Understanding the seismic responses of cities around the world is essential for the risk assessment of earthquake hazards. One of the important parameters is the elastic structure of the sites, in particular, near-surface seismic wave speed, that influences the level of ground shaking. Many methods have been developed to constrain the elastic structure of the populated sites or urban basins, and here, we introduce a new technique based on analyzing the polarization content or the three-dimensional particle motion of seismic phases arriving at the sites. Polarization analysis of three-component seismic data was widely used up to about two decades ago, to detect signals and identify different types of seismic arrivals. Today, we have good understanding of the expected polarization direction and ray parameter for seismic wave arrivals that are calculated based on a reference seismic model. The polarization of a given phase is also strongly sensitive to the elastic wave speed immediately beneath the station. This allows us to compare the observed and predicted polarization directions of incoming body waves and infer the near-surface wave speed. This approach is applied to High-Sensitivity Seismograph Network in Japan, where we benchmark the results against the well-log data that are available at most stations. There is a good agreement between our estimates of seismic wave speeds and those from well logs, confirming the efficacy of the new method. In most urban environments, where well logging is not a practical option for measuring the seismic wave speeds, this method can provide a reliable, non-invasive, and computationally inexpensive estimate of near-surface elastic properties.

Instabilities in dynamic anti-plane sliding of an elastic layer on a dissimilar elastic half-space

NASA Astrophysics Data System (ADS)

Kunnath, R.

2012-12-01

The stability of dynamic anti-plane sliding at an interface between an elastic layer and an elastic half-space with dissimilar elastic properties is studied. Friction at the interface is assumed to follow a rate- and state-dependent law, with a positive instantaneous dependence on slip velocity and a rate weakening behavior in the steady state. The perturbations are of the form exp(ikx+pt), where k is the wavenumber, x is the coordinate along the interface, p is the time response to the perturbation and t is time. The results of the stability analysis are shown in Figs. 1 and 2 with the velocity weakening parameter b/a=5, shear wave speed ratio cs'/cs=1.2, shear modulus ratio μ'/μ=1.2 and non-dimensional layer thickness H=100. The normalized instability growth rate and normalized phase velocity are plotted as a function of wavenumber. Fig.1 is for a non-dimensional unperturbed slip velocity ɛ=5 (rapid sliding) while Fig. 2 is for ɛ=0.05 (slow sliding). The results show the destabilization of interfacial waves. For slow sliding, destabilization of interfacial waves is still seen, indicating that the quasi-static approximation to slow sliding is not valid. This is in agreement with the result of Ranjith (Int. J. Solids and Struct., 2009, 46, 3086-3092) who predicted an instability of long-wavelength Love waves in slow sliding.

Shear-wave elasticity measurements of three-dimensional cell cultures for mechanobiology

PubMed Central

Kuo, Po-Ling; Charng, Ching-Che; Wu, Po-Chen

2017-01-01

ABSTRACT Studying mechanobiology in three-dimensional (3D) cell cultures better recapitulates cell behaviors in response to various types of mechanical stimuli in vivo. Stiffening of the extracellular matrix resulting from cell remodeling potentiates many pathological conditions, including advanced cancers. However, an effective tool for measuring the spatiotemporal changes in elastic properties of such 3D cell cultures without directly contacting the samples has not been reported previously. We describe an ultrasonic shear-wave-based platform for quantitatively evaluating the spatiotemporal dynamics of the elasticity of a matrix remodeled by cells cultured in 3D environments. We used this approach to measure the elasticity changes of 3D matrices grown with highly invasive lung cancer cells and cardiac myoblasts, and to delineate the principal mechanism underlying the stiffening of matrices remodeled by these cells. The described approach can be a useful tool in fields investigating and manipulating the mechanotransduction of cells in 3D contexts, and also has potential as a drug-screening platform. PMID:27505887

Propagation of ultrasonic Love waves in nonhomogeneous elastic functionally graded materials.

PubMed

Kiełczyński, P; Szalewski, M; Balcerzak, A; Wieja, K

2016-02-01

This paper presents a theoretical study of the propagation behavior of ultrasonic Love waves in nonhomogeneous functionally graded elastic materials, which is a vital problem in the mechanics of solids. The elastic properties (shear modulus) of a semi-infinite elastic half-space vary monotonically with the depth (distance from the surface of the material). The Direct Sturm-Liouville Problem that describes the propagation of Love waves in nonhomogeneous elastic functionally graded materials is formulated and solved by using two methods: i.e., (1) Finite Difference Method, and (2) Haskell-Thompson Transfer Matrix Method. The dispersion curves of phase and group velocity of surface Love waves in inhomogeneous elastic graded materials are evaluated. The integral formula for the group velocity of Love waves in nonhomogeneous elastic graded materials has been established. The effect of elastic non-homogeneities on the dispersion curves of Love waves is discussed. Two Love wave waveguide structures are analyzed: (1) a nonhomogeneous elastic surface layer deposited on a homogeneous elastic substrate, and (2) a semi-infinite nonhomogeneous elastic half-space. Obtained in this work, the phase and group velocity dispersion curves of Love waves propagating in the considered nonhomogeneous elastic waveguides have not previously been reported in the scientific literature. The results of this paper may give a deeper insight into the nature of Love waves propagation in elastic nonhomogeneous functionally graded materials, and can provide theoretical guidance for the design and optimization of Love wave based devices. Copyright © 2015 Elsevier B.V. All rights reserved.

Scattering of Airy elastic sheets by a cylindrical cavity in a solid.

PubMed

Mitri, F G

2017-11-01

The prediction of the elastic scattering by voids (and cracks) in materials is an important process in structural health monitoring, phononic crystals, metamaterials and non-destructive evaluation/imaging to name a few examples. Earlier analytical theories and numerical computations considered the elastic scattering by voids in plane waves of infinite extent. However, current research suggesting the use of (limited-diffracting, accelerating and self-healing) Airy acoustical-sheet beams for non-destructive evaluation or imaging applications in elastic solids requires the development of an improved analytical formalism to predict the scattering efficiency used as a priori information in quantitative material characterization. Based on the definition of the time-averaged scattered power flow density, an analytical expression for the scattering efficiency of a cylindrical empty cavity (i.e., void) encased in an elastic medium is derived for compressional and normally-polarized shear-wave Airy beams. The multipole expansion method using cylindrical wave functions is utilized. Numerical computations for the scattering energy efficiency factors for compressional and shear waves illustrate the analysis with particular emphasis on the Airy beam parameters and the non-dimensional frequency, for various elastic materials surrounding the cavity. The ratio of the compressional to the shear wave speed stimulates the generation of elastic resonances, which are manifested as a series of peaks in the scattering efficiency plots. The present analysis provides an improved method for the computations of the scattering energy efficiency factors using compressional and shear-wave Airy beams in elastic materials as opposed to plane waves of infinite extent. Copyright © 2017 Elsevier B.V. All rights reserved.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional Broer-Kaup-Kupershmidt system in the shallow water of uniform depth

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Mao, Bing-Qing

2017-03-01

Under investigation in this paper is a (2+1)-dimensional Broer-Kaup-Kupershmidt system for the nonlinear and dispersive long gravity waves on two horizontal directions in the shallow water of uniform depth. Bilinear forms, Bäcklund transformation and Lax pair are derived based on the Bell polynomials and symbolic computation. One- and two-soliton solutions with a real function ϕ(y) are constructed via the Hirota method, where y is the scaled space coordinate. Propagation and interaction of the solitons are illustrated graphically: (i) ϕ(y) affects the shape of the solitons. (ii) Interaction of the solitons including the elastic and inelastic interactions are discussed. When the solitons' interaction is elastic, the amplitude, velocity and shape of the soliton remain invariant after the interaction except for a phase shift, and the smaller-amplitude soliton has a larger phase shift. (iii) Height of the water surface above a horizontal bottom can be a bell-shaped soliton or an upside-down bell-shaped soliton under certain conditions, while horizontal velocity of the water wave always keeps bell-shaped.

Bäcklund transformation, infinitely-many conservation laws, solitary and periodic waves of an extended (3 + 1)-dimensional Jimbo-Miwa equation with time-dependent coefficients

NASA Astrophysics Data System (ADS)

Deng, Gao-Fu; Gao, Yi-Tian; Gao, Xin-Yi

2018-07-01

In this paper, an extended (3+1)-dimensional Jimbo-Miwa equation with time-dependent coefficients is investigated, which comes from the second member of the Kadomtsev-Petviashvili hierarchy and is shown to be conditionally integrable. Bilinear form, Bäcklund transformation, Lax pair and infinitely-many conservation laws are derived via the binary Bell polynomials and symbolic computation. With the help of the bilinear form, one-, two- and three-soliton solutions are obtained via the Hirota method, one-periodic wave solutions are constructed via the Riemann theta function. Additionally, propagation and interaction of the solitons are investigated analytically and graphically, from which we find that the interaction between the solitons is elastic and the time-dependent coefficients can affect the soliton velocities, but the soliton amplitudes remain unchanged. One-periodic waves approach the one-solitary waves with the amplitudes vanishing and can be viewed as a superposition of the overlapping solitary waves, placed one period apart.

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2015-07-20

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-fieldmore » technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.« less

International Conference on Materials and Mechanisms of Superconductivity -- High Temperature Superconductors

DTIC Science & Technology

1989-10-01

wide range of Selds and temperatures.’ is the symmetrized two-dimensional strain matrix, A The .L der?.nn criterion assumes wave vector -inde- and A are...plificatioG, especially if fluctuations are important. A then (assuming 2 1 + A >> ) more accurate theory would use wave vector dependent k8 T elastic...with this siri’ M respect to B, H and Ha; the three latter approach; e.g., a possible anisotropy in the vectors are almost the same in"’’e and basal

The direct field boundary impedance of two-dimensional periodic structures with application to high frequency vibration prediction.

PubMed

Langley, Robin S; Cotoni, Vincent

2010-04-01

Large sections of many types of engineering construction can be considered to constitute a two-dimensional periodic structure, with examples ranging from an orthogonally stiffened shell to a honeycomb sandwich panel. In this paper, a method is presented for computing the boundary (or edge) impedance of a semi-infinite two-dimensional periodic structure, a quantity which is referred to as the direct field boundary impedance matrix. This terminology arises from the fact that none of the waves generated at the boundary (the direct field) are reflected back to the boundary in a semi-infinite system. The direct field impedance matrix can be used to calculate elastic wave transmission coefficients, and also to calculate the coupling loss factors (CLFs), which are required by the statistical energy analysis (SEA) approach to predicting high frequency vibration levels in built-up systems. The calculation of the relevant CLFs enables a two-dimensional periodic region of a structure to be modeled very efficiently as a single subsystem within SEA, and also within related methods, such as a recently developed hybrid approach, which couples the finite element method with SEA. The analysis is illustrated by various numerical examples involving stiffened plate structures.

Two-dimensional Shear Wave Elastography on Conventional Ultrasound Scanners with Time Aligned Sequential Tracking (TAST) and Comb-push Ultrasound Shear Elastography (CUSE)

PubMed Central

Song, Pengfei; Macdonald, Michael C.; Behler, Russell H.; Lanning, Justin D.; Wang, Michael H.; Urban, Matthew W.; Manduca, Armando; Zhao, Heng; Callstrom, Matthew R.; Alizad, Azra; Greenleaf, James F.; Chen, Shigao

2014-01-01

Two-dimensional (2D) shear wave elastography presents 2D quantitative shear elasticity maps of tissue, which are clinically useful for both focal lesion detection and diffuse disease diagnosis. Realization of 2D shear wave elastography on conventional ultrasound scanners, however, is challenging due to the low tracking pulse-repetition-frequency (PRF) of these systems. While some clinical and research platforms support software beamforming and plane wave imaging with high PRF, the majority of current clinical ultrasound systems do not have the software beamforming capability, which presents a critical challenge for translating the 2D shear wave elastography technique from laboratory to clinical scanners. To address this challenge, this paper presents a Time Aligned Sequential Tracking (TAST) method for shear wave tracking on conventional ultrasound scanners. TAST takes advantage of the parallel beamforming capability of conventional systems and realizes high PRF shear wave tracking by sequentially firing tracking vectors and aligning shear wave data in the temporal direction. The Comb-push Ultrasound Shear Elastography (CUSE) technique was used to simultaneously produce multiple shear wave sources within the field-of-view (FOV) to enhance shear wave signal-to-noise-ratio (SNR) and facilitate robust reconstructions of 2D elasticity maps. TAST and CUSE were realized on a conventional ultrasound scanner (the General Electric LOGIQ E9). A phantom study showed that the shear wave speed measurements from the LOGIQ E9 were in good agreement to the values measured from other 2D shear wave imaging technologies. An inclusion phantom study showed that the LOGIQ E9 had comparable performance to the Aixplorer (Supersonic Imagine) in terms of bias and precision in measuring different sized inclusions. Finally, in vivo case analysis of a breast with a malignant mass, and a liver from a healthy subject demonstrated the feasibility of using the LOGIQ E9 for in vivo 2D shear wave elastography. These promising results indicate that the proposed technique can enable the implementation of 2D shear wave elastography on conventional ultrasound scanners and potentially facilitate wider clinical applications with shear wave elastography. PMID:25643079

Elastic dependence of defect modes in one-dimensional photonic crystals with a cholesteric elastomer slab

NASA Astrophysics Data System (ADS)

Avendanño, Carlos G.; Martínez, Daniel

2018-07-01

We studied the transmission spectra in a one-dimensional dielectric multilayer photonic structure containing a cholesteric liquid crystal elastomer layer as a defect. For circularly polarized incident electromagnetic waves, we analyzed the optical defect modes induced in the band gap spectrum as a function of the incident angle and the axial strain applied along the same axis as the periodic medium. The physical parameters of the structure were chosen in such a way the photonic band gap of the cholesteric elastomer lies inside that of the multilayer. We found that, in addition to the defect modes associated with the thickness of the defect layer and the anisotropy of the elastic polymer, two new defect modes appear at both band edges of the cholesteric structure, whose amplitudes and spectral positions can be elastically tuned. Particularly, we showed that, at normal incidence, the defect modes shift toward the long-wavelength region with the strain; whereas, for constant elongation, such defects move toward larger frequencies with the incidence angle.

Coherent transmission of an ultrasonic shock wave through a multiple scattering medium.

PubMed

Viard, Nicolas; Giammarinaro, Bruno; Derode, Arnaud; Barrière, Christophe

2013-08-01

We report measurements of the transmitted coherent (ensemble-averaged) wave resulting from the interaction of an ultrasonic shock wave with a two-dimensional random medium. Despite multiple scattering, the coherent waveform clearly shows the steepening that is typical of nonlinear harmonic generation. This is taken advantage of to measure the elastic mean free path and group velocity over a broad frequency range (2-15 MHz) in only one experiment. Experimental results are found to be in good agreement with a linear theoretical model taking into account spatial correlations between scatterers. These results show that nonlinearity and multiple scattering are both present, yet uncoupled.

A framework for assessing the uncertainty in wave energy delivery to targeted subsurface formations

NASA Astrophysics Data System (ADS)

Karve, Pranav M.; Kallivokas, Loukas F.; Manuel, Lance

2016-02-01

Stress wave stimulation of geological formations has potential applications in petroleum engineering, hydro-geology, and environmental engineering. The stimulation can be applied using wave sources whose spatio-temporal characteristics are designed to focus the emitted wave energy into the target region. Typically, the design process involves numerical simulations of the underlying wave physics, and assumes a perfect knowledge of the material properties and the overall geometry of the geostructure. In practice, however, precise knowledge of the properties of the geological formations is elusive, and quantification of the reliability of a deterministic approach is crucial for evaluating the technical and economical feasibility of the design. In this article, we discuss a methodology that could be used to quantify the uncertainty in the wave energy delivery. We formulate the wave propagation problem for a two-dimensional, layered, isotropic, elastic solid truncated using hybrid perfectly-matched-layers (PMLs), and containing a target elastic or poroelastic inclusion. We define a wave motion metric to quantify the amount of the delivered wave energy. We, then, treat the material properties of the layers as random variables, and perform a first-order uncertainty analysis of the formation to compute the probabilities of failure to achieve threshold values of the motion metric. We illustrate the uncertainty quantification procedure using synthetic data.

Flexural wave suppression by an elastic metamaterial beam with zero bending stiffness

NASA Astrophysics Data System (ADS)

Zhang, Yong Yan; Wu, Jiu Hui; Hu, Guang Zhong; Wang, Yu Chun

2017-04-01

In this paper, different from Bragg scattering or local resonance mechanisms, a novel mechanism of an ultra-low-frequency broadband for flexural waves propagating in a one-dimensional elastic metamaterial beam with zero bending stiffness is proposed, which consists of periodic hinge-linked blocks. The dispersion relationship of this kind of metamaterial beam is derived and analyzed, from which we find that these hinge-linked blocks can produce the zero bending stiffness. Thus, the flexural waves within the metamaterial beam can be suppressed, and an ultra-low-frequency wide band-gap is formed in which the first branch is generated by the zero bending spring and the second branch by the negative velocity of the metamaterial beam. Numerical results show that the elastic metamaterial beams with zero bending stiffness can indeed generate an ultra-low-frequency wide band gap even starting from almost zero frequency, such as from 0 Hz to 525 Hz in our structure. Therefore, the puzzle of realizing an ultra-low-frequency broadband of flexural waves may have been better solved, which could be applied in controlling ultra-low-frequency elastic waves in engineering.

Lump Solitons in Surface Tension Dominated Flows

NASA Astrophysics Data System (ADS)

Milewski, Paul; Berger, Kurt

1999-11-01

The Kadomtsev-Petviashvilli I equation (KPI) which models small-amplitude, weakly three-dimensional surface-tension dominated long waves is integrable and allows for algebraically decaying lump solitary waves. It is not known (theoretically or numerically) whether the full free-surface Euler equations support such solutions. We consider an intermediate model, the generalised Benney-Luke equation (gBL) which is isotropic (not weakly three-dimensional) and contains KPI as a limit. We show numerically that: 1. gBL supports lump solitary waves; 2. These waves collide elastically and are stable; 3. They are generated by resonant flow over an obstacle.

System and method to estimate compressional to shear velocity (VP/VS) ratio in a region remote from a borehole

DOEpatents

Vu, Cung; Nihei, Kurt T; Schmitt, Denis P; Skelt, Christopher; Johnson, Paul A; Guyer, Robert; TenCate, James A; Le Bas, Pierre-Yves

2012-10-16

In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region remote from a borehole using a conveyed logging tool is disclosed. In some aspects, the method includes arranging a first source in the borehole and generating a steered beam of elastic energy at a first frequency; arranging a second source in the borehole and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location away from the borehole; receiving at the borehole by a sensor a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole; determining a location of a three wave mixing region based on the arrangement of the first and second sources and on properties of the third wave signal; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and determining at a plurality of azimuths, inclinations and longitudinal locations within the borehole. The method is additionally used to generate three dimensional images of the ratio of compressional to shear acoustic velocity of the same volume surrounding the borehole.

Reflection of shear elastic waves from the interface of a ferromagnetic half–space

NASA Astrophysics Data System (ADS)

Atoyan, L. H.; Terzyan, S. H.

2018-04-01

In this paper, the problems of reflection and refraction of a pure elastic wave incident from a nonmagnetic medium on the surface of contact between two semi-infinite media of an infinite nonmagnetic/magnetic structure are considered. The resonance character of the interaction between elastic and magnetic waves is shown, and the dependence of the magnetoelastic wave amplitudes on the the incident elastic wave amplitude is also established.

Wave dispersion and propagation in state-based peridynamics

NASA Astrophysics Data System (ADS)

Butt, Sahir N.; Timothy, Jithender J.; Meschke, Günther

2017-11-01

Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.

Bandgaps and directional propagation of elastic waves in 2D square zigzag lattice structures

NASA Astrophysics Data System (ADS)

Wang, Yan-Feng; Wang, Yue-Sheng; Zhang, Chuanzeng

2014-12-01

In this paper we propose various types of two-dimensional (2D) square zigzag lattice structures, and we study their bandgaps and directional propagation of elastic waves. The band structures and the transmission spectra of the systems are calculated by using the finite element method. The effects of the geometry parameters of the 2D-zigzag lattices on the bandgaps are investigated and discussed. The mechanism of the bandgap generation is analyzed by studying the vibration modes at the bandgap edges. Multiple wide complete bandgaps are found in a wide porosity range owing to the separation of the degeneracy by introducing bending arms. The bandgaps are sensitive to the geometry parameters of the systems. The deformed displacement fields of the transient response of finite structures subjected to time-harmonic loads are presented to show the directional wave propagation. The research in this paper is relevant to the practical design of cellular structures with enhanced vibro-acoustics performance.

A study of self-propelled elastic cylindrical micro-swimmers using modeling and computation

NASA Astrophysics Data System (ADS)

Shi, Lingling; Čanić, Sunčica; Quaini, Annalisa; Pan, Tsorng-Whay

2016-06-01

We study propulsion of micro-swimmers in 3D creeping flow. The swimmers are assumed to be made of elastic cylindrical hollow tubes. The swimming is generated by the contractions of the tube's elastic membrane walls producing a traveling wave in the form of a ;step-function; traversing the swimmer from right to left, propelling the swimmer from left to right. The problem is motivated by medical applications such as drug delivery. The influence of several non-dimensional design parameters on the velocity of the swimmer is investigated, including the swimmer aspect ratio, and the amplitude of the traveling wave relative to the swimmer radius. An immersed boundary method based on a finite element method approach is successfully combined with an elastic spring network model to simulate the two-way fluid-structure interaction coupling between the elastic cylindrical tube and the flow of a 3D viscous, incompressible fluid. To gain a deeper insight into the influence of various parameters on the swimmer speed, a reduced 1D fluid-structure interaction model was derived and validated. It was found that fast swimmers are those with large tube aspect ratios, and with the amplitude of the traveling wave which is roughly 50% of the reference swimmer radius. It was shown that the speed of our ;optimal swimmer; is around 1.5 swimmer lengths per second, which is at the top of the class of all currently manufactured micro-swimmers swimming in low Reynolds number flows (Re =10-6), reported in [11].

Microfabricated bulk wave acoustic bandgap device

DOEpatents

Olsson, Roy H.; El-Kady, Ihab F.; McCormick, Frederick; Fleming, James G.; Fleming, Carol

2010-06-08

A microfabricated bulk wave acoustic bandgap device comprises a periodic two-dimensional array of scatterers embedded within the matrix material membrane, wherein the scatterer material has a density and/or elastic constant that is different than the matrix material and wherein the periodicity of the array causes destructive interference of the acoustic wave within an acoustic bandgap. The membrane can be suspended above a substrate by an air or vacuum gap to provide acoustic isolation from the substrate. The device can be fabricated using microelectromechanical systems (MEMS) technologies. Such microfabricated bulk wave phononic bandgap devices are useful for acoustic isolation in the ultrasonic, VHF, or UHF regime (i.e., frequencies of order 1 MHz to 10 GHz and higher, and lattice constants of order 100 .mu.m or less).

Microfabricated bulk wave acoustic bandgap device

DOEpatents

Olsson, Roy H.; El-Kady, Ihab F.; McCormick, Frederick; Fleming, James G.; Fleming, legal representative, Carol

2010-11-23

A microfabricated bulk wave acoustic bandgap device comprises a periodic two-dimensional array of scatterers embedded within the matrix material membrane, wherein the scatterer material has a density and/or elastic constant that is different than the matrix material and wherein the periodicity of the array causes destructive interference of the acoustic wave within an acoustic bandgap. The membrane can be suspended above a substrate by an air or vacuum gap to provide acoustic isolation from the substrate. The device can be fabricated using microelectromechanical systems (MEMS) technologies. Such microfabricated bulk wave phononic bandgap devices are useful for acoustic isolation in the ultrasonic, VHF, or UHF regime (i.e., frequencies of order 1 MHz to 10 GHz and higher, and lattice constants of order 100 .mu.m or less).

Sound transmission through lined, composite panel structures: Transversely isotropic poro-elastic model

NASA Astrophysics Data System (ADS)

Kim, Jeong-Woo

A joint experimental and analytical investigation of the sound transmission loss (STL) and two-dimensional free wave propagation in composite sandwich panels is presented here. An existing panel, a Nomex honeycomb sandwich panel, was studied in detail. For the purpose of understanding the typical behavior of sandwich panels, a composite structure comprising two aluminum sheets with a relatively soft, poro-elastic foam core was also constructed and studied. The cores of both panels were modeled using an anisotropic (transversely isotropic) poro-elastic material theory. Several estimation methods were used to obtain the material properties of the honeycomb core and the skin plates to be used in the numerical calculations. Appropriate values selected from among the estimates were used in the STL and free wave propagation models. The prediction model was then verified in two ways: first, the calculated wave speeds and STL of a single poro-elastic layer were numerically verified by comparison with the predictions of a previously developed isotropic model. Secondly, to physically validate the transversely isotropic model, the measured STL and the phase speeds of the sandwich panels were compared with their predicted values. To analyze the actual treatment of a fuselage structure, multi-layered configurations, including a honeycomb panel and several layers such as air gaps, acoustic blankets and membrane partitions, were formulated. Then, to find the optimal solution for improving the sound barrier performance of an actual fuselage system, air layer depth and glass fiber lining effects were investigated by using these multi-layer models. By using the free wave propagation model, the first anti-symmetric and symmetric modes of the sandwich panels were characterized to allow the identification of the coincidence frequencies of the sandwich panel. The behavior of the STL could then be clearly explained by comparison with the free wave propagation solutions. By performing a parameter study based both on the STL and free wave propagation speeds, the mass, stiffness and damping-controlled regions of the STL were identified. The structural factors that can be adjusted to improve STL performance were also identified.

An accurate boundary element method for the exterior elastic scattering problem in two dimensions

NASA Astrophysics Data System (ADS)

Bao, Gang; Xu, Liwei; Yin, Tao

2017-11-01

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller [1] boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula [2] is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.

The instability of the spiral wave induced by the deformation of elastic excitable media

NASA Astrophysics Data System (ADS)

Ma, Jun; Jia, Ya; Wang, Chun-Ni; Li, Shi-Rong

2008-09-01

There are some similarities between the spiral wave in excitable media and in cardiac tissue. Much evidence shows that the appearance and instability of the spiral wave in cardiac tissue can be linked to one kind of heart disease. There are many models that can be used to investigate the formation and instability of the spiral wave. Cardiac tissue is excitable and elastic, and it is interesting to simulate the transition and instability of the spiral wave induced by media deformation. For simplicity, a class of the modified Fitzhugh-Nagumo (MFHN) model, which can generate a stable rotating spiral wave, meandering spiral wave and turbulence within appropriate parameter regions, will be used to simulate the instability of the spiral wave induced by the periodical deformation of media. In the two-dimensional case, the total acreage of elastic media is supposed to be invariable in the presence of deformation, and the problem is described with Lx × Ly = N × ΔxN × Δy = L'xL'y = N × Δx'N × Δy'. In our studies, elastic media are decentralized into N × N sites and the space of the adjacent sites is changed to simulate the deformation of elastic media. Based on the nonlinear dynamics theory, the deformation effect on media is simplified and simulated by perturbing the diffusion coefficients Dx and Dy with different periodical signals, but the perturbed diffusion coefficients are compensatory. The snapshots of our numerical results find that the spiral wave can coexist with the spiral turbulence, instability of the spiral wave and weak deformation of the spiral wave in different conditions. The ratio parameter ɛ and the frequency of deformation forcing play a deterministic role in inducing instability of the spiral wave. Extensive studies confirm that the instability of the spiral wave can be induced and developed only if an appropriate frequency for deformation is used. We analyze the power spectrum for the time series of the mean activator of four sampled sites which are selected symmetrically in different cases, such as the condition that the spiral wave coexists with the spiral turbulence, spiral wave without evident deformation, complete instability of the spiral wave (turbulence) and weak deformation of the spiral wave. It is found that more new peaks appear in the power spectrum and the distribution of frequency becomes sparser when the spiral wave encounters instability.

Near field effect on elasticity measurement for cartilage-bone structure using Lamb wave method.

PubMed

Xu, Hao; Chen, Shigao; An, Kai-Nan; Luo, Zong-Ping

2017-10-30

Cartilage elasticity changes with cartilage degeneration. Hence, cartilage elasticity detection might be an alternative to traditional imaging methods for the early diagnosis of osteoarthritis. Based on the wave propagation measurement, Shear wave elastography (SWE) become an emerging non-invasive elasticity detection method. The wave propagation model, which is affected by tissue shapes, is crucial for elasticity estimating in SWE. However, wave propagation model for cartilage was unclear. This study aimed to establish a wave propagation model for the cartilage-bone structure. We fabricated a cartilage-bone structure, and studied the elasticity measurement and wave propagation by experimental and numerical Lamb wave method (LWM). Results indicated the wave propagation model satisfied the lamb wave theory for two-layered structure. Moreover, a near field region, which affects wave speed measurements and whose occurrence can be prevented if the wave frequency is larger than one critical frequency, was observed. Our findings would provide a theoretical foundation for further application of LWM in elasticity measurement of cartilage in vivo. It can help the application of LWM to the diagnosis of osteoarthritis.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

Attenuation of the dynamic yield point of shocked aluminum using elastodynamic simulations of dislocation dynamics.

PubMed

Gurrutxaga-Lerma, Beñat; Balint, Daniel S; Dini, Daniele; Eakins, Daniel E; Sutton, Adrian P

2015-05-01

When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the farther it travels into the metal: this is known as "the decay of the elastic precursor." The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behavior. In this Letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum and its dependence on strain rate.

Multicomponent long-wave-short-wave resonance interaction system: Bright solitons, energy-sharing collisions, and resonant solitons.

PubMed

Sakkaravarthi, K; Kanna, T; Vijayajayanthi, M; Lakshmanan, M

2014-11-01

We consider a general multicomponent (2+1)-dimensional long-wave-short-wave resonance interaction (LSRI) system with arbitrary nonlinearity coefficients, which describes the nonlinear resonance interaction of multiple short waves with a long wave in two spatial dimensions. The general multicomponent LSRI system is shown to be integrable by performing the Painlevé analysis. Then we construct the exact bright multisoliton solutions by applying the Hirota's bilinearization method and study the propagation and collision dynamics of bright solitons in detail. Particularly, we investigate the head-on and overtaking collisions of bright solitons and explore two types of energy-sharing collisions as well as standard elastic collision. We have also corroborated the obtained analytical one-soliton solution by direct numerical simulation. Also, we discuss the formation and dynamics of resonant solitons. Interestingly, we demonstrate the formation of resonant solitons admitting breather-like (localized periodic pulse train) structure and also large amplitude localized structures akin to rogue waves coexisting with solitons. For completeness, we have also obtained dark one- and two-soliton solutions and studied their dynamics briefly.

Comb-push ultrasound shear elastography of breast masses: initial results show promise.

PubMed

Denis, Max; Mehrmohammadi, Mohammad; Song, Pengfei; Meixner, Duane D; Fazzio, Robert T; Pruthi, Sandhya; Whaley, Dana H; Chen, Shigao; Fatemi, Mostafa; Alizad, Azra

2015-01-01

To evaluate the performance of Comb-push Ultrasound Shear Elastography (CUSE) for classification of breast masses. CUSE is an ultrasound-based quantitative two-dimensional shear wave elasticity imaging technique, which utilizes multiple laterally distributed acoustic radiation force (ARF) beams to simultaneously excite the tissue and induce shear waves. Female patients who were categorized as having suspicious breast masses underwent CUSE evaluations prior to biopsy. An elasticity estimate within the breast mass was obtained from the CUSE shear wave speed map. Elasticity estimates of various types of benign and malignant masses were compared with biopsy results. Fifty-four female patients with suspicious breast masses from our ongoing study are presented. Our cohort included 31 malignant and 23 benign breast masses. Our results indicate that the mean shear wave speed was significantly higher in malignant masses (6 ± 1.58 m/s) in comparison to benign masses (3.65 ± 1.36 m/s). Therefore, the stiffness of the mass quantified by the Young's modulus is significantly higher in malignant masses. According to the receiver operating characteristic curve (ROC), the optimal cut-off value of 83 kPa yields 87.10% sensitivity, 82.61% specificity, and 0.88 for the area under the curve (AUC). CUSE has the potential for clinical utility as a quantitative diagnostic imaging tool adjunct to B-mode ultrasound for differentiation of malignant and benign breast masses.

Application of 3D and 2D quantitative shear wave elastography (SWE) to differentiate between benign and malignant breast masses.

PubMed

Tian, Jie; Liu, Qianqi; Wang, Xi; Xing, Ping; Yang, Zhuowen; Wu, Changjun

2017-01-20

As breast cancer tissues are stiffer than normal tissues, shear wave elastography (SWE) can locally quantify tissue stiffness and provide histological information. Moreover, tissue stiffness can be observed on three-dimensional (3D) colour-coded elasticity maps. Our objective was to evaluate the diagnostic performances of quantitative features in differentiating breast masses by two-dimensional (2D) and 3D SWE. Two hundred ten consecutive women with 210 breast masses were examined with B-mode ultrasound (US) and SWE. Quantitative features of 3D and 2D SWE were assessed, including elastic modulus standard deviation (E SD E ) measured on SWE mode images and E SD U measured on B-mode images, as well as maximum elasticity (E max ). Adding quantitative features to B-mode US improved the diagnostic performance (p < 0.05) and reduced false-positive biopsies (p < 0.0001). The area under the receiver operating characteristic curve (AUC) of 3D SWE was similar to that of 2D SWE for E SD E (p = 0.026) and E SD U (p = 0.159) but inferior to that of 2D SWE for E max (p = 0.002). Compared with E SD U , E SD E showed a higher AUC on 2D (p = 0.0038) and 3D SWE (p = 0.0057). Our study indicates that quantitative features of 3D and 2D SWE can significantly improve the diagnostic performance of B-mode US, especially 3D SWE E SD E , which shows considerable clinical value.

Acoustic scattering reduction using layers of elastic materials

NASA Astrophysics Data System (ADS)

Dutrion, Cécile; Simon, Frank

2017-02-01

Making an object invisible to acoustic waves could prove useful for military applications or measurements in confined space. Different passive methods have been proposed in recent years to avoid acoustic scattering from rigid obstacles. These techniques are exclusively based on acoustic phenomena, and use for instance multiple resonators or scatterers. This paper examines the possibility of designing an acoustic cloak using a bi-layer elastic cylindrical shell to eliminate the acoustic field scattered from a rigid cylinder hit by plane waves. This field depends on the dimensional and mechanical characteristics of the elastic layers. It is computed by a semi-analytical code modelling the vibrations of the coating under plane wave excitation. Optimization by genetic algorithm is performed to determine the characteristics of a bi-layer material minimizing the scattering. Considering an external fluid consisting of air, realistic configurations of elastic coatings emerge, composed of a thick internal orthotopic layer and a thin external isotropic layer. These coatings are shown to enable scattering reduction at a precise frequency or over a larger frequency band.

Two modified symplectic partitioned Runge-Kutta methods for solving the elastic wave equation

NASA Astrophysics Data System (ADS)

Su, Bo; Tuo, Xianguo; Xu, Ling

2017-08-01

Based on a modified strategy, two modified symplectic partitioned Runge-Kutta (PRK) methods are proposed for the temporal discretization of the elastic wave equation. The two symplectic schemes are similar in form but are different in nature. After the spatial discretization of the elastic wave equation, the ordinary Hamiltonian formulation for the elastic wave equation is presented. The PRK scheme is then applied for time integration. An additional term associated with spatial discretization is inserted into the different stages of the PRK scheme. Theoretical analyses are conducted to evaluate the numerical dispersion and stability of the two novel PRK methods. A finite difference method is used to approximate the spatial derivatives since the two schemes are independent of the spatial discretization technique used. The numerical solutions computed by the two new schemes are compared with those computed by a conventional symplectic PRK. The numerical results, which verify the new method, are superior to those generated by traditional conventional methods in seismic wave modeling.

Folding and faulting of an elastic continuum

NASA Astrophysics Data System (ADS)

Bigoni, Davide; Gourgiotis, Panos A.

2016-03-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called `chevrons') and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures.

Folding and faulting of an elastic continuum

PubMed Central

Gourgiotis, Panos A.

2016-01-01

Folding is a process in which bending is localized at sharp edges separated by almost undeformed elements. This process is rarely encountered in Nature, although some exceptions can be found in unusual layered rock formations (called ‘chevrons’) and seashell patterns (for instance Lopha cristagalli). In mechanics, the bending of a three-dimensional elastic solid is common (for example, in bulk wave propagation), but folding is usually not achieved. In this article, the route leading to folding is shown for an elastic solid obeying the couple-stress theory with an extreme anisotropy. This result is obtained with a perturbation technique, which involves the derivation of new two-dimensional Green's functions for applied concentrated force and moment. While the former perturbation reveals folding, the latter shows that a material in an extreme anisotropic state is also prone to a faulting instability, in which a displacement step of finite size emerges. Another failure mechanism, namely the formation of dilation/compaction bands, is also highlighted. Finally, a geophysical application to the mechanics of chevron formation shows how the proposed approach may explain the formation of natural structures. PMID:27118925

Multi-soliton solutions and Bäcklund transformation for a two-mode KdV equation in a fluid

NASA Astrophysics Data System (ADS)

Xiao, Zi-Jian; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Wu, Xiao-Yu

2017-01-01

In this paper, we investigate a two-mode Korteweg-de Vries equation, which describes the one-dimensional propagation of shallow water waves with two modes in a weakly nonlinear and dispersive fluid system. With the binary Bell polynomial and an auxiliary variable, bilinear forms, multi-soliton solutions in the two-wave modes and Bell polynomial-type Bäcklund transformation for such an equation are obtained through the symbolic computation. Soliton propagation and collisions between the two solitons are presented. Based on the graphic analysis, it is shown that the increase in s can lead to the increase in the soliton velocities under the condition of ?, but the soliton amplitudes remain unchanged when s changes, where s means the difference between the phase velocities of two-mode waves, ? and ? are the nonlinearity parameter and dispersion parameter respectively. Elastic collisions between the two solitons in both two modes are analyzed with the help of graphic analysis.

Three-Dimensional Anisotropic Acoustic and Elastic Full-Waveform Seismic Inversion

NASA Astrophysics Data System (ADS)

Warner, M.; Morgan, J. V.

2013-12-01

Three-dimensional full-waveform inversion is a high-resolution, high-fidelity, quantitative, seismic imaging technique that has advanced rapidly within the oil and gas industry. The method involves the iterative improvement of a starting model using a series of local linearized updates to solve the full non-linear inversion problem. During the inversion, forward modeling employs the full two-way three-dimensional heterogeneous anisotropic acoustic or elastic wave equation to predict the observed raw field data, wiggle-for-wiggle, trace-by-trace. The method is computationally demanding; it is highly parallelized, and runs on large multi-core multi-node clusters. Here, we demonstrate what can be achieved by applying this newly practical technique to several high-density 3D seismic datasets that were acquired to image four contrasting sedimentary targets: a gas cloud above an oil reservoir, a radially faulted dome, buried fluvial channels, and collapse structures overlying an evaporate sequence. We show that the resulting anisotropic p-wave velocity models match in situ measurements in deep boreholes, reproduce detailed structure observed independently on high-resolution seismic reflection sections, accurately predict the raw seismic data, simplify and sharpen reverse-time-migrated reflection images of deeper horizons, and flatten Kirchhoff-migrated common-image gathers. We also show that full-elastic 3D full-waveform inversion of pure pressure data can generate a reasonable shear-wave velocity model for one of these datasets. For two of the four datasets, the inclusion of significant transversely isotropic anisotropy with a vertical axis of symmetry was necessary in order to fit the kinematics of the field data properly. For the faulted dome, the full-waveform-inversion p-wave velocity model recovers the detailed structure of every fault that can be seen on coincident seismic reflection data. Some of the individual faults represent high-velocity zones, some represent low-velocity zones, some have more-complex internal structure, and some are visible merely as offsets between two regions with contrasting velocity. Although this has not yet been demonstrated quantitatively for this dataset, it seems likely that at least some of this fine structure in the recovered velocity model is related to the detailed lithology, strain history and fluid properties within the individual faults. We have here applied this technique to seismic data that were acquired by the extractive industries, however this inversion scheme is immediately scalable and applicable to a much wider range of problems given sufficient quality and density of observed data. Potential targets range from shallow magma chambers beneath active volcanoes, through whole-crustal sections across plate boundaries, to regional and whole-Earth models.

Analysis of coiled stator ultrasound motor: Fundamental study on analysis of wave propagation on acoustic waveguide for coiled stator

NASA Astrophysics Data System (ADS)

Ozeki, Seiya; Kurita, Keisuke; Uehara, Choyu; Nakane, Noriaki; Sato, Toshio; Takeuchi, Shinichi

2018-07-01

In our research group, we previously developed a coiled stator ultrasound motor (CS-USM) for medical applications such as intravascular ultrasound (IVUS) devices. However, wave propagation on acoustic waveguides has not been investigated sufficiently in previous studies. In this study, we analyze the propagation velocity of elastic waves from the simulated the vibration displacement mode profile along a straight line acoustic waveguide via three-dimensional finite element method (FEM). Concerning results, elastic waves with vibration displacement along the thickness direction show dispersion characteristics corresponding to the a0 and a1 mode plate waves (Lamb waves) in the acoustic waveguide. Our theoretical hypotheses of the propagation velocities were closely borne out by experimental results. We further find that the dispersion characteristic is affected by the width of the acoustic waveguide. We believe that our findings can contribute to improved CS-USM designs for practical application.

Elastic-wave propagation and site amplification in the Salt Lake Valley, Utah, from simulated normal faulting earthquakes

USGS Publications Warehouse

Benz, H.M.; Smith, R.B.

1988-01-01

The two-dimensional seismic response of the Salt Lake valley to near- and far-field earthquakes has been investigated from simulations of vertically incident plane waves and from normal-faulting earthquakes generated on the basin-bounding Wasatch fault. The plane-wave simulations were compared with observed site amplifications in the Salt Lake valley, based on seismic recordings from nuclear explosions in southern Nevada, that show 10 times greater amplification with the basin than measured values on hard-rock sites. Synthetic seismograms suggest that in the frequency band 0.3 to 1.5 Hz at least one-half the site amplitication can be attributed to the impedance contrast between the basin sediments and higher velocity basement rocks. -from Authors

A method for the computational modeling of the physics of heart murmurs

NASA Astrophysics Data System (ADS)

Seo, Jung Hee; Bakhshaee, Hani; Garreau, Guillaume; Zhu, Chi; Andreou, Andreas; Thompson, William R.; Mittal, Rajat

2017-05-01

A computational method for direct simulation of the generation and propagation of blood flow induced sounds is proposed. This computational hemoacoustic method is based on the immersed boundary approach and employs high-order finite difference methods to resolve wave propagation and scattering accurately. The current method employs a two-step, one-way coupled approach for the sound generation and its propagation through the tissue. The blood flow is simulated by solving the incompressible Navier-Stokes equations using the sharp-interface immersed boundary method, and the equations corresponding to the generation and propagation of the three-dimensional elastic wave corresponding to the murmur are resolved with a high-order, immersed boundary based, finite-difference methods in the time-domain. The proposed method is applied to a model problem of aortic stenosis murmur and the simulation results are verified and validated by comparing with known solutions as well as experimental measurements. The murmur propagation in a realistic model of a human thorax is also simulated by using the computational method. The roles of hemodynamics and elastic wave propagation on the murmur are discussed based on the simulation results.

An efficient Matlab script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions

USGS Publications Warehouse

Boyd, O.S.

2006-01-01

We have created a second-order finite-difference solution to the anisotropic elastic wave equation in three dimensions and implemented the solution as an efficient Matlab script. This program allows the user to generate synthetic seismograms for three-dimensional anisotropic earth structure. The code was written for teleseismic wave propagation in the 1-0.1 Hz frequency range but is of general utility and can be used at all scales of space and time. This program was created to help distinguish among various types of lithospheric structure given the uneven distribution of sources and receivers commonly utilized in passive source seismology. Several successful implementations have resulted in a better appreciation for subduction zone structure, the fate of a transform fault with depth, lithospheric delamination, and the effects of wavefield focusing and defocusing on attenuation. Companion scripts are provided which help the user prepare input to the finite-difference solution. Boundary conditions including specification of the initial wavefield, absorption and two types of reflection are available. ?? 2005 Elsevier Ltd. All rights reserved.

Inverse methods for 3D quantitative optical coherence elasticity imaging (Conference Presentation)

NASA Astrophysics Data System (ADS)

Dong, Li; Wijesinghe, Philip; Hugenberg, Nicholas; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.

2017-02-01

In elastography, quantitative elastograms are desirable as they are system and operator independent. Such quantification also facilitates more accurate diagnosis, longitudinal studies and studies performed across multiple sites. In optical elastography (compression, surface-wave or shear-wave), quantitative elastograms are typically obtained by assuming some form of homogeneity. This simplifies data processing at the expense of smearing sharp transitions in elastic properties, and/or introducing artifacts in these regions. Recently, we proposed an inverse problem-based approach to compression OCE that does not assume homogeneity, and overcomes the drawbacks described above. In this approach, the difference between the measured and predicted displacement field is minimized by seeking the optimal distribution of elastic parameters. The predicted displacements and recovered elastic parameters together satisfy the constraint of the equations of equilibrium. This approach, which has been applied in two spatial dimensions assuming plane strain, has yielded accurate material property distributions. Here, we describe the extension of the inverse problem approach to three dimensions. In addition to the advantage of visualizing elastic properties in three dimensions, this extension eliminates the plane strain assumption and is therefore closer to the true physical state. It does, however, incur greater computational costs. We address this challenge through a modified adjoint problem, spatially adaptive grid resolution, and three-dimensional decomposition techniques. Through these techniques the inverse problem is solved on a typical desktop machine within a wall clock time of 20 hours. We present the details of the method and quantitative elasticity images of phantoms and tissue samples.

Competing effects of particle and medium inertia on particle diffusion in viscoelastic materials, and their ramifications for passive microrheology.

PubMed

Indei, Tsutomu; Schieber, Jay D; Córdoba, Andrés

2012-04-01

We analyze the appropriate form for the generalized Stokes-Einstein relation (GSER) for viscoelastic solids and fluids when bead inertia and medium inertia are taken into account, which we call the inertial GSER. It was previously shown for Maxwell fluids that the Basset (or Boussinesq) force arising from medium inertia can act purely dissipatively at high frequencies, where elasticity of the medium is dominant. In order to elucidate the cause of this counterintuitive result, we consider Brownian motion in a purely elastic solid where ordinary Stokes-type dissipation is not possible. The fluctuation-dissipation theorem requires the presence of a dissipative mechanism for the particle to experience fluctuating Brownian forces in a purely elastic solid. We show that the mechanism for such dissipation arises from the radiation of elastic waves toward the system boundaries. The frictional force associated with this mechanism is the Basset force, and it exists only when medium inertia is taken into consideration in the analysis of such a system. We consider first a one-dimensional harmonic lattice where all terms in the generalized Langevin equation--i.e., the elastic term, the memory kernel, and Brownian forces-can be found analytically from projection-operator methods. We show that the dissipation is purely from radiation of elastic waves. A similar analysis is made on a particle in a continuum, three-dimensional purely elastic solid, where the memory kernel is determined from continuum mechanics. Again, dissipation arises only from radiation of elastic shear waves toward infinite boundaries when medium inertia is taken into account. If the medium is a viscoelastic solid, Stokes-type dissipation is possible in addition to radiational dissipation so that the wave decays at the penetration depth. Inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a possible resonant oscillation of the mean-square displacement (MSD) of the bead. On the other hand, medium inertia (the Basset force) tends to attenuate the oscillations by the dissipation mechanism described above. Thus competition between bead inertia and medium inertia determines whether or not the MSD oscillates. We find that, if the medium density is larger than 4/7 of the bead density, the Basset damping will suppress oscillations in the MSD; this criterion is sufficient but not necessary to present oscillations.

Three-dimensional simulations of ground motions in the San Bernardino Valley, California, for hypothetical earthquakes on the San Andreas Fault

USGS Publications Warehouse

Frankel, A.

1993-01-01

Three-dimensional finite difference simulations of elastic waves in the San Bernardino Valley were performed for two hypothetical earthquakes on the San Andreas fault: a point source with moment magnitude M5 and an extended rupture with M6.5. A method is presented for incorporating a source with arbitrary focal mechanism in the grid. Synthetics from the 3-D simulations are compared with those derived from 2-D (vertical cross section) and 1-D (flat-layered) models. The synthetic seismograms from the 3-D and 2-D simulations exhibit large surface waves produced by conversion of incident S waves at the edge of the basin. Seismograms from the flat-layered model do not contain these converted surface waves and underestimate the duration of shaking. Maps of maximum ground velocities occur in localized portions of the basin. The location of the largest velocities changes with the rupture propagation direction. Contours of maximum shaking are also dependent on asperity positions and radiation pattern. -from Author

Non-reciprocal elastic wave propagation in 2D phononic membranes with spatiotemporally varying material properties

NASA Astrophysics Data System (ADS)

Attarzadeh, M. A.; Nouh, M.

2018-05-01

One-dimensional phononic materials with material fields traveling simultaneously in space and time have been shown to break elastodynamic reciprocity resulting in unique wave propagation features. In the present work, a comprehensive mathematical analysis is presented to characterize and fully predict the non-reciprocal wave dispersion in two-dimensional space. The analytical dispersion relations, in the presence of the spatiotemporal material variations, are validated numerically using finite 2D membranes with a prescribed number of cells. Using omnidirectional excitations at the membrane's center, wave propagations are shown to exhibit directional asymmetry that increases drastically in the direction of the material travel and vanishes in the direction perpendicular to it. The topological nature of the predicted dispersion in different propagation directions are evaluated using the computed Chern numbers. Finally, the degree of the 2D non-reciprocity is quantified using a non-reciprocity index (NRI) which confirms the theoretical dispersion predictions as well as the finite simulations. The presented framework can be extended to plate-type structures as well as 3D spatiotemporally modulated phononic crystals.

Propagation of acoustic waves in a one-dimensional macroscopically inhomogeneous poroelastic material.

PubMed

Gautier, G; Kelders, L; Groby, J P; Dazel, O; De Ryck, L; Leclaire, P

2011-09-01

Wave propagation in macroscopically inhomogeneous porous materials has received much attention in recent years. The wave equation, derived from the alternative formulation of Biot's theory of 1962, was reduced and solved recently in the case of rigid frame inhomogeneous porous materials. This paper focuses on the solution of the full wave equation in which the acoustic and the elastic properties of the poroelastic material vary in one-dimension. The reflection coefficient of a one-dimensional macroscopically inhomogeneous porous material on a rigid backing is obtained numerically using the state vector (or the so-called Stroh) formalism and Peano series. This coefficient can then be used to straightforwardly calculate the scattered field. To validate the method of resolution, results obtained by the present method are compared to those calculated by the classical transfer matrix method at both normal and oblique incidence and to experimental measurements at normal incidence for a known two-layers porous material, considered as a single inhomogeneous layer. Finally, discussion about the absorption coefficient for various inhomogeneity profiles gives further perspectives. © 2011 Acoustical Society of America

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Dominant phonon polarization conversion across dimensionally mismatched interfaces: Carbon-nanotube-graphene junction

NASA Astrophysics Data System (ADS)

Shi, Jingjing; Lee, Jonghoon; Dong, Yalin; Roy, Ajit; Fisher, Timothy S.; Ruan, Xiulin

2018-04-01

Dimensionally mismatched interfaces are emerging for thermal management applications, but thermal transport physics remains poorly understood. Here we consider the carbon-nanotube-graphene junction, which is a dimensionally mismatched interface between one- and two-dimensional materials and is the building block for carbon-nanotube (CNT)-graphene three-dimensional networks. We predict the transmission function of individual phonon modes using the wave packet method; surprisingly, most incident phonon modes show predominantly polarization conversion behavior. For instance, longitudinal acoustic (LA) polarizations incident from CNTs transmit mainly into flexural transverse (ZA) polarizations in graphene. The frequency stays the same as the incident mode, indicating elastic transmission. Polarization conversion is more significant as the phonon wavelength increases. We attribute such unique phonon polarization conversion behavior to the dimensional mismatch across the interface, and it opens significantly new phonon transport channels as compared to existing theories where polarization conversion is neglected.

Numerical Simulation of Detonation in Condensed Phase Explosives

DTIC Science & Technology

1998-08-01

34Numerical modelling of shocks in solids with elastic-plastic conditions", Shock Waves, 3: 55-66. 22. Jones, D.A., Oran, E.S. and Guirguis , R. (1990). "A...China Lake, CA 93555-6001, preprint. 55. P.J. Miller , P.J. and G.T. Sutherland, G.T. (1996) Reaction Rate Modelling of PBXN- 110, Shock Compression...report describes the development of a two-dimensional multi-material Eulerian hydrocode to model the effects of detonating condensed phase explosives on

Dispersive wave propagation in two-dimensional rigid periodic blocky materials with elastic interfaces

NASA Astrophysics Data System (ADS)

Bacigalupo, Andrea; Gambarotta, Luigi

2017-05-01

Dispersive waves in two-dimensional blocky materials with periodic microstructure made up of equal rigid units, having polygonal centro-symmetric shape with mass and gyroscopic inertia, connected with each other through homogeneous linear interfaces, have been analyzed. The acoustic behavior of the resulting discrete Lagrangian model has been obtained through a Floquet-Bloch approach. From the resulting eigenproblem derived by the Euler-Lagrange equations for harmonic wave propagation, two acoustic branches and an optical branch are obtained in the frequency spectrum. A micropolar continuum model to approximate the Lagrangian model has been derived based on a second-order Taylor expansion of the generalized macro-displacement field. The constitutive equations of the equivalent micropolar continuum have been obtained, with the peculiarity that the positive definiteness of the second-order symmetric tensor associated to the curvature vector is not guaranteed and depends both on the ratio between the local tangent and normal stiffness and on the block shape. The same results have been obtained through an extended Hamiltonian derivation of the equations of motion for the equivalent continuum that is related to the Hill-Mandel macro homogeneity condition. Moreover, it is shown that the hermitian matrix governing the eigenproblem of harmonic wave propagation in the micropolar model is exact up to the second order in the norm of the wave vector with respect to the same matrix from the discrete model. To appreciate the acoustic behavior of some relevant blocky materials and to understand the reliability and the validity limits of the micropolar continuum model, some blocky patterns have been analyzed: rhombic and hexagonal assemblages and running bond masonry. From the results obtained in the examples, the obtained micropolar model turns out to be particularly accurate to describe dispersive functions for wavelengths greater than 3-4 times the characteristic dimension of the block. Finally, in consideration that the positive definiteness of the second order elastic tensor of the micropolar model is not guaranteed, the hyperbolicity of the equation of motion has been investigated by considering the Legendre-Hadamard ellipticity conditions requiring real values for the wave velocity.

Experimental evidence of locally resonant sonic band gap in two-dimensional phononic stubbed plates

NASA Astrophysics Data System (ADS)

Oudich, Mourad; Senesi, Matteo; Assouar, M. Badreddine; Ruzenne, Massimo; Sun, Jia-Hong; Vincent, Brice; Hou, Zhilin; Wu, Tsung-Tsong

2011-10-01

We provide experimental evidence of the existence of a locally resonant sonic band gap in a two-dimensional stubbed plate. Structures consisting of a periodic arrangement of silicone rubber stubs deposited on a thin aluminium plate were fabricated and characterized. Brillouin spectroscopy analysis is carried out to determine the elastic constants of the used rubber. The constants are then implemented in an efficient finite-element model that predicts the band structure and transmission to identify the theoretical band gap. We measure a complete sonic band gap for the out-of-plane Lamb wave modes propagating in various samples fabricated with different stub heights. Frequency domain measurements of full wave field and transmission are performed through a scanning laser Doppler vibrometer. A complete band gap from 1.9 to 2.6 kHz is showed using a sample with 6-mm stub diameter, 5-mm thickness, and 1-cm structure periodicity. Very good agreement between numerical and experimental results is obtained.

Numerical simulations of SHPB experiments for the dynamic compressive strength and failure of ceramics

NASA Astrophysics Data System (ADS)

Anderson, Charles E., Jr.; O'Donoghue, Padraic E.; Lankford, James; Walker, James D.

1992-06-01

Complementary to a study of the compressive strength of ceramic as a function of strain rate and confinement, numerical simulations of the split-Hopkinson pressure bar (SHPB) experiments have been performed using the two-dimensional wave propagation computer program HEMP. The numerical effort had two main thrusts. Firstly, the interpretation of the experimental data relies on several assumptions. The numerical simulations were used to investigate the validity of these assumptions. The second part of the effort focused on computing the idealized constitutive response of a ceramic within the SHPB experiment. These numerical results were then compared against experimental data. Idealized models examined included a perfectly elastic material, an elastic-perfectly plastic material, and an elastic material with failure. Post-failure material was modeled as having either no strength, or a strength proportional to the mean stress. The effects of confinement were also studied. Conclusions concerning the dynamic behavior of a ceramic up to and after failure are drawn from the numerical study.

Numerical study of interfacial solitary waves propagating under an elastic sheet

PubMed Central

Wang, Zhan; Părău, Emilian I.; Milewski, Paul A.; Vanden-Broeck, Jean-Marc

2014-01-01

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field. PMID:25104909

Lamb-type waves generated by a cylindrical bubble oscillating between two planar elastic walls

PubMed Central

Mekki-Berrada, F.; Thibault, P.; Marmottant, P.

2016-01-01

The volume oscillation of a cylindrical bubble in a microfluidic channel with planar elastic walls is studied. Analytical solutions are found for the bulk scattered wave propagating in the fluid gap and the surface waves of Lamb-type propagating at the fluid–solid interfaces. This type of surface wave has not yet been described theoretically. A dispersion equation for the Lamb-type waves is derived, which allows one to evaluate the wave speed for different values of the channel height h. It is shown that for h<λt, where λt is the wavelength of the transverse wave in the walls, the speed of the Lamb-type waves decreases with decreasing h, while for h on the order of or greater than λt, their speed tends to the Scholte wave speed. The solutions for the wave fields in the elastic walls and in the fluid are derived using the Hankel transforms. Numerical simulations are carried out to study the effect of the surface waves on the dynamics of a bubble confined between two elastic walls. It is shown that its resonance frequency can be up to 50% higher than the resonance frequency of a similar bubble confined between two rigid walls. PMID:27274695

Two Dimensional Finite Element Analysis for the Effect of a Pressure Wave in the Human Brain

NASA Astrophysics Data System (ADS)

Ponce L., Ernesto; Ponce S., Daniel

2008-11-01

Brain injuries in people of all ages is a serious, world-wide health problem, with consequences as varied as attention or memory deficits, difficulties in problem-solving, aggressive social behavior, and neuro degenerative diseases such as Alzheimer's and Parkinson's. Brain injuries can be the result of a direct impact, but also pressure waves and direct impulses. The aim of this work is to develop a predictive method to calculate the stress generated in the human brain by pressure waves such as high power sounds. The finite element method is used, combined with elastic wave theory. The predictions of the generated stress levels are compared with the resistance of the arterioles that pervade the brain. The problem was focused to the Chilean mining where there are some accidents happen by detonations and high sound level. There are not formal medical investigation, however these pressure waves could produce human brain damage.

Comb-Push Ultrasound Shear Elastography of Breast Masses: Initial Results Show Promise

PubMed Central

Song, Pengfei; Fazzio, Robert T.; Pruthi, Sandhya; Whaley, Dana H.; Chen, Shigao; Fatemi, Mostafa

2015-01-01

Purpose or Objective To evaluate the performance of Comb-push Ultrasound Shear Elastography (CUSE) for classification of breast masses. Materials and Methods CUSE is an ultrasound-based quantitative two-dimensional shear wave elasticity imaging technique, which utilizes multiple laterally distributed acoustic radiation force (ARF) beams to simultaneously excite the tissue and induce shear waves. Female patients who were categorized as having suspicious breast masses underwent CUSE evaluations prior to biopsy. An elasticity estimate within the breast mass was obtained from the CUSE shear wave speed map. Elasticity estimates of various types of benign and malignant masses were compared with biopsy results. Results Fifty-four female patients with suspicious breast masses from our ongoing study are presented. Our cohort included 31 malignant and 23 benign breast masses. Our results indicate that the mean shear wave speed was significantly higher in malignant masses (6 ± 1.58 m/s) in comparison to benign masses (3.65 ± 1.36 m/s). Therefore, the stiffness of the mass quantified by the Young’s modulus is significantly higher in malignant masses. According to the receiver operating characteristic curve (ROC), the optimal cut-off value of 83 kPa yields 87.10% sensitivity, 82.61% specificity, and 0.88 for the area under the curve (AUC). Conclusion CUSE has the potential for clinical utility as a quantitative diagnostic imaging tool adjunct to B-mode ultrasound for differentiation of malignant and benign breast masses. PMID:25774978

Three-Dimensional Computer-Assisted Two-Layer Elastic Models of the Face.

PubMed

Ueda, Koichi; Shigemura, Yuka; Otsuki, Yuki; Fuse, Asuka; Mitsuno, Daisuke

2017-11-01

To make three-dimensional computer-assisted elastic models for the face, we decided on five requirements: (1) an elastic texture like skin and subcutaneous tissue; (2) the ability to take pen marking for incisions; (3) the ability to be cut with a surgical knife; (4) the ability to keep stitches in place for a long time; and (5) a layered structure. After testing many elastic solvents, we have made realistic three-dimensional computer-assisted two-layer elastic models of the face and cleft lip from the computed tomographic and magnetic resonance imaging stereolithographic data. The surface layer is made of polyurethane and the inner layer is silicone. Using this elastic model, we taught residents and young doctors how to make several typical local flaps and to perform cheiloplasty. They could experience realistic simulated surgery and understand three-dimensional movement of the flaps.

Comb-push Ultrasound Shear Elastography (CUSE) with Various Ultrasound Push Beams

PubMed Central

Song, Pengfei; Urban, Matthew W.; Manduca, Armando; Zhao, Heng; Greenleaf, James F.; Chen, Shigao

2013-01-01

Comb-push Ultrasound Shear Elastography (CUSE) has recently been shown to be a fast and accurate two-dimensional (2D) elasticity imaging technique that can provide a full field-of- view (FOV) shear wave speed map with only one rapid data acquisition. The initial version of CUSE was termed U-CUSE because unfocused ultrasound push beams were used. In this paper, we present two new versions of CUSE – Focused CUSE (F-CUSE) and Marching CUSE (M-CUSE), which use focused ultrasound push beams to improve acoustic radiation force penetration and produce stronger shear waves in deep tissues (e.g. kidney and liver). F-CUSE divides transducer elements into several subgroups which transmit multiple focused ultrasound beams simultaneously. M-CUSE uses more elements for each focused push beam and laterally marches the push beams. Both F-CUSE and M-CUSE can generate comb-shaped shear wave fields that have shear wave motion at each imaging pixel location so that a full FOV 2D shear wave speed map can be reconstructed with only one data acquisition. Homogeneous phantom experiments showed that U-CUSE, F-CUSE and M-CUSE can all produce smooth shear wave speed maps with accurate shear wave speed estimates. An inclusion phantom experiment showed that all CUSE methods could provide good contrast between the inclusion and background with sharp boundaries while F-CUSE and M-CUSE require shorter push durations to achieve shear wave speed maps with comparable SNR to U-CUSE. A more challenging inclusion phantom experiment with a very stiff and deep inclusion shows that better shear wave penetration could be gained by using F-CUSE and M-CUSE. Finally, a shallow inclusion experiment showed that good preservations of inclusion shapes could be achieved by both U-CUSE and F-CUSE in the near field. Safety measurements showed that all safety parameters are below FDA regulatory limits for all CUSE methods. These promising results suggest that, using various push beams, CUSE is capable of reconstructing a 2D full FOV shear elasticity map using only one push-detection data acquisition in a wide range of depths for soft tissue elasticity imaging. PMID:23591479

Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

NASA Astrophysics Data System (ADS)

Kharibegashvili, S. S.; Jokhadze, O. M.

2014-04-01

A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles.

Excitation of surface waves on one-dimensional solid–fluid phononic crystals and the beam displacement effect

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moiseyenko, Rayisa P.; Georgia Institute of Technology, UMI Georgia Tech – CNRS, George W. Woodruff School of Mechanical Engineering, Georgia Tech Lorraine, 2 rue Marconi, 57070 Metz-Technopole; Liu, Jingfei

The possibility of surface wave generation by diffraction of pressure waves on deeply corrugated one-dimensional phononic crystal gratings is studied both theoretically and experimentally. Generation of leaky surface waves, indeed, is generally invoked in the explanation of the beam displacement effect that can be observed upon reflection on a shallow grating of an acoustic beam of finite width. True surface waves of the grating, however, have a dispersion that lies below the sound cone in water. They thus cannot satisfy the phase-matching condition for diffraction from plane waves of infinite extent incident from water. Diffraction measurements indicate that deeply corrugatedmore » one-dimensional phononic crystal gratings defined in a silicon wafer are very efficient diffraction gratings. They also confirm that all propagating waves detected in water follow the grating law. Numerical simulations however reveal that in the sub-diffraction regime, acoustic energy of a beam of finite extent can be transferred to elastic waves guided at the surface of the grating. Their leakage to the specular direction along the grating surface explains the apparent beam displacement effect.« less

Mechanical low-frequency filter via modes separation in 3D periodic structures

NASA Astrophysics Data System (ADS)

D'Alessandro, L.; Belloni, E.; Ardito, R.; Braghin, F.; Corigliano, A.

2017-12-01

This work presents a strategy to design three-dimensional elastic periodic structures endowed with complete bandgaps, the first of which is ultra-wide, where the top limits of the first two bandgaps are overstepped in terms of wave transmission in the finite structure. Thus, subsequent bandgaps are merged, approaching the behaviour of a three-dimensional low-pass mechanical filter. This result relies on a proper organization of the modal characteristics, and it is validated by performing numerical and analytical calculations over the unit cell. A prototype of the analysed layout, made of Nylon by means of additive manufacturing, is experimentally tested to assess the transmission spectrum of the finite structure, obtaining good agreement with numerical predictions. The presented strategy paves the way for the development of a class of periodic structures to be used in robust and reliable wave attenuation over a wide frequency band.

Sound transmission through stiffened double-panel structures lined with elastic porous materials

NASA Astrophysics Data System (ADS)

Mathur, Gopal P.; Tran, Boi N.; Bolton, J. S.; Shiau, Nae-Ming

This paper presents transmission loss prediction models for a periodically stiffened panel and stiffened double-panel structures using the periodic structure theory. The inter-panel cavity in the double-panels structures can be modeled as being separated by an airspace or filled with an elastic porous layer in various configurations. The acoustic behavior of elastic porous layer is described by a theory capable of accounting fully for multi-dimensional wave propagation in such materials. The predicted transmission loss of a single stiffened panel is compared with the measured data.

An acousto-optic sensor based on resonance grating waveguide structure

PubMed Central

Xie, Antonio Jou; Song, Fuchuan; Seo, Sang-Woo

2014-01-01

This paper presents an acousto-optic (AO) sensor based on resonance grating waveguide structure. The sensor is fabricated using elastic polymer materials to achieve a good sensitivity to ultrasound pressure waves. Ultrasound pressure waves modify the structural parameters of the sensor and result in the optical resonance shift of the sensor. This converts into a light intensity modulation. A commercial ultrasound transducer at 20 MHz is used to characterize a fabricated sensor and detection sensitivity at different optical source wavelength within a resonance spectrum is investigated. Practical use of the sensor at a fixed optical source wavelength is presented. Ultimately, the geometry of the planar sensor structure is suitable for two-dimensional, optical pressure imaging applications such as pressure wave detection and mapping, and ultrasound imaging. PMID:25045203

Acoustic resonances in cylinder bundles oscillating in a compressibile fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, W.H.; Raptis, A.C.

1984-12-01

This paper deals with an analytical study on acoustic resonances of elastic oscillations of a group of parallel, circular, thin cylinders in an unbounded volume of barotropic, compressible, inviscid fluid. The perturbed motion of the fluid is assumed due entirely to the flexural oscillations of the cylinders. The motion of the fluid disturbances is first formulated in a three-dimensional wave form and then casted into a two-dimensional Helmholtz equation for the harmonic motion in time and in axial space. The acoustic motion in the fluid and the elastic motion in the cylinders are solved simultaneously. Acoustic resonances were approximately determinedmore » from the secular (eigenvalue) equation by the method of successive iteration with the use of digital computers for a given set of the fluid properties and the cylinders' geometry and properties. Effects of the flexural wavenumber and the configuration of and the spacing between the cylinders on the acoustic resonances were thoroughly investigated.« less

Multi-soliton interaction of a generalized Schrödinger-Boussinesq system in a magnetized plasma

NASA Astrophysics Data System (ADS)

Zhao, Xue-Hui; Tian, Bo; Chai, Jun; Wu, Xiao-Yu; Guo, Yong-Jiang

2017-04-01

Under investigation in this paper is a generalized Schrödinger-Boussinesq system, which describes the stationary propagation of coupled upper-hybrid waves and magnetoacoustic waves in a magnetized plasma. Bilinear forms, one-, two- and three-soliton solutions are derived by virtue of the Hirota method and symbolic computation. Propagation and interaction for the solitons are illustrated graphically: Coefficients β1^{} and β2^{} can affect the velocities and propagation directions of the solitary waves. Amplitude, velocity and shape of the one solitary wave keep invariant during the propagation, implying that the transport of the energy is stable in the upper-hybrid and magnetoacoustic waves, and amplitude of the upper-hybrid wave is bigger than that of the magnetoacoustic wave. For the upper-hybrid and magnetoacoustic waves, head-on, overtaking and bound-state interaction between the two solitary waves are asymptotically depicted, respectively, indicating that the interaction between the two solitary waves is elastic. Elastic interaction between the bound-state soliton and a single one soliton is also displayed, and interaction among the three solitary waves is all elastic.

Wave-packet rectification in nonlinear electronic systems: A tunable Aharonov-Bohm diode

PubMed Central

Li, Yunyun; Zhou, Jun; Marchesoni, Fabio; Li, Baowen

2014-01-01

Rectification of electron wave-packets propagating along a quasi-one dimensional chain is commonly achieved via the simultaneous action of nonlinearity and longitudinal asymmetry, both confined to a limited portion of the chain termed wave diode. However, it is conceivable that, in the presence of an external magnetic field, spatial asymmetry perpendicular to the direction of propagation suffices to ensure rectification. This is the case of a nonlinear ring-shaped lattice with different upper and lower halves (diode), which is attached to two elastic chains (leads). The resulting device is mirror symmetric with respect to the ring vertical axis, but mirror asymmetric with respect to the chain direction. Wave propagation along the two diode paths can be modeled for simplicity by a discrete Schrödinger equation with cubic nonlinearities. Numerical simulations demonstrate that, thanks to the Aharonov-Bohm effect, such a diode can be operated by tuning the magnetic flux across the ring. PMID:24691462

Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with functionally graded interlayers.

PubMed

Guo, Xiao; Wei, Peijun; Lan, Man; Li, Li

2016-08-01

The effects of functionally graded interlayers on dispersion relations of elastic waves in a one-dimensional piezoelectric/piezomagnetic phononic crystal are studied in this paper. First, the state transfer equation of the functionally graded interlayer is derived from the motion equation by the reduction of order (from second order to first order). The transfer matrix of the functionally graded interlayer is obtained by solving the state transfer equation with the spatial-varying coefficient. Based on the transfer matrixes of the piezoelectric slab, the piezomagnetic slab and the functionally graded interlayers, the total transfer matrix of a single cell is obtained. Further, the Bloch theorem is used to obtain the resultant dispersion equations of in-plane and anti-plane Bloch waves. The dispersion equations are solved numerically and the numerical results are shown graphically. Five kinds of profiles of functionally graded interlayers between a piezoelectric slab and a piezomagnetic slab are considered. It is shown that the functionally graded interlayers have evident influences on the dispersion curves and the band gaps. Copyright © 2016 Elsevier B.V. All rights reserved.

A forward-adjoint operator pair based on the elastic wave equation for use in transcranial photoacoustic computed tomography

PubMed Central

Mitsuhashi, Kenji; Poudel, Joemini; Matthews, Thomas P.; Garcia-Uribe, Alejandro; Wang, Lihong V.; Anastasio, Mark A.

2017-01-01

Photoacoustic computed tomography (PACT) is an emerging imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to an inverse source problem in which the initial pressure distribution is recovered from measurements of the radiated wavefield. A major challenge in transcranial PACT brain imaging is compensation for aberrations in the measured data due to the presence of the skull. Ultrasonic waves undergo absorption, scattering and longitudinal-to-shear wave mode conversion as they propagate through the skull. To properly account for these effects, a wave-equation-based inversion method should be employed that can model the heterogeneous elastic properties of the skull. In this work, a forward model based on a finite-difference time-domain discretization of the three-dimensional elastic wave equation is established and a procedure for computing the corresponding adjoint of the forward operator is presented. Massively parallel implementations of these operators employing multiple graphics processing units (GPUs) are also developed. The developed numerical framework is validated and investigated in computer19 simulation and experimental phantom studies whose designs are motivated by transcranial PACT applications. PMID:29387291

Temperature and porosity effects on wave propagation in nanobeams using bi-Helmholtz nonlocal strain-gradient elasticity

NASA Astrophysics Data System (ADS)

Reza Barati, Mohammad

2018-05-01

In this paper, applying a general nonlocal strain-gradient elasticity model with two nonlocal and one strain-gradient parameters, wave dispersion behavior of thermally affected and elastically bonded nanobeams is investigated. The two nanobeams are considered to have material imperfections or porosities evenly dispersed across the thickness. Each nanobeam has uniform thickness and is modeled by refined shear deformation beam theory with sinusoidal transverse shear strains. The governing equations of the system are derived by Hamilton's rule and are analytically solved to obtain wave frequencies and the velocity of wave propagation. In the presented graphs, one can see that porosities, temperature, nonlocal, strain gradient and bonding springs have great influences on the wave characteristics of the system.

Three-dimensional vs. two-dimensional shear-wave elastography of the testes - preliminary study on a healthy collective.

PubMed

Marcon, J; Trottmann, M; Rübenthaler, J; D'Anastasi, M; Stief, C G; Reiser, M F; Clevert, D A

2016-01-01

Shear wave elastography (SWE) and its derivative Supersonic Shear Imaging (SSI) are newer techniques for the determination of tissue elasticity by measuring the velocity of generated shear waves (SWV), which correlates positively with tissue stiffness.The techniques are integrated into many modern ultrasound systems and have been examined in the evaluation of viscoelastic properties of different organ systems. Two-dimensional shear wave elastography (2D SWE) of the testes has been found to be a useful tool in recent studies which included the determination of standard values in healthy volunteers. Three-dimensional shear wave elastography (3D SWE) is the latest development in elastography and is made possible by generation of a multiplanar three-dimensional map via volumetric acquisition with a special ultrasound transducer. This technique allows the assessment of tissue elasticity in a three-dimensional, fully accessible organ map.The aim of this preliminary study was to both evaluate the feasibility of 3D SWE and to compare 2D and 3D SWE standard values in the testes of healthy subjects. We examined the testes of healthy male volunteers (n = 32) with a mean age of 51.06±17.75 years (range 25-77 years) by B-mode ultrasound, 2D and 3D SWE techniques in September of 2016. Volunteers with a history of testicular pathologies were excluded. For all imaging procedures the SL15-4 linear transducer (bandwidth 4-15 MHz) as well as the SLV16-4 volumetric probe (bandwidth 4-16 MHz) of the Aixplorer® ultrasound device (SuperSonic Imagine, Aix-en-Provence, France) were used. Seven regions of interest (ROI, Q-Box®) within the testes were evaluated for SWV using both procedures. SWV values were described in m/s. Results were statistically evaluated using univariateanalysis. Mean SWV values were 1.05 m/s for the 2D SWE and 1.12 m/s for the 3D SWE.Comparisons of local areas delivered no statistically significant differences (p = 0.11 to p = 0.66), except for the region in the central portion in the superior part of the coronal plane (p = 0.03). Testicular volume was significanty higher by a mean of 1.72 ml when measured with 3D SWE (p = 0.001). 3D SWE proved to be a feasible diagnostic tool in the assessment of testicular tissue, providing the examiner with a fully accessible three-dimensional map in a multiplanar or multislice view. With this technique a more precise testicular imaging - especially if combined with the display of tissue stiffness in SWE - is available and therefore could improve the diagnostic work-up of scrotal masses or the routine investigation of infertile men. Further studies for a better understanding in the context of various testicular pathologies will be required.

Anisotropic elastic scattering of stripe/line-shaped scatters to two-dimensional electron gas: Model and illustrations in a nonpolar AlGaN/GaN hetero-junction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Jinfeng, E-mail: jfzhang@xidian.edu.cn; Li, Yao; Yan, Ran

In a semiconductor hetero-junction, the stripe/line-shaped scatters located at the hetero-interface lead to the anisotropic transport of two-dimensional electron gas (2DEG). The elastic scattering of infinitely long and uniform stripe/line-shaped scatters to 2DEG is theoretically investigated based on a general theory of anisotropic 2DEG transport [J. Schliemann and D. Loss, Phys. Rev. B 68(16), 165311 (2003)], and the resulting 2DEG mobility along the applied electrical field is modeled to be a function of the angle between the field and the scatters. The anisotropy of the scattering and the mobility originate in essence from that the stripe/line-shaped scatters act upon themore » injecting two-dimensional wave vector by changing only its component perpendicular to the scatters. Three related scattering mechanisms in a nonpolar AlGaN/GaN hetero-junction are discussed as illustrations, including the striated morphology caused interface roughness scattering, and the polarization induced line charge dipole scattering and the misfit dislocation scattering at the AlGaN/GaN interface. Different anisotropic behaviors of the mobility limited by these scattering mechanisms are demonstrated, but analysis shows that all of them are determined by the combined effects of the anisotropic bare scattering potential and the anisotropic dielectric response of the 2DEG.« less

Elastic plate spallation

NASA Technical Reports Server (NTRS)

Oline, L.; Medaglia, J.

1972-01-01

The dynamic finite element method was used to investigate elastic stress waves in a plate. Strain displacement and stress strain relations are discussed along with the stiffness and mass matrix. The results of studying point load, and distributed load over small, intermediate, and large radii are reported. The derivation of finite element matrices, and the derivation of lumped and consistent matrices for one dimensional problems with Laplace transfer solutions are included. The computer program JMMSPALL is also included.

Effect of Liquid Viscosity on Dispersion of Quasi-Lamb Waves in an Elastic-Layer-Viscous-Liquid-Layer System

NASA Astrophysics Data System (ADS)

Guz, A. N.; Bagno, A. M.

2017-07-01

The dispersion curves are constructed and propagation of quasi-Lamb waves are studied for wide range of frequencies based on the Navier -Stokes three-dimensional linearized equations for a viscous liquid and linear equations of the classical theory of elasticity for an elastic layer. For a thick liquid layer, the effect of the viscosity of the liquid and the thickness of elastic and liquid layers on the phase velocities and attenuation coefficients of quasi-Lamb modes is analyzed. It is shown that in the case of a thick liquid layer for all modes, there are elastic layers of certain thickness with minimal effect of liquid viscosity on the phase velocities and attenuation coefficients of modes. It is also discovered that for some modes, there are both certain thicknesses and certain ranges of thickness where the effect of liquid viscosity on the phase velocities and attenuation coefficients of these modes is considerable. We ascertain that liquid viscosity promotes decrease of the penetration depth of the lowest quasi-Lamb mode into the liquid. The developed approach and the obtained results make it possible to ascertain for wave processes the limits of applicability of the model of ideal compressible fluid. Numerical results in the form of graphs are adduced and analyzed.

Simulation study of axial ultrasound transmission in heterogeneous cortical bone model

NASA Astrophysics Data System (ADS)

Takano, Koki; Nagatani, Yoshiki; Matsukawa, Mami

2017-07-01

Ultrasound propagation in a heterogeneous cortical bone was studied. Using a bovine radius, the longitudinal wave velocity distribution in the axial direction was experimentally measured in the MHz range. The bilinear interpolation and piecewise cubic Hermite interpolation methods were applied to create a three-dimensional (3D) precise velocity model of the bone using experimental data. By assuming the uniaxial anisotropy of the bone, the distributions of all elastic moduli of a 3D heterogeneous model were estimated. The elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation. The wave propagation in the initial model was compared with that in the thinner model, where the inner part of the cortical bone model was removed. The wave front of the first arriving signal (FAS) slightly depended on the heterogeneity in each model. Owing to the decrease in bone thickness, the propagation behavior also changed and the FAS velocity clearly decreased.

Subwavelength elastic joints connecting torsional waveguides to maximize the power transmission coefficient

NASA Astrophysics Data System (ADS)

Lee, Joong Seok; Lee, Il Kyu; Seung, Hong Min; Lee, Jun Kyu; Kim, Yoon Young

2017-03-01

Joints with slowly varying tapered shapes, such as linear or exponential profiles, are known to transmit incident wave power efficiently between two waveguides with dissimilar impedances. This statement is valid only when the considered joint length is longer than the wavelengths of the incident waves. When the joint length is shorter than the wavelengths, however, appropriate shapes of such subwavelength joints for efficient power transmission have not been explored much. In this work, considering one-dimensional torsional wave motion in a cylindrical elastic waveguide system, optimal shapes or radial profiles of a subwavelength joint maximizing the power transmission coefficient are designed by a gradient-based optimization formulation. The joint is divided into a number of thin disk elements using the transfer matrix approach and optimal radii of the disks are determined by iterative shape optimization processes for several single or bands of wavenumbers. Due to the subwavelength constraint, the optimized joint profiles were found to be considerably different from the slowly varying tapered shapes. Specifically, for bands of wavenumbers, peculiar gourd-like shapes were obtained as optimal shapes to maximize the power transmission coefficient. Numerical results from the proposed optimization formulation were also experimentally realized to verify the validity of the present designs.

Three-dimensional elastic wave analysis of the October 2, 2004 tremor at Mount St. Helens, Washington.

NASA Astrophysics Data System (ADS)

Denlinger, R. P.

2006-12-01

On October 2, 2004, three component, broad-frequency band seismometers as far as 250 km away from Mount St. Helens volcano detected a prominent low-frequency resonance associated with the onset of eruptive volcanic activity. The energy is dominantly in the 0.5 to 10 Hz range. Since gas emissions were low, I investigate a gas-free tremor mechanism generated by sudden extension of a pressurized, cylindrical, visco- elastic magma conduit beneath the mountain as it forces its way through a brittle crust. The concept is that rapid faulting of the crust around and above the magma results in a sudden drop in resistance and, consequently, a concurrent extension of the magma in the magma column at a rate greater than magma can resupply the column. The result is a rapid pressure drop in the magma, causing the column to oscillate and radiate elastic energy into the surrounding crust. The full wavefield generated by this physical mechanism is analyzed using the finite volume method of Leveque (2002), with the approximation outlined in Langseth and Leveque (2000) for hyperbolic conservation laws. In this method, the three-dimensional equations of elasticity are written as a first order set of conservation equations, with a solution vector composed of 3 velocity components and 6 stress components. The eigenvectors of the jacobian matrices of these conservation equations are used in a fourth-order Taylors series expansion of the solution vector around a small increment in time. This method is robust, allows waves to cleanly propagate off of a finite computational grid, and includes surface and interface waves. The method also allows for extremely large contrasts in elastic moduli across internal boundaries in the grid, necessary to accommodate the large variations in rigidity between a hot, visco-elastic magma at depth and the Earth's crust. Analyzing the October 2, 2004 tremor observed at Johnson Ridge Observatory, 9 km north of the mountain, for pressure drop in a 10 km long conduit, I obtain 0.3 +/- .05 MPa, which is consistent with elastic analysis of crustal deformation around the mountain during this time period. Langseth, J.O., and R.J. LeVeque, 2000, A wave propagation method for 3D hyperbolic conservation laws, J. Comp. Phys., 165, 126-166. Leveque, R.J., 2002, Finite volume methods for hyperbolic problems, Cambridge U. Press, 558 p.

The physics of a popsicle stick bomb

NASA Astrophysics Data System (ADS)

Sautel, Jérémy; Bourges, Andréane; Caussarieu, Aude; Plihon, Nicolas; Taberlet, Nicolas

2017-10-01

Popsicle sticks can be interlocked in the so-called "cobra weave" to form a chain under tension. When one end of the chain is released, the sticks rapidly disentangle, forming a traveling wave that propagates down the chain. In this paper, the properties of the traveling front are studied experimentally, and classical results from the theory of elasticity allow for a dimensional analysis of the height and speed of the traveling wave. The study presented here can help undergraduate students familiarize themselves with experimental techniques of image processing, and it also demonstrates the power of dimensional analysis and scaling laws.

Modeling of fracture of protective concrete structures under impact loads

NASA Astrophysics Data System (ADS)

Radchenko, P. A.; Batuev, S. P.; Radchenko, A. V.; Plevkov, V. S.

2015-10-01

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.

Elastic metamaterials for tuning circular polarization of electromagnetic waves

PubMed Central

Zárate, Yair; Babaee, Sahab; Kang, Sung H.; Neshev, Dragomir N.; Shadrivov, Ilya V.; Bertoldi, Katia; Powell, David A.

2016-01-01

Electromagnetic resonators are integrated with advanced elastic material to develop a new type of tunable metamaterial. An electromagnetic-elastic metamaterial able to switch on and off its electromagnetic chiral response is experimentally demonstrated. Such tunability is attained by harnessing the unique buckling properties of auxetic elastic materials (buckliballs) with embedded electromagnetic resonators. In these structures, simple uniaxial compression results in a complex but controlled pattern of deformation, resulting in a shift of its electromagnetic resonance, and in the structure transforming to a chiral state. The concept can be extended to the tuning of three-dimensional materials constructed from the meta-molecules, since all the components twist and deform into the same chiral configuration when compressed. PMID:27320212

Elastic metamaterials for tuning circular polarization of electromagnetic waves.

PubMed

Zárate, Yair; Babaee, Sahab; Kang, Sung H; Neshev, Dragomir N; Shadrivov, Ilya V; Bertoldi, Katia; Powell, David A

2016-06-20

Electromagnetic resonators are integrated with advanced elastic material to develop a new type of tunable metamaterial. An electromagnetic-elastic metamaterial able to switch on and off its electromagnetic chiral response is experimentally demonstrated. Such tunability is attained by harnessing the unique buckling properties of auxetic elastic materials (buckliballs) with embedded electromagnetic resonators. In these structures, simple uniaxial compression results in a complex but controlled pattern of deformation, resulting in a shift of its electromagnetic resonance, and in the structure transforming to a chiral state. The concept can be extended to the tuning of three-dimensional materials constructed from the meta-molecules, since all the components twist and deform into the same chiral configuration when compressed.

Real-Time Shear Wave versus Transient Elastography for Predicting Fibrosis: Applicability, and Impact of Inflammation and Steatosis. A Non-Invasive Comparison.

PubMed

Poynard, Thierry; Pham, Tam; Perazzo, Hugo; Munteanu, Mona; Luckina, Elena; Elaribi, Djamel; Ngo, Yen; Bonyhay, Luminita; Seurat, Noemie; Legroux, Muriel; Ngo, An; Deckmyn, Olivier; Thabut, Dominique; Ratziu, Vlad; Lucidarme, Olivier

2016-01-01

Real-time shear wave elastography (2D-SWE) is a two-dimensional transient elastography and a competitor as a biomarker of liver fibrosis in comparison with the standard reference transient elastography by M probe (TE-M). The aims were to compare several criteria of applicability, and to assess inflammation and steatosis impact on elasticity values, two unmet needs. We took FibroTest as the fibrosis reference and ActiTest and SteatoTest as quantitative estimates of inflammation and steatosis. After standardization of estimates, analyses used curve fitting, quantitative Lin concordance coefficient [LCC], and multivariate logistic regression. A total of 2,251 consecutive patients were included. We validated the predetermined 0.2 kPa cut-off as a too low minimal elasticity value identifying not-reliable 2D-SWE results (LCC with FibroTest = 0.0281[-0.119;0.175]. Other criteria, elasticity CV, body mass index and depth of measures were not sufficiently discriminant. The applicability of 2D-SWE (95%CI) 89.6%(88.2-90.8), was significantly higher than that of TE, 85.6%(84.0-87.0; P<0.0001). In patients with non-advanced fibrosis (METAVIR F0F1F2), elasticity values estimated by 2D-SWE was less impacted by inflammation and steatosis than elasticity value estimated by TE-M: LCC (95%CI) 0.039 (0.021;0.058) vs 0.090 (0.068;0.112;P<0.01) and 0.105 (0.068;0.141) vs 0.192 (0.153;0.230; P<0.01) respectively. The three analyses methods gave similar results. Elasticity results including very low minimal signal in the region of interest should be considered not reliable. 2D-SWE had a higher applicability than TE, the reference elastography, with less impact of inflammation and steatosis especially in patients with non-advanced fibrosis, as presumed by blood tests. ClinicalTrials.gov NCT01927133.

Wave propagation in piezoelectric layered structures of film bulk acoustic resonators.

PubMed

Zhu, Feng; Qian, Zheng-Hua; Wang, Bin

2016-04-01

In this paper, we studied the wave propagation in a piezoelectric layered plate consisting of a piezoelectric thin film on an electroded elastic substrate with or without a driving electrode. Both plane-strain and anti-plane waves were taken into account for the sake of completeness. Numerical results on dispersion relations, cut-off frequencies and vibration distributions of selected modes were given. The effects of mass ratio of driving electrode layer to film layer on the dispersion curve patterns and cut-off frequencies of the plane-strain waves were discussed in detail. Results show that the mass ratio does not change the trend of dispersion curves but larger mass ratio lowers corresponding frequency at a fixed wave number and may extend the frequency range for energy trapping. Those results are of fundamental importance and can be used as a reference to develop effective two-dimensional plate equations for structural analysis and design of film bulk acoustic resonators. Copyright © 2016 Elsevier B.V. All rights reserved.

Electrostatic Field Invisibility Cloak

NASA Astrophysics Data System (ADS)

Lan, Chuwen; Yang, Yuping; Geng, Zhaoxin; Li, Bo; Zhou, Ji

2015-11-01

The invisibility cloak has been drawing much attention due to its new concept for manipulating many physical fields, from oscillating wave fields (electromagnetic, acoustic and elastic) to static magnetic fields, dc electric fields, and diffusive fields. Here, an electrostatic field invisibility cloak has been theoretically investigated and experimentally demonstrated to perfectly hide two dimensional objects without disturbing their external electrostatic fields. The desired cloaking effect has been achieved via both cancelling technology and transformation optics (TO). This study demonstrates a novel way for manipulating electrostatic fields, which shows promise for a wide range of potential applications.

Steering elastic SH waves in an anomalous way by metasurface

NASA Astrophysics Data System (ADS)

Cao, Liyun; Yang, Zhichun; Xu, Yanlong

2018-03-01

Metasurface, which does not exist in nature, has exhibited exotic essence on the manipulation of both electromagnetic and acoustic waves. In this paper, the concept of metasurface is extended to the field of elastic SH waves, and the anomalous refractions of SH waves across the designed elastic SH wave metasurfaces (SHWMs) are demonstrated numerically. Firstly, a SHWM is designed with supercells, each supercell is composed of four subunits. It is demonstrated that this configuration has the ability of deflecting the vertical and oblique incident waves in an arbitrary desired direction. Then, a unique SHWM with supercell composed of only two subunits is designed. Numerical simulation shows its ability of splitting the vertical and oblique incident waves into two tunable transmitted wave beams, respectively. In the process of steering SH waves, it is also found that two kinds of leakages of transmitted waves across the designed SHWM will occur in some particular situations, which will affect the desired transmitted wave. The mechanisms of the leakages, which are different from that of the common high-order diffraction mentioned in existing literatures, are revealed. The current study can offer theoretical guidance not only for designing devices of directional ultrasonic detection and splitting SH waves but also for steering other kinds of classical waves.

Nonclassical models of the theory of plates and shells

NASA Astrophysics Data System (ADS)

Annin, Boris D.; Volchkov, Yuri M.

2017-11-01

Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the complete system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each of the unknown functions (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

Laser generated guided waves and finite element modeling for the thickness gauging of thin layers.

PubMed

Lefevre, F; Jenot, F; Ouaftouh, M; Duquennoy, M; Ourak, M

2010-03-01

In this paper, nondestructive testing has been performed on a thin gold layer deposited on a 2 in. silicon wafer. Guided waves were generated and studied using a laser ultrasonic setup and a two-dimensional fast Fourier transform technique was employed to obtain the dispersion curves. A gold layer thickness of 1.33 microm has been determined with a +/-5% margin of error using the shape of the two first propagating modes, assuming for the substrate and the layer an uncertainty on the elastic parameters of +/-2.5%. A finite element model has been implemented to validate the data post-treatment and the experimental results. A good agreement between the numerical simulation, the analytical modeling and the experimentations has been observed. This method was considered suitable for thickness layer higher than 0.7 microm.

Quantitative Estimation of Seismic Velocity Changes Using Time-Lapse Seismic Data and Elastic-Wave Sensitivity Approach

NASA Astrophysics Data System (ADS)

Denli, H.; Huang, L.

2008-12-01

Quantitative monitoring of reservoir property changes is essential for safe geologic carbon sequestration. Time-lapse seismic surveys have the potential to effectively monitor fluid migration in the reservoir that causes geophysical property changes such as density, and P- and S-wave velocities. We introduce a novel method for quantitative estimation of seismic velocity changes using time-lapse seismic data. The method employs elastic sensitivity wavefields, which are the derivatives of elastic wavefield with respect to density, P- and S-wave velocities of a target region. We derive the elastic sensitivity equations from analytical differentiations of the elastic-wave equations with respect to seismic-wave velocities. The sensitivity equations are coupled with the wave equations in a way that elastic waves arriving in a target reservoir behave as a secondary source to sensitivity fields. We use a staggered-grid finite-difference scheme with perfectly-matched layers absorbing boundary conditions to simultaneously solve the elastic-wave equations and the elastic sensitivity equations. By elastic-wave sensitivities, a linear relationship between relative seismic velocity changes in the reservoir and time-lapse seismic data at receiver locations can be derived, which leads to an over-determined system of equations. We solve this system of equations using a least- square method for each receiver to obtain P- and S-wave velocity changes. We validate the method using both surface and VSP synthetic time-lapse seismic data for a multi-layered model and the elastic Marmousi model. Then we apply it to the time-lapse field VSP data acquired at the Aneth oil field in Utah. A total of 10.5K tons of CO2 was injected into the oil reservoir between the two VSP surveys for enhanced oil recovery. The synthetic and field data studies show that our new method can quantitatively estimate changes in seismic velocities within a reservoir due to CO2 injection/migration.

Elastic waves in periodic and non-periodic sets of hollow cylinders

NASA Astrophysics Data System (ADS)

Nikitov, S. A.; Gulyaev, Yu. V.; Lisenkov, I. V.; Popov, R. S.; Grigorievkii, A. V.; Grigorievkii, V. I.

2008-06-01

Two ways of modeling of elastic wave propagation in microstructured acoustic fiber are considered. First one is the calculation of band gap parameters by FEM for phononic crystal forming cross section of fiber. Second one is immediate calculation of dispersion characteristics of elastic fiber containing hole cylindric chanels. For fiber made of fused β quarz numerical results are proposed. For the first type full forbidden gap obtained and for second two different types of modes was found.

The Effect of Sedimentary Basins on Through-Passing Short-Period Surface Waves

NASA Astrophysics Data System (ADS)

Feng, L.; Ritzwoller, M. H.

2017-12-01

Surface waves propagating through sedimentary basins undergo elastic wave field complications that include multiple scattering, amplification, the formation of secondary wave fronts, and subsequent wave front healing. Unless these effects are accounted for accurately, they may introduce systematic bias to estimates of source characteristics, the inference of the anelastic structure of the Earth, and ground motion predictions for hazard assessment. Most studies of the effects of basins on surface waves have centered on waves inside the basins. In contrast, we investigate wave field effects downstream from sedimentary basins, with particular emphasis on continental basins and propagation paths, elastic structural heterogeneity, and Rayleigh waves at 10 s period. Based on wave field simulations through a recent 3D crustal and upper mantle model of East Asia, we demonstrate significant Rayleigh wave amplification downstream from sedimentary basins in eastern China such that Ms measurements obtained on the simulated wave field vary by more than a magnitude unit. We show that surface wave amplification caused by basins results predominantly from elastic focusing and that amplification effects produced through 3D basin models are reproduced using 2D membrane wave simulations through an appropriately defined phase velocity map. The principal characteristics of elastic focusing in both 2D and 3D simulations include (1) retardation of the wave front inside the basins; (2) deflection of the wave propagation direction; (3) formation of a high amplitude lineation directly downstream from the basin bracketed by two low amplitude zones; and (4) formation of a secondary wave front. Finally, by comparing the impact of elastic focusing with anelastic attenuation, we argue that on-continent sedimentary basins are expected to affect surface wave amplitudes more strongly through elastic focusing than through the anelastic attenuation.

Directional asymmetry of the nonlinear wave phenomena in a three-dimensional granular phononic crystal under gravity.

PubMed

Merkel, A; Tournat, V; Gusev, V

2014-08-01

We report the experimental observation of the gravity-induced asymmetry for the nonlinear transformation of acoustic waves in a noncohesive granular phononic crystal. Because of the gravity, the contact precompression increases with depth inducing space variations of not only the linear and nonlinear elastic moduli but also of the acoustic wave dissipation. We show experimentally and explain theoretically that, in contrast to symmetric propagation of linear waves, the amplitude of the nonlinearly self-demodulated wave depends on whether the propagation of the waves is in the direction of the gravity or in the opposite direction. Among the observed nonlinear processes, we report frequency mixing of the two transverse-rotational modes belonging to the optical band of vibrations and propagating with negative phase velocities, which results in the excitation of a longitudinal wave belonging to the acoustic band of vibrations and propagating with positive phase velocity. We show that the measurements of the gravity-induced asymmetry in the nonlinear acoustic phenomena can be used to compare the in-depth distributions of the contact nonlinearity and of acoustic absorption.

One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes.

PubMed

Cheviakov, A F; Ganghoffer, J-F

2016-05-01

The framework of incompressible nonlinear hyperelasticity and viscoelasticity is applied to the derivation of one-dimensional models of nonlinear wave propagation in fiber-reinforced elastic solids. Equivalence transformations are used to simplify the resulting wave equations and to reduce the number of parameters. Local conservation laws and global conserved quantities of the models are systematically computed and discussed, along with other related mathematical properties. Sample numerical solutions are presented. The models considered in the paper are appropriate for the mathematical description of certain aspects of the behavior of biological membranes and similar structures. Copyright © 2015 Elsevier Ltd. All rights reserved.

Head-on collision of the second mode internal solitary waves

NASA Astrophysics Data System (ADS)

Terletska, Kateryna; Maderich, Vladimir; Jung, Kyung Tae

2017-04-01

Second mode internal waves are widespread in offshore areas, and they frequently follow the first mode internal waves on the oceanic shelf. Large amplitude internal solitary waves (ISW) of second mode containing trapped cores associated with closed streamlines can also transport plankton and nutrients. An interaction of ISWs with trapped cores takes place in a specific manner. It motivated us to carry out a computational study of head-on collision of ISWs of second mode propagating in a laboratory-scale numerical tank using the nonhydrostatic 3D numerical model based on the Navier-Stokes equations for a continuously stratified fluid. Three main classes of ISW of second mode propagating in the pycnocline layer of thickness h between homogeneous deep layers can be identified: (i) the weakly nonlinear waves; (ii) the stable strongly nonlinear waves with trapped cores; and (iii) the shear unstable strongly nonlinear waves (Maderich et al., 2015). Four interaction regimes for symmetric collision were separated from simulation results using this classification: (A) an almost elastic interaction of the weakly nonlinear waves; (B) a non-elastic interaction of waves with trapped cores when ISW amplitudes were close to critical non-dimensional amplitude a/h; (C) an almost elastic interaction of stable strongly nonlinear waves with trapped cores; (D) non-elastic interaction of the unstable strongly nonlinear waves. The unexpected result of simulation was that relative loss of energy due to the collision was maximal for regime B. New regime appeared when ISW of different amplitudes belonged to class (ii) collide. In result of interaction the exchange of mass between ISW occurred: the trapped core of smaller wave was entrained by core of larger ISW without mixing forming a new ISW of larger amplitude whereas in smaller ISW core of smaller wave totally substituted by fluid from larger wave. Overall, the wave characteristics induced by head-on collision agree well with the results of several available laboratory experiments. References [1] V. Maderich, K. T. Jung, K. Terletska, I. Brovchenko, T. Talipova, "Incomplete similarity of internal solitary waves with trapped core," Fluid Dynamics Research 47, 035511 (2015).

Longitudinal waves in carbon nanotubes in the presence of transverse magnetic field and elastic medium

NASA Astrophysics Data System (ADS)

Liu, Hu; Liu, Hua; Yang, Jialing

2017-09-01

In the present paper, the coupling effect of transverse magnetic field and elastic medium on the longitudinal wave propagation along a carbon nanotube (CNT) is studied. Based on the nonlocal elasticity theory and Hamilton's principle, a unified nonlocal rod theory which takes into account the effects of small size scale, lateral inertia and radial deformation is proposed. The existing rod theories including the classic rod theory, the Rayleigh-Love theory and Rayleigh-Bishop theory for macro solids can be treated as the special cases of the present model. A two-parameter foundation model (Pasternak-type model) is used to represent the elastic medium. The influence of transverse magnetic field, Pasternak-type elastic medium and small size scale on the longitudinal wave propagation behavior of the CNT is investigated in detail. It is shown that the influences of lateral inertia and radial deformation cannot be neglected in analyzing the longitudinal wave propagation characteristics of the CNT. The results also show that the elastic medium and the transverse magnetic field will also affect the longitudinal wave dispersion behavior of the CNT significantly. The results obtained in this paper are helpful for understanding the mechanical behaviors of nanostructures embedded in an elastic medium.

Nonlinear Dispersive Elastic Waves in Solids: Exact, Approximate, and Numerical Solutions

NASA Astrophysics Data System (ADS)

Khajehtourian, Romik

Wave motion lies at the heart of many disciplines in the physical sciences and engineering. For example, problems and applications involving light, sound, heat, or fluid flow are all likely to involve wave dynamics at some level. A particular class of problems is concerned with the propagation of elastic waves in a solid medium, such as a fiber-reinforced composite material responding to vibratory excitations, or soil and rock admitting seismic waves moments after the onset of an earthquake, or phonon transport in a semiconducting crystal like silicon. Regardless of the type of wave, the dispersion relation provides a fundamental characterization of the elastodynamic properties of the medium. The first part of the dissertation examines the propagation of a large-amplitude elastic wave in a one-dimensional homogeneous medium with a focus on the effects of inherent nonlinearities on the dispersion relation. Considering a thin rod, where the thickness is small compared to the wavelength, an exact, closed-form formulation is presented for the treatment of two types of nonlinearity in the strain-displacement gradient relation: Green-Lagrange and Hencky. The derived relation is then verified by direct time-domain simulations, examining both instantaneous dispersion (by direct observation) and short-term, pre-breaking dispersion (by Fourier transformation). A high-order perturbation analysis is also conducted yielding an explicit analytical space-time solution, which is shown to be spectrally accurate. The results establish a perfect match between theory and simulation and reveal that regardless of the strength of the nonlinearity, the dispersion relation fully embodies all information pertaining to the nonlinear harmonic generation mechanism that unfolds as an arbitrary-profiled wave evolves in the medium. In the second part of the dissertation, the analysis is extended to a continuous periodic thin rod exhibiting multiple phases or embedded local resonators. The extended method, which is based on a standard transfer-matrix formulation augmented with a nonlinear enrichment at the constitutive material level, yields an approximate band structure that is accurate to an amplitude that is roughly one eighth of the unit cell length. This approach represents a new paradigm for examining the balance between periodicity and nonlinearity in shaping the nature of wave motion.

Re-radiation of acoustic waves from the A0 wave on a submerged elastic shell

NASA Astrophysics Data System (ADS)

Ahyi, A. C.; Cao, Hui; Raju, P. K.; Überall, Herbert

2005-07-01

We consider evacuated thin semi-infinite shells immersed in a fluid, which may be either of cylindrical shape with a hemispherical shell endcap, or formed two-dimensionally by semi-infinite parallel plates joined together by a semi-cylinder. The connected shell portions are joined in a manner to satisfy continuity but with a discontinuous radius of curvature. Acoustic waves are considered incident along the axis of symmetry (say the z axis) onto the curved portion of the shell, where they, at the critical angle of coincidence, generate Lamb and Stoneley-type waves in the shell. Computations were carried out using a code developed by Cao et al. [Chinese J. Acoust. 14, 317 (1995)] and was used in order to computationally visualize the waves in the fluid that have been re-radiated by the shell waves a the critical angle. The frequency range was below that of the lowest Lamb wave, and only the A0 wave (and partly the S0 wave) was observed to re-radiate into the fluid under our assumptions. The results will be compared to experimental results in which the re-radiated waves are optically visualized by the Schardin-Cranz schlieren method. .

Vibration and flutter of mistuned bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Kaza, K. R. V.; Kielb, R. E.

1984-01-01

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbofans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Vibration and flutter of mistuned bladed-disk assemblies

NASA Technical Reports Server (NTRS)

Rao, K.; Kaza, V.; Kielb, R. E.

1984-01-01

An analytical model for investigating vibration and flutter of mistuned bladed disk assemblies is presented. This model accounts for elastic, inertial and aerodynamic coupling between bending and torsional motions of each individual blade, elastic and inertial couplings between the blades and the disk, and aerodynamic coupling among the blades. The disk was modeled as a circular plate with constant thickness and each blade was represented by a twisted, slender, straight, nonuniform, elastic beam with a symmetric cross section. The elastic axis, inertia axis, and the tension axis were taken to be noncoincident and the structural warping of the section was explicitly considered. The blade aerodynamic loading in the subsonic and supersonic flow regimes was obtained from two-dimensional unsteady, cascade theories. All the possible standing wave modes of the disk and traveling wave modes of the blades were included. The equations of motion were derived by using the energy method in conjunction with the assumed mode shapes for the disk and the blades. Continuities of displacement and slope at the blade-disk junction were maintained. The equations were solved to investigate the effects of blade-disk coupling and blade frequency mistuning on vibration and flutter. Results showed that the flexibility of practical disks such as those used for current generation turbufans did not have a significant influence on either the tuned or mistuned flutter characteristics. However, the disk flexibility may have a strong influence on some of the system frequencies and on forced response.

Measurements of radiated elastic wave energy from dynamic tensile cracks

NASA Technical Reports Server (NTRS)

Boler, Frances M.

1990-01-01

The role of fracture-velocity, microstructure, and fracture-energy barriers in elastic wave radiation during a dynamic fracture was investigated in experiments in which dynamic tensile cracks of two fracture cofigurations of double cantilever beam geometry were propagating in glass samples. The first, referred to as primary fracture, consisted of fractures of intact glass specimens; the second configuration, referred to as secondary fracture, consisted of a refracture of primary fracture specimens which were rebonded with an intermittent pattern of adhesive to produce variations in fracture surface energy along the crack path. For primary fracture cases, measurable elastic waves were generated in 31 percent of the 16 fracture events observed; the condition for radiation of measurable waves appears to be a local abrupt change in the fracture path direction, such as occurs when the fracture intersects a surface flaw. For secondary fractures, 100 percent of events showed measurable elastic waves; in these fractures, the ratio of radiated elastic wave energy in the measured component to fracture surface energy was 10 times greater than for primary fracture.

Tunable evolutions of shock absorption and energy partitioning in magnetic granular chains

NASA Astrophysics Data System (ADS)

Leng, Dingxin; Liu, Guijie; Sun, Lingyu

2018-01-01

In this paper, we investigate the tunable characteristics of shock waves propagating in one-dimensional magnetic granular chains at various chain lengths and magnetic flux densities. According to the Hertz contact theory and Maxwell principle, a discrete element model with coupling elastic and field-induced interaction potentials of adjacent magnetic grains is proposed. We also present hard-sphere approximation analysis to describe the energy partitioning features of magnetic granular chains. The results demonstrate that, for a fixed magnetic field strength, when the chain length is greater than two times of the wave width of the solitary wave, the chain length has little effect on the output energy of the system; for a fixed chain length, the shock absorption and energy partitioning features of magnetic granular chains are remarkably influenced by varying magnetic flux densities. This study implies that the magnetic granular chain is potential to construct adaptive shock absorption components for impulse mitigation.

Numerical simulation of deformation and fracture of space protective shell structures from concrete and fiber concrete under pulse loading

NASA Astrophysics Data System (ADS)

Radchenko, P. A.; Batuev, S. P.; Radchenko, A. V.; Plevkov, V. S.

2015-11-01

This paper presents results of numerical simulation of interaction between aircraft Boeing 747-400 and protective shell of nuclear power plant. The shell is presented as complex multilayered cellular structure comprising layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was held three-dimensionally using the author's algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. The dynamics of stress-strain state and fracture of structure were studied. Destruction is described using two-stage model that allows taking into account anisotropy of elastic and strength properties of concrete and fiber concrete. It is shown that wave processes initiate destruction of shell cellular structure—cells start to destruct in unloading wave, originating after output of compression wave to the free surfaces of cells.

Modeling of fracture of protective concrete structures under impact loads

DOE Office of Scientific and Technical Information (OSTI.GOV)

Radchenko, P. A., E-mail: radchenko@live.ru; Batuev, S. P.; Radchenko, A. V.

This paper presents results of numerical simulation of interaction between a Boeing 747-400 aircraft and the protective shell of a nuclear power plant. The shell is presented as a complex multilayered cellular structure consisting of layers of concrete and fiber concrete bonded with steel trusses. Numerical simulation was performed three-dimensionally using the original algorithm and software taking into account algorithms for building grids of complex geometric objects and parallel computations. Dynamics of the stress-strain state and fracture of the structure were studied. Destruction is described using a two-stage model that allows taking into account anisotropy of elastic and strength propertiesmore » of concrete and fiber concrete. It is shown that wave processes initiate destruction of the cellular shell structure; cells start to destruct in an unloading wave originating after the compression wave arrival at free cell surfaces.« less

Two-dimensional fluid-filled closed-cell cellular solid as an acoustic metamaterial with negative index

NASA Astrophysics Data System (ADS)

Dorodnitsyn, V.; Van Damme, B.

2016-04-01

A concept for acoustic metamaterials consisting of a cellular medium with fluid-filled cells is fabricated and studied experimentally. In such a system, the fluid and solid structure explicitly interact, and elastic wave propagation is coupled to both phases. Focusing here on shear wave behavior, we confirm previous numerical studies in three steps. We first measure the material deformations pertaining to three qualitatively different shear wave modes in the frequency range below 3.5 kHz. We then measure the group velocity and demonstrate that, within a certain frequency interval, the group and phase velocity have opposite signs. This shows that the system acts as a negative-index metamaterial. Finally, we confirm the presence of band gaps due to the locally resonant behavior of the cell walls. The demonstrated concept of a closed, fluid-filled cellular material as an acoustic metamaterial opens a wide space for applications.

Ice Floe Breaking in Contemporary Third Generation Operational Wave Models

NASA Astrophysics Data System (ADS)

Sévigny, C.; Baudry, J.; Gauthier, J. C.; Dumont, D.

2016-02-01

The dynamical zone observed at the edge of the consolidated ice area where are found the wave-fractured floes (i.e. marginal ice zone or MIZ) has become an important topic in ocean modeling. As both operational and climate ocean models now seek to reproduce the complex atmosphere-ice-ocean system with realistic coupling processes, many theoretical and numerical studies have focused on understanding and modeling this zone. Few attempts have been made to embed wave-ice interactions specific to the MIZ within a two-dimensional model, giving the possibility to calculate both the attenuation of surface waves by sea ice and the concomitant breaking of the sea ice-cover into smaller floes. One of the first challenges consists in improving the parameterization of wave-ice dynamics in contemporary third generation operational wave models. A simple waves-in-ice model (WIM) similar to the one proposed by Williams et al. (2013a,b) was implemented in WAVEWATCH III. This WIM considers ice floes as floating elastic plates and predicts the dimensionless attenuation coefficient by the use of a lookup-table-based, wave scattering scheme. As in Dumont et al. (2011), the different frequencies are treated individually and floe breaking occurs for a particular frequency when the expected wave amplitude exceeds the allowed strain amplitude, which considers ice floes properties and wavelength in ice field. The model is here further refined and tested in idealized two-dimensional cases, giving preliminary results of the performance and sensitivity of the parameterization to initial wave and ice conditions. The effects of the wave-ice coupling over the incident wave spectrum are analyzed as well as the resulting floe size distribution. The model gives prognostic values of the lateral extent of the marginal ice zone with maximum ice floe diameter that progressively increases with distance from the ice edge.

Numerical investigation of band gaps in 3D printed cantilever-in-mass metamaterials

NASA Astrophysics Data System (ADS)

Qureshi, Awais; Li, Bing; Tan, K. T.

2016-06-01

In this research, the negative effective mass behavior of elastic/mechanical metamaterials is exhibited by a cantilever-in-mass structure as a proposed design for creating frequency stopping band gaps, based on local resonance of the internal structure. The mass-in-mass unit cell model is transformed into a cantilever-in-mass model using the Bernoulli-Euler beam theory. An analytical model of the cantilever-in-mass structure is derived and the effects of geometrical dimensions and material parameters to create frequency band gaps are examined. A two-dimensional finite element model is created to validate the analytical results, and excellent agreement is achieved. The analytical model establishes an easily tunable metamaterial design to realize wave attenuation based on locally resonant frequency. To demonstrate feasibility for 3D printing, the analytical model is employed to design and fabricate 3D printable mechanical metamaterial. A three-dimensional numerical experiment is performed using COMSOL Multiphysics to validate the wave attenuation performance. Results show that the cantilever-in-mass metamaterial is capable of mitigating stress waves at the desired resonance frequency. Our study successfully presents the use of one constituent material to create a 3D printed cantilever-in-mass metamaterial with negative effective mass density for stress wave mitigation purposes.

AELAS: Automatic ELAStic property derivations via high-throughput first-principles computation

NASA Astrophysics Data System (ADS)

Zhang, S. H.; Zhang, R. F.

2017-11-01

The elastic properties are fundamental and important for crystalline materials as they relate to other mechanical properties, various thermodynamic qualities as well as some critical physical properties. However, a complete set of experimentally determined elastic properties is only available for a small subset of known materials, and an automatic scheme for the derivations of elastic properties that is adapted to high-throughput computation is much demanding. In this paper, we present the AELAS code, an automated program for calculating second-order elastic constants of both two-dimensional and three-dimensional single crystal materials with any symmetry, which is designed mainly for high-throughput first-principles computation. Other derivations of general elastic properties such as Young's, bulk and shear moduli as well as Poisson's ratio of polycrystal materials, Pugh ratio, Cauchy pressure, elastic anisotropy and elastic stability criterion, are also implemented in this code. The implementation of the code has been critically validated by a lot of evaluations and tests on a broad class of materials including two-dimensional and three-dimensional materials, providing its efficiency and capability for high-throughput screening of specific materials with targeted mechanical properties. Program Files doi:http://dx.doi.org/10.17632/f8fwg4j9tw.1 Licensing provisions: BSD 3-Clause Programming language: Fortran Nature of problem: To automate the calculations of second-order elastic constants and the derivations of other elastic properties for two-dimensional and three-dimensional materials with any symmetry via high-throughput first-principles computation. Solution method: The space-group number is firstly determined by the SPGLIB code [1] and the structure is then redefined to unit cell with IEEE-format [2]. Secondly, based on the determined space group number, a set of distortion modes is automatically specified and the distorted structure files are generated. Afterwards, the total energy for each distorted structure is calculated by the first-principles codes, e.g. VASP [3]. Finally, the second-order elastic constants are determined from the quadratic coefficients of the polynomial fitting of the energies vs strain relationships and other elastic properties are accordingly derived. References [1] http://atztogo.github.io/spglib/. [2] A. Meitzler, H.F. Tiersten, A.W. Warner, D. Berlincourt, G.A. Couqin, F.S. Welsh III, IEEE standard on piezoelectricity, Society, 1988. [3] G. Kresse, J. Furthmüller, Phys. Rev. B 54 (1996) 11169.

P-Wave to Rayleigh-wave conversion coefficients for wedge corners; model experiments

USGS Publications Warehouse

Gangi, A.F.; Wesson, R.L.

1978-01-01

An analytic solution is not available for the diffraction of elastic waves by wedges; however, numerical solutions of finite-difference type are available for selected wedge angles. The P- to Rayleigh-wave conversion coefficients at wedge tips have been measured on two-dimensional seismic models for stress-free wedges with wedge angles, ??0, of 10, 30, 60, 90 and 120??. The conversion coefficients show two broad peaks and a minimum as a function of the angle between the wedge face and the direction of the incident P-wave. The minimum occurs for the P wave incident parallel to the wedge face and one maximum is near an incidence angle of 90?? to the wedge face. The amplitude of this maximum, relative to the other, decreases as the wedge angle increases. The asymmetry of the conversion coefficients, CPR(??; ??0), relative to parallel incidence (?? = 0) increases as the wedge angle increases. The locations of the maxima and the minimum as well as the asymmetry can be explained qualitatively. The conversion coefficients are measured with an accuracy of ??5% in those regions where there are no interfering waves. A comparison of the data for the 10?? wedge with the theoretical results for a half plane (0?? wedge) shows good correlation. ?? 1978.

Two dimensional modeling of elastic wave propagation in solids containing cracks with rough surfaces and friction - Part II: Numerical implementation.

PubMed

Delrue, Steven; Aleshin, Vladislav; Truyaert, Kevin; Bou Matar, Olivier; Van Den Abeele, Koen

2018-01-01

Our study aims at the creation of a numerical toolbox that describes wave propagation in samples containing internal contacts (e.g. cracks, delaminations, debondings, imperfect intergranular joints) of known geometry with postulated contact interaction laws including friction. The code consists of two entities: the contact model and the solid mechanics module. Part I of the paper concerns an in-depth description of a constitutive model for realistic contacts or cracks that takes into account the roughness of the contact faces and the associated effects of friction and hysteresis. In the crack model, three different contact states can be recognized: contact loss, total sliding and partial slip. Normal (clapping) interactions between the crack faces are implemented using a quadratic stress-displacement relation, whereas tangential (friction) interactions were introduced using the Coulomb friction law for the total sliding case, and the Method of Memory Diagrams (MMD) in case of partial slip. In the present part of the paper, we integrate the developed crack model into finite element software in order to simulate elastic wave propagation in a solid material containing internal contacts or cracks. We therefore implemented the comprehensive crack model in MATLAB® and introduced it in the Structural Mechanics Module of COMSOL Multiphysics®. The potential of the approach for ultrasound based inspection of solids with cracks showing acoustic nonlinearity is demonstrated by means of an example of shear wave propagation in an aluminum sample containing a single crack with rough surfaces and friction. Copyright © 2017 Elsevier B.V. All rights reserved.

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

NASA Astrophysics Data System (ADS)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Anomalous incident-angle and elliptical-polarization rotation of an elastically refracted P-wave

NASA Astrophysics Data System (ADS)

Fa, Lin; Fa, Yuxiao; Zhang, Yandong; Ding, Pengfei; Gong, Jiamin; Li, Guohui; Li, Lijun; Tang, Shaojie; Zhao, Meishan

2015-08-01

We report a newly discovered anomalous incident-angle of an elastically refracted P-wave, arising from a P-wave impinging on an interface between two VTI media with strong anisotropy. This anomalous incident-angle is found to be located in the post-critical incident-angle region corresponding to a refracted P-wave. Invoking Snell’s law for a refracted P-wave provides two distinctive solutions before and after the anomalous incident-angle. For an inhomogeneously refracted and elliptically polarized P-wave at the anomalous incident-angle, its rotational direction experiences an acute variation, from left-hand elliptical to right-hand elliptical polarization. The new findings provide us an enhanced understanding of acoustical-wave scattering and lead potentially to widespread and novel applications.

How does the Textural Character of Alpine Fault Rocks Influence their Elasticity and Anisotropy

NASA Astrophysics Data System (ADS)

Guerin-Marthe, S.; Adam, L.; Townend, J.; Toy, V.; Doan, M. L.; Faulkner, D.

2015-12-01

The DFDP-1A and DFDP-1B boreholes drilled in 2011 enabled the collection of samples of unaltered Alpine Fault Zone rock. We present laboratory measurements of the elastic properties of these samples, as well as protoliths collected at outcrops. These data were collected with a unique non-contacting laser ultrasonic system, and transducers under a range of pressure conditions representative of the upper-crust. Based on the laser measurements we conclude that there is strong anisotropy in the foliated protoliths, particularly in the protomylonites. We also show that even at core scale, the anisotropy is scale dependent (there are systematic relationships between wavelength and mineral foliation). For the cataclasites, preliminary data show that elastic wave anisotropy decreases as we approach the Principal Slip Zone, in the two boreholes. The P-wave velocities exhibit a high pressure dependence for the borehole samples, meaning that most of the cracks are closed before an effective pressure of 5MPa, reducing the elastic anisotropy. However, on a cataclasite sample, the S-wave velocity measurements, polarized perpendicular and parallel to the fractures, exhibit weak anisotropy (γ=13%) at 20MPa, even when the P-wave velocity - pressure curve displays an asymptotic shape. This observation probably indicates that elastic anisotropy results from preferred mineral orientation rather than fractures. The elastic wave measurements are complemented with petrographical, XRD, XRF, SEM and CT scan analyses to understand the source of the elastic wave anisotropic behavior in the Alpine Fault damaged zone. Finally, the laboratory data are compared to the P-wave sonic log to understand the effect of elastic wave anisotropy, fluid pressures and mineralogy.

Probe Oscillation Shear Elastography (PROSE): A High Frame-Rate Method for Two-Dimensional Ultrasound Shear Wave Elastography.

PubMed

Mellema, Daniel C; Song, Pengfei; Kinnick, Randall R; Urban, Matthew W; Greenleaf, James F; Manduca, Armando; Chen, Shigao

2016-09-01

Ultrasound shear wave elastography (SWE) utilizes the propagation of induced shear waves to characterize the shear modulus of soft tissue. Many methods rely on an acoustic radiation force (ARF) "push beam" to generate shear waves. However, specialized hardware is required to generate the push beams, and the thermal stress that is placed upon the ultrasound system, transducer, and tissue by the push beams currently limits the frame-rate to about 1 Hz. These constraints have limited the implementation of ARF to high-end clinical systems. This paper presents Probe Oscillation Shear Elastography (PROSE) as an alternative method to measure tissue elasticity. PROSE generates shear waves using a harmonic mechanical vibration of an ultrasound transducer, while simultaneously detecting motion with the same transducer under pulse-echo mode. Motion of the transducer during detection produces a "strain-like" compression artifact that is coupled with the observed shear waves. A novel symmetric sampling scheme is proposed such that pulse-echo detection events are acquired when the ultrasound transducer returns to the same physical position, allowing the shear waves to be decoupled from the compression artifact. Full field-of-view (FOV) two-dimensional (2D) shear wave speed images were obtained by applying a local frequency estimation (LFE) technique, capable of generating a 2D map from a single frame of shear wave motion. The shear wave imaging frame rate of PROSE is comparable to the vibration frequency, which can be an order of magnitude higher than ARF based techniques. PROSE was able to produce smooth and accurate shear wave images from three homogeneous phantoms with different moduli, with an effective frame rate of 300 Hz. An inclusion phantom study showed that increased vibration frequencies improved the accuracy of inclusion imaging, and allowed targets as small as 6.5 mm to be resolved with good contrast (contrast-to-noise ratio ≥ 19 dB) between the target and background.

Probe Oscillation Shear Elastography (PROSE): A High Frame-Rate Method for Two-Dimensional Ultrasound Shear Wave Elastography

PubMed Central

Mellema, Daniel C.; Song, Pengfei; Kinnick, Randall R.; Urban, Matthew W.; Greenleaf, James F.; Manduca, Armando; Chen, Shigao

2017-01-01

Ultrasound shear wave elastography (SWE) utilizes the propagation of induced shear waves to characterize the shear modulus of soft tissue. Many methods rely on an acoustic radiation force (ARF) “push beam” to generate shear waves. However, specialized hardware is required to generate the push beams, and the thermal stress that is placed upon the ultrasound system, transducer, and tissue by the push beams currently limits the frame-rate to about 1 Hz. These constraints have limited the implementation of ARF to high-end clinical systems. This paper presents Probe Oscillation Shear Elastography (PROSE) as an alternative method to measure tissue elasticity. PROSE generates shear waves using a harmonic mechanical vibration of an ultrasound transducer, while simultaneously detecting motion with the same transducer under pulse-echo mode. Motion of the transducer during detection produces a “strain-like” compression artifact that is coupled with the observed shear waves. A novel symmetric sampling scheme is proposed such that pulse-echo detection events are acquired when the ultrasound transducer returns to the same physical position, allowing the shear waves to be decoupled from the compression artifact. Full field-of-view (FOV) two-dimensional (2D) shear wave speed images were obtained by applying a local frequency estimation (LFE) technique, capable of generating a 2D map from a single frame of shear wave motion. The shear wave imaging frame rate of PROSE is comparable to the vibration frequency, which can be an order of magnitude higher than ARF based techniques. PROSE was able to produce smooth and accurate shear wave images from three homogeneous phantoms with different moduli, with an effective frame rate of 300Hz. An inclusion phantom study showed that increased vibration frequencies improved the accuracy of inclusion imaging, and allowed targets as small as 6.5 mm to be resolved with good contrast (contrast-to-noise ratio ≥19 dB) between the target and background. PMID:27076352

Effective-medium theory of elastic waves in random networks of rods.

PubMed

Katz, J I; Hoffman, J J; Conradi, M S; Miller, J G

2012-06-01

We formulate an effective medium (mean field) theory of a material consisting of randomly distributed nodes connected by straight slender rods, hinged at the nodes. Defining wavelength-dependent effective elastic moduli, we calculate both the static moduli and the dispersion relations of ultrasonic longitudinal and transverse elastic waves. At finite wave vector k the waves are dispersive, with phase and group velocities decreasing with increasing wave vector. These results are directly applicable to networks with empty pore space. They also describe the solid matrix in two-component (Biot) theories of fluid-filled porous media. We suggest the possibility of low density materials with higher ratios of stiffness and strength to density than those of foams, aerogels, or trabecular bone.

Wave bandgap formation and its evolution in two-dimensional phononic crystals composed of rubber matrix with periodic steel quarter-cylinders

NASA Astrophysics Data System (ADS)

Li, Peng; Wang, Guan; Luo, Dong; Cao, Xiaoshan

2018-02-01

The band structure of a two-dimensional phononic crystal, which is composed of four homogenous steel quarter-cylinders immersed in rubber matrix, is investigated and compared with the traditional steel/rubber crystal by the finite element method (FEM). It is revealed that the frequency can then be tuned by changing the distance between adjacent quarter-cylinders. When the distance is relatively small, the integrality of scatterers makes the inner region inside them almost motionless, so that they can be viewed as a whole at high-frequencies. In the case of relatively larger distance, the interaction between each quarter-cylinder and rubber will introduce some new bandgaps at relatively low-frequencies. Lastly, the point defect states induced by the four quarter-cylinders are revealed. These results will be helpful in fabricating devices, such as vibration insulators and acoustic/elastic filters, whose band frequencies can be manipulated artificially.

Kikuchi ultrafast nanodiffraction in four-dimensional electron microscopy

PubMed Central

Yurtsever, Aycan; Zewail, Ahmed H.

2011-01-01

Coherent atomic motions in materials can be revealed using time-resolved X-ray and electron Bragg diffraction. Because of the size of the beam used, typically on the micron scale, the detection of nanoscale propagating waves in extended structures hitherto has not been reported. For elastic waves of complex motions, Bragg intensities contain all polarizations and they are not straightforward to disentangle. Here, we introduce Kikuchi diffraction dynamics, using convergent-beam geometry in an ultrafast electron microscope, to selectively probe propagating transverse elastic waves with nanoscale resolution. It is shown that Kikuchi band shifts, which are sensitive only to the tilting of atomic planes, reveal the resonance oscillations, unit cell angular amplitudes, and the polarization directions. For silicon, the observed wave packet temporal envelope (resonance frequency of 33 GHz), the out-of-phase temporal behavior of Kikuchi’s edges, and the magnitude of angular amplitude (0.3 mrad) and polarization elucidate the nature of the motion: one that preserves the mass density (i.e., no compression or expansion) but leads to sliding of planes in the antisymmetric shear eigenmode of the elastic waveguide. As such, the method of Kikuchi diffraction dynamics, which is unique to electron imaging, can be used to characterize the atomic motions of propagating waves and their interactions with interfaces, defects, and grain boundaries at the nanoscale. PMID:21245348

Elastic parabolic equation solutions for underwater acoustic problems using seismic sources.

PubMed

Frank, Scott D; Odom, Robert I; Collis, Jon M

2013-03-01

Several problems of current interest involve elastic bottom range-dependent ocean environments with buried or earthquake-type sources, specifically oceanic T-wave propagation studies and interface wave related analyses. Additionally, observed deep shadow-zone arrivals are not predicted by ray theoretic methods, and attempts to model them with fluid-bottom parabolic equation solutions suggest that it may be necessary to account for elastic bottom interactions. In order to study energy conversion between elastic and acoustic waves, current elastic parabolic equation solutions must be modified to allow for seismic starting fields for underwater acoustic propagation environments. Two types of elastic self-starter are presented. An explosive-type source is implemented using a compressional self-starter and the resulting acoustic field is consistent with benchmark solutions. A shear wave self-starter is implemented and shown to generate transmission loss levels consistent with the explosive source. Source fields can be combined to generate starting fields for source types such as explosions, earthquakes, or pile driving. Examples demonstrate the use of source fields for shallow sources or deep ocean-bottom earthquake sources, where down slope conversion, a known T-wave generation mechanism, is modeled. Self-starters are interpreted in the context of the seismic moment tensor.

Dynamic crack propagation in a 2D elastic body: The out-of-plane case

NASA Astrophysics Data System (ADS)

Nicaise, Serge; Sandig, Anna-Margarete

2007-05-01

Already in 1920 Griffith has formulated an energy balance criterion for quasistatic crack propagation in brittle elastic materials. Nowadays, a generalized energy balance law is used in mechanics [F. Erdogan, Crack propagation theories, in: H. Liebowitz (Ed.), Fracture, vol. 2, Academic Press, New York, 1968, pp. 498-586; L.B. Freund, Dynamic Fracture Mechanics, Cambridge Univ. Press, Cambridge, 1990; D. Gross, Bruchmechanik, Springer-Verlag, Berlin, 1996] in order to predict how a running crack will grow. We discuss this situation in a rigorous mathematical way for the out-of-plane state. This model is described by two coupled equations in the reference configuration: a two-dimensional scalar wave equation for the displacement fields in a cracked bounded domain and an ordinary differential equation for the crack position derived from the energy balance law. We handle both equations separately, assuming at first that the crack position is known. Then the weak and strong solvability of the wave equation will be studied and the crack tip singularities will be derived under the assumption that the crack is straight and moves tangentially. Using the energy balance law and the crack tip behavior of the displacement fields we finally arrive at an ordinary differential equation for the motion of the crack tip.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1982-01-01

The extended method of equivalent inclusion developed is applied to study the specific wave problems of the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and of the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. The eigenstrains are expanded as a geometric series and the method of integration for the inhomogeneous Helmholtz operator given by Fu and Mura is adopted. The results obtained by using a limited number of terms in the eigenstrain expansion are compared with exact solutions for the layer problem and for a perfect sphere. Two parameters are singled out for this comparison: the ratio of elastic moduli, and the ratio of the mass densities. General trends for three different situations are shown.

Elastic model for crimped collagen fibrils

NASA Technical Reports Server (NTRS)

Freed, Alan D.; Doehring, Todd C.

2005-01-01

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendinece.

Anisotropy of Solid Breast Lesions in 2D Shear Wave Elastography is an Indicator of Malignancy.

PubMed

Skerl, Katrin; Vinnicombe, Sarah; Thomson, Kim; McLean, Denis; Giannotti, Elisabetta; Evans, Andrew

2016-01-01

To investigate if anisotropy at two-dimensional shear wave elastography (SWE) suggests malignancy and whether it correlates with prognostic and predictive factors in breast cancer. Study group A of 244 solid breast lesions was imaged with SWE between April 2013 and May 2014. Each lesion was imaged in radial and in antiradial planes, and the maximum elasticity, mean elasticity, and standard deviation were recorded and correlated with benign/malignant status, and if malignant, correlated with conventional predictive and prognostic factors. The results were compared to a study group B of 968 solid breast lesions, which were imaged in sagittal and in axial planes between 2010 and 2013. Neither benign nor malignant lesion anisotropy is plane dependent. However, malignant lesions are more anisotropic than benign lesions (P ≤ 0.001). Anisotropy correlates with increasing elasticity parameters, breast imaging-reporting and data system categories, core biopsy result, and tumor grade. Large cancers are significantly more anisotropic than small cancers (P ≤ 0.001). The optimal anisotropy cutoff threshold for benign/malignant differentiation of 150 kPa(2) achieves the best sensitivity (74%) with a reasonable specificity (63%). Anisotropy may be useful during benign/malignant differentiation of solid breast masses using SWE. Anisotropy also correlates with some prognostic factors in breast cancer. Crown Copyright © 2016. Published by Elsevier Inc. All rights reserved.

Theoretical relationship between elastic wave velocity and electrical resistivity

NASA Astrophysics Data System (ADS)

Lee, Jong-Sub; Yoon, Hyung-Koo

2015-05-01

Elastic wave velocity and electrical resistivity have been commonly applied to estimate stratum structures and obtain subsurface soil design parameters. Both elastic wave velocity and electrical resistivity are related to the void ratio; the objective of this study is therefore to suggest a theoretical relationship between the two physical parameters. Gassmann theory and Archie's equation are applied to propose a new theoretical equation, which relates the compressional wave velocity to shear wave velocity and electrical resistivity. The piezo disk element (PDE) and bender element (BE) are used to measure the compressional and shear wave velocities, respectively. In addition, the electrical resistivity is obtained by using the electrical resistivity probe (ERP). The elastic wave velocity and electrical resistivity are recorded in several types of soils including sand, silty sand, silty clay, silt, and clay-sand mixture. The appropriate input parameters are determined based on the error norm in order to increase the reliability of the proposed relationship. The predicted compressional wave velocities from the shear wave velocity and electrical resistivity are similar to the measured compressional velocities. This study demonstrates that the new theoretical relationship may be effectively used to predict the unknown geophysical property from the measured values.

Non-Destructive Evaluation of Material System Using Highly Nonlinear Acoustic Waves

NASA Astrophysics Data System (ADS)

Khatri, Devvrath

A chain of granular particles is one of the most studied examples of highly nonlinear systems deriving its response from the nonlinear Hertzian contact interaction between particles. Interest in these systems derives from their tunable dynamic response, encompassing linear, weakly nonlinear, and strongly nonlinear regimes, controlled by varying the static and dynamic load applied. In chains with a very weak (or zero) static precompression, the system supports the formation and propagation of highly nonlinear solitary waves (HNSWs). The dual-nonlinear interaction between particles (i.e., a power-law type contact potential in compression, and zero strength in tension) combined with discreteness of the system, makes the granular system highly tunable. The propagation properties of these waves, such as traveling pulse width, wave speed, number of separated pulses (single or train of pulses), etc., can be controlled by modifying one or many of the parameters, like the particle's dimension, material properties, static and dynamic force amplitude, the type and duration of the initial excitation applied to the system, and/or the periodicity of the chain. The ability to control the wave properties in such chains has been proposed for several different practical engineering applications. The dynamic properties of these granular chains have been conventionally studied using discrete particle models (DPMs) which consider the particles in the chains as point masses connected by nonlinear Hertzian springs with the neighboring particles. Although, this is a good approximation under proper circumstances, it does not capture many features of the three dimensional elastic particles such as the elastic wave propagation within the particles, the local deformation of the particles in the vicinity of the contact point, the corresponding changes in the contact area, and the collective vibrations of the particles among others. This thesis focuses on the development of a finite element model (FEM) using the commercially available software Abaqus, which takes into account many of these characteristic features. The finite element model discretizes particles by considering them as three-dimensional deformable bodies of revolution and describes the nonlinear dynamic response of one-dimensional granular chains composed of particles with various geometries and orientations. We showed that particles' geometries and orientations provide additional design parameters for controlling the dynamic response of the system, compared to chains composed of spherical particles. We also showed that the tunable and compact nature of these waves can be used to tailor the properties of HNSWs for specific application, such as information carriers for actuation and sensing of mechanical properties and boundary effects of adjoining media in Non-Destructive Evaluation (NDE) and Structural Health Monitoring (SHM). Using experiments and numerics, we characterized interface dynamics between granular media and adjoining linear elastic media, and found that the coupling produced temporary localization of the incident waves at the boundaries between the two media and their decomposition into reflected waves. We monitored the formation of reflected solitary waves propagating back from the interface and found that their properties are sensitive to the geometric and material properties of the adjoining media. The work done in this research enhances our understanding of the basic physics and tunability of nonlinear granular media, and further establishes a theoretical and numerical foundation in the applications of HNSWs as information carriers.

Physical interpretation and application of principles of ultrasonic nondestructive evaluation of high-performance materials

NASA Technical Reports Server (NTRS)

Miller, James G.

1990-01-01

An ultrasonic measurement system employed in the experimental interrogation of the anisotropic properties (through the measurement of the elastic stiffness constants) of the uniaxial graphite-epoxy composites is presented. The continuing effort for the development of improved visualization techniques for physical parameters is discussed. The background is set for the understanding and visualization of the relationship between the phase and energy/group velocity for propagation in high-performance anisotropic materials by investigating the general requirements imposed by the classical wave equation. The consequences are considered when the physical parameters of the anisotropic material are inserted into the classical wave equation by a linear elastic model. The relationship is described between the phase velocity and the energy/group velocity three dimensional surfaces through graphical techniques.

Theoretical requirements for broadband perfect absorption of acoustic waves by ultra-thin elastic meta-films

PubMed Central

Duan, Yuetao; Luo, Jie; Wang, Guanghao; Hang, Zhi Hong; Hou, Bo; Li, Jensen; Sheng, Ping; Lai, Yun

2015-01-01

We derive and numerically demonstrate that perfect absorption of elastic waves can be achieved in two types of ultra-thin elastic meta-films: one requires a large value of almost pure imaginary effective mass density and a free space boundary, while the other requires a small value of almost pure imaginary effective modulus and a hard wall boundary. When the pure imaginary density or modulus exhibits certain frequency dispersions, the perfect absorption effect becomes broadband, even in the low frequency regime. Through a model analysis, we find that such almost pure imaginary effective mass density with required dispersion for perfect absorption can be achieved by elastic metamaterials with large damping. Our work provides a feasible approach to realize broadband perfect absorption of elastic waves in ultra-thin films. PMID:26184117

Scatter of elastic waves by a thin flat elliptical inhomogeneity

NASA Technical Reports Server (NTRS)

Fu, L. S.

1983-01-01

Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.

Elasticity study of textured barium strontium titanate thin films by X-ray diffraction and laser acoustic waves

NASA Astrophysics Data System (ADS)

Chaabani, Anouar; Njeh, Anouar; Donner, Wolfgang; Klein, Andreas; Hédi Ben Ghozlen, Mohamed

2017-05-01

Ba0.65Sr0.35TiO3 (BST) thin films of 300 nm were deposited on Pt(111)/TiO2/SiO2/Si(001) substrates by radio frequency magnetron sputtering. Two thin films with different (111) and (001) fiber textures were prepared. X-ray diffraction was applied to measure texture. The raw pole figure data were further processed using the MTEX quantitative texture analysis software for plotting pole figures and calculating elastic constants and Young’s modulus from the orientation distribution function (ODF) for each type of textured fiber. The calculated elastic constants were used in the theoretical studies of surface acoustics waves (SAW) propagating in two types of multilayered BST systems. Theoretical dispersion curves were plotted by the application of the ordinary differential equation (ODE) and the stiffness matrix methods (SMM). A laser acoustic waves (LAW) technique was applied to generate surface acoustic waves (SAW) propagating in the BST films, and from a recursive process, the effective Young’s modulus are determined for the two samples. These methods are used to extract and compare elastic properties of two types of BST films, and quantify the influence of texture on the direction-dependent Young’s modulus.

MR elastography of the breast:preliminary clinical results.

PubMed

Lorenzen, J; Sinkus, R; Lorenzen, M; Dargatz, M; Leussler, C; Röschmann, P; Adam, G

2002-07-01

Imaging of breast tumors and various breast tissues using magnetic resonance (MR) elastography (MRE) to explore the potential of elasticity as a new parameter for the diagnosis of breast lesions. Low-frequency mechanical waves are transmitted into breast tissue by means of an oscillator. The local characteristics of the mechanical wave are determined by the underlying elastic properties of the tissue. Theses waves can be displayed by means of a motion-sensitive spin-echo MR sequence within the phase of the MR image. Elasticity reconstruction is performed on the basis of 8 "snapshots" of each wave within the three spatial directions. We performed in-vivo measurements in 15 female patients with malignant tumors of the breast, 5 patients with benign breast tumors, and 15 healthy volunteers. Malignant invasive breast tumors documented the highest values of elasticity with a median of 15.9 kPa and a wide range of stiffnesses between 8 and 28 kPa. In contrast, benign breast lesions represented low values of elasticity, which were significantly different from malignant breast tumors (median elasticity: 7.0 kPa; p = 0.0012). This was comparable to the stiffest tissue areas in healthy volunteers (median elasticity 7.0 kPa), whereas breast parenchyma (median: 2.5 kPa) and fatty breast tissue (median: 1.7 kPa) showed the lowest values of elasticity. Two invasive ductal carcinomas had elasticity values of 8 kPa and two stiff parenchyma areas in healthy volunteers had elasticities of 13 and 15 kPa. These lesions could not be differentiated by their elasticity. We conclude that MRE is a promising new imaging modality with the capability to assess the viscoelastic properties of breast tumors and the surrounding tissues. However, from our preliminary results in a small number of patients it is obvious that there is an overlap in the elasticity ranges of soft malignant tumors and stiff benign lesions.

Lamb wave detection of limpet mines on ship hulls.

PubMed

Bingham, Jill; Hinders, Mark; Friedman, Adam

2009-12-01

This paper describes the use of ultrasonic guided waves for identifying the mass loading due to underwater limpet mines on ship hulls. The Dynamic Wavelet Fingerprint Technique (DFWT) is used to render the guided wave mode information in two-dimensional binary images because the waveform features of interest are too subtle to identify in time domain. The use of wavelets allows both time and scale features from the original signals to be retained, and image processing can be used to automatically extract features that correspond to the arrival times of the guided wave modes. For further understanding of how the guided wave modes propagate through the real structures, a parallel processing, 3D elastic wave simulation is developed using the finite integration technique (EFIT). This full field, technique models situations that are too complex for analytical solutions, such as built up 3D structures. The simulations have produced informative visualizations of the guided wave modes in the structures as well as mimicking directly the output from sensors placed in the simulation space for direct comparison to experiments. Results from both drydock and in-water experiments with dummy mines are also shown.

Effects of Defect Size and Number Density on the Transmission and Reflection of Guided Elastic Waves

DTIC Science & Technology

2016-04-22

localized region, a photoacoustic source generates elastic waves on one side of the damaged region, and then two ultrasound transducers measure the...where the defects are of the same order as the wavelength of the ultrasound , we find ourselves confronted with Mie scattering, which has weaker

Guided waves in anisotropic and quasi-isotropic aerospace composites: three-dimensional simulation and experiment.

PubMed

Leckey, Cara A C; Rogge, Matthew D; Raymond Parker, F

2014-01-01

Three-dimensional (3D) elastic wave simulations can be used to investigate and optimize nondestructive evaluation (NDE) and structural health monitoring (SHM) ultrasonic damage detection techniques for aerospace materials. 3D anisotropic elastodynamic finite integration technique (EFIT) has been implemented for ultrasonic waves in carbon fiber reinforced polymer (CFRP) composite laminates. This paper describes 3D EFIT simulations of guided wave propagation in undamaged and damaged anisotropic and quasi-isotropic composite plates. Comparisons are made between simulations of guided waves in undamaged anisotropic composite plates and both experimental laser Doppler vibrometer (LDV) wavefield data and dispersion curves. Time domain and wavenumber domain comparisons are described. Wave interaction with complex geometry delamination damage is then simulated to investigate how simulation tools incorporating realistic damage geometries can aid in the understanding of wave interaction with CFRP damage. In order to move beyond simplistic assumptions of damage geometry, volumetric delamination data acquired via X-ray microfocus computed tomography is directly incorporated into the simulation. Simulated guided wave interaction with the complex geometry delamination is compared to experimental LDV time domain data and 3D wave interaction with the volumetric damage is discussed. Published by Elsevier B.V.

Use of shear wave elastography to differentiate benign and malignant breast lesions.

PubMed

Çebi Olgun, Deniz; Korkmazer, Bora; Kılıç, Fahrettin; Dikici, Atilla Süleyman; Velidedeoğlu, Mehmet; Aydoğan, Fatih; Kantarcı, Fatih; Yılmaz, Mehmet Halit

2014-01-01

We aimed to determine the correlations between the elasticity values of solid breast masses and histopathological findings to define cutoff elasticity values differentiating malignant from benign lesions. A total of 115 solid breast lesions of 109 consecutive patients were evaluated prospectively using shear wave elastography (SWE). Two orthogonal elastographic images of each lesion were obtained. Minimum, mean, and maximum elasticity values were calculated in regions of interest placed over the stiffest areas on the two images; we also calculated mass/fat elasticity ratios. Correlation of elastographic measurements with histopathological results were studied. Eighty-three benign and thirty-two malignant lesions were histopathologically diagnosed. The minimum, mean, and maximum elasticity values, and the mass/fat elasticity ratios of malignant lesions, were significantly higher than those of benign lesions. The cutoff value was 45.7 kPa for mean elasticity (sensitivity, 96%; specificity, 95%), 54.3 kPa for maximum elasticity (sensitivity, 95%; specificity, 94%), 37.1 kPa for minimum elasticity (sensitivity, 96%; specificity, 95%), and 4.6 for the mass/fat elasticity ratio (sensitivity, 97%; specificity, 95%). SWE yields additional valuable quantitative data to ultrasonographic examination on solid breast lesions. SWE may serve as a complementary tool for diagnosis of breast lesions. Long-term clinical studies are required to accurately select lesions requiring biopsy.

Real-Time Shear Wave versus Transient Elastography for Predicting Fibrosis: Applicability, and Impact of Inflammation and Steatosis. A Non-Invasive Comparison

PubMed Central

Poynard, Thierry; Pham, Tam; Perazzo, Hugo; Munteanu, Mona; Luckina, Elena; Elaribi, Djamel; Ngo, Yen; Bonyhay, Luminita; Seurat, Noemie; Legroux, Muriel; Ngo, An; Deckmyn, Olivier; Thabut, Dominique; Ratziu, Vlad; Lucidarme, Olivier

2016-01-01

Background and Aims Real-time shear wave elastography (2D-SWE) is a two-dimensional transient elastography and a competitor as a biomarker of liver fibrosis in comparison with the standard reference transient elastography by M probe (TE-M). The aims were to compare several criteria of applicability, and to assess inflammation and steatosis impact on elasticity values, two unmet needs. Methods We took FibroTest as the fibrosis reference and ActiTest and SteatoTest as quantitative estimates of inflammation and steatosis. After standardization of estimates, analyses used curve fitting, quantitative Lin concordance coefficient [LCC], and multivariate logistic regression. Results A total of 2,251 consecutive patients were included. We validated the predetermined 0.2 kPa cut-off as a too low minimal elasticity value identifying not-reliable 2D-SWE results (LCC with FibroTest = 0.0281[-0.119;0.175]. Other criteria, elasticity CV, body mass index and depth of measures were not sufficiently discriminant. The applicability of 2D-SWE (95%CI) 89.6%(88.2–90.8), was significantly higher than that of TE, 85.6%(84.0–87.0; P<0.0001). In patients with non-advanced fibrosis (METAVIR F0F1F2), elasticity values estimated by 2D-SWE was less impacted by inflammation and steatosis than elasticity value estimated by TE-M: LCC (95%CI) 0.039 (0.021;0.058) vs 0.090 (0.068;0.112;P<0.01) and 0.105 (0.068;0.141) vs 0.192 (0.153;0.230; P<0.01) respectively. The three analyses methods gave similar results. Conclusions Elasticity results including very low minimal signal in the region of interest should be considered not reliable. 2D-SWE had a higher applicability than TE, the reference elastography, with less impact of inflammation and steatosis especially in patients with non-advanced fibrosis, as presumed by blood tests. Trial Registration ClinicalTrials.gov NCT01927133 PMID:27706177

FORTRAN programs for calculating nonlinear seismic ground response in two dimensions

USGS Publications Warehouse

Joyner, W.B.

1978-01-01

The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.

Nonlinear coherent structures in granular crystals

NASA Astrophysics Data System (ADS)

Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.

2017-10-01

The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

Guided elastic waves in a pre-stressed compressible interlayer

PubMed

Sotiropoulos

2000-03-01

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

NASA Astrophysics Data System (ADS)

Sid, S.; Terrapon, V. E.; Dubief, Y.

2018-02-01

The goal of the present study is threefold: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bidimensional instability in three-dimensional EIT flows, and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of viscoelastic fluid flows are performed in both two- and three-dimensional straight periodic channels using the Peterlin finitely extensible nonlinear elastic model (FENE-P). The Reynolds number is set to Reτ=85 , which is subcritical for two-dimensional flows but beyond the transition for three-dimensional ones. The polymer properties selected correspond to those of typical dilute polymer solutions, and two moderate Weissenberg numbers, Wiτ=40 ,100 , are considered. The simulation results show that sustained turbulence can be observed in two-dimensional subcritical flows, confirming the existence of a bidimensional elasto-inertial instability. The same type of instability is also observed in three-dimensional simulations where both Newtonian and elasto-inertial turbulent structures coexist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of small elastic scales is investigated by introducing global artificial diffusion (GAD) in the hyperbolic transport equation for polymers. The aim is to measure how the flow reacts when the smallest elastic scales are progressively filtered out. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to flow laminarization. A sufficiently high Schmidt number (weakly diffusive polymers) is necessary to allow self-sustained turbulence to settle. Although EIT can withstand a low amount of diffusion and remains in a nonlaminar chaotic state, adding a finite amount of GAD in the system can have an impact on the dynamics and lead to important quantitative changes, even for Schmidt numbers as large as 102. The use of GAD should therefore be avoided in viscoelastic flow simulations.

Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

NASA Astrophysics Data System (ADS)

Harris, John G.

2001-10-01

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements.

PubMed

Alastruey, Jordi; Khir, Ashraf W; Matthys, Koen S; Segers, Patrick; Sherwin, Spencer J; Verdonck, Pascal R; Parker, Kim H; Peiró, Joaquim

2011-08-11

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476-3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10(-6)) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost. Copyright © 2011 Elsevier Ltd. All rights reserved.

Oscillation of satellite droplets in an Oldroyd-B viscoelastic liquid jet

NASA Astrophysics Data System (ADS)

Li, Fang; Yin, Xie-Yuan; Yin, Xie-Zhen

2017-01-01

A one-dimensional numerical simulation is carried out to study the oscillation characteristics of satellite droplets in the beads-on-a-string structure of an Oldroyd-B viscoelastic liquid jet. The oscillation of satellite droplets is compared with the linear oscillation of a single viscoelastic droplet. It is found that, contrary to the predictions of linear theory, the period of oscillation of satellite droplets decreases with time, despite the increase in droplet volume. The mechanism may lie in the existence of the filament, which exerts an extra resistance on droplets. On the other hand, the oscillation of droplets does not influence very much the thinning of the filament. The influence of the axial wave number, viscosity, and elasticity on the oscillation of satellite droplets is examined. Increasing the wave number may result in the decrease in the period and the increase in the decay rate of oscillation, while increasing viscosity may lead to the increase in both the period and the decay rate of oscillation. Elasticity is shown to suppress the oscillation at large wave numbers, but its influence is limited at small wave numbers.

Elasticity, slowness, thermal conductivity and the anisotropies in the Mn3Cu1-xGexN compounds

NASA Astrophysics Data System (ADS)

Li, Guan-Nan; Chen, Zhi-Qian; Lu, Yu-Ming; Hu, Meng; Jiao, Li-Na; Zhao, Hao-Ting

2018-03-01

We perform the first-principles to systematically investigate the elastic properties, minimum thermal conductivity and anisotropy of the negative thermal expansion compounds Mn3Cu1-xGexN. The elastic constant, bulk modulus, shear modulus, Young’s modulus and Poisson ratio are calculated for all the compounds. The results of the elastic constant indicate that all the compounds are mechanically stable and the doped Ge can adjust the ductile character of the compounds. According to the values of the percent ratio of the elastic anisotropy AB, AE and AG, shear anisotropic factors A1, A2 and A3, all the Mn3Cu1-xGexN compounds are elastic anisotropy. The three-dimensional diagrams of elastic moduli in space also show that all the compounds are elastic anisotropy. In addition, the acoustic wave speed, slowness, minimum thermal conductivity and Debye temperature are also calculated. When the ratio of content for Cu and Ge arrived to 1:1, the compound has the lowest thermal conductivity and the highest Debye temperature.

Two-Dimensional Imaging Velocimetry of Heterogeneous Flow and Brittle Failure in Diamond

NASA Astrophysics Data System (ADS)

Ali, S. J.; Smith, R.; Erskine, D.; Eggert, J.; Celliers, P. M.; Collins, G. W.; Jeanloz, R.

2014-12-01

Understanding the nature and dynamics of heterogeneous flow in diamond subjected to shock compression is important for many fields of research, from inertial confinement fusion to the study of carbon rich planets. Waves propagating through a shocked material can be significantly altered by the various deformation mechanisms present in shocked materials, including anisotropic sound speeds, phase transformations, plastic/inelastic flow and brittle failure. Quantifying the spatial and temporal effects of these deformation mechanisms has been limited by a lack of diagnostics capable of obtaining simultaneous micron resolution spatial measurements and nanosecond resolution time measurements. We have utilized the 2D Janus High Resolution Velocimeter at LLNL to study the time and space dependence of fracture in shock-compressed diamond above the Hugoniot elastic limit. Previous work on the OMEGA laser facility (Rochester) has shown that the free-surface reflectivity of μm-grained diamond samples drops linearly with increasing sample pressure, whereas under the same conditions the reflectivity of nm-grained samples remains unaffected. These disparate observations can be understood by way of better documenting fracture in high-strain compression of diamond. To this end, we have imaged the development and evolution of elastic-wave propagation, plastic-wave propagation and fracture networks in the three primary orientations of single-crystal diamond, as well as in microcrystalline and nanocrystalline diamond, and find that the deformation behavior depends sensitively on the orientation and crystallinity of the diamonds.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

Elastic metamaterials with simultaneously negative effective shear modulus and mass density.

PubMed

Wu, Ying; Lai, Yun; Zhang, Zhao-Qing

2011-09-02

We propose a type of elastic metamaterial comprising fluid-solid composite inclusions which can possess a negative shear modulus and negative mass density over a large frequency region. Such a material has the unique property that only transverse waves can propagate with a negative dispersion while longitudinal waves are forbidden. This leads to many interesting phenomena such as negative refraction, which is demonstrated by using a wedge sample and a significant amount of mode conversion from transverse waves to longitudinal waves that cannot occur on the interface of two natural solids.

Waveguiding by a locally resonant metasurface

NASA Astrophysics Data System (ADS)

Maznev, A. A.; Gusev, V. E.

2015-09-01

Dispersion relations for acoustic and electromagnetic waves guided by resonant inclusions located at the surface of an elastic solid or an interface between two media are analyzed theoretically within the effective medium approximation. Oscillators on the surface of an elastic half-space are shown to give rise to a Love-type surface acoustic wave only existing below the oscillator frequency. A simple dispersion relation governing this system is shown to also hold for electromagnetic waves guided by Lorentz oscillators at an interface between two media with equal dielectric constants. Different kinds of behavior of the dispersion of the resonantly guided mode are identified, depending on whether the bulk wave in the absence of oscillators can propagate along the surface or interface.

Linear elastic properties derivation from microstructures representative of transport parameters.

PubMed

Hoang, Minh Tan; Bonnet, Guy; Tuan Luu, Hoang; Perrot, Camille

2014-06-01

It is shown that three-dimensional periodic unit cells (3D PUC) representative of transport parameters involved in the description of long wavelength acoustic wave propagation and dissipation through real foam samples may also be used as a standpoint to estimate their macroscopic linear elastic properties. Application of the model yields quantitative agreement between numerical homogenization results, available literature data, and experiments. Key contributions of this work include recognizing the importance of membranes and properties of the base material for the physics of elasticity. The results of this paper demonstrate that a 3D PUC may be used to understand and predict not only the sound absorbing properties of porous materials but also their transmission loss, which is critical for sound insulation problems.

Effect of rotation and magnetic field on free vibrations in a spherical non-homogeneous embedded in an elastic medium

NASA Astrophysics Data System (ADS)

Bayones, F. S.; Abd-Alla, A. M.

2018-06-01

The prime objective of the present paper is to analyze the effect of magnetic field and rotation on the free vibrations of an elastic hollow sphere. The one-dimensional equation of motion is solved in terms of radial displacement. The frequency equation is obtained when the boundaries are free and fixed boundary conditions. The determination is concerned with the eigenvalues of the natural frequency of the free vibrations in the case of harmonic vibrations. The natural frequencies and the mode shapes are calculated numericall and the effects of rotation and magnetic field are discussed. It was shown that the dispersion curves of waves were significantly influenced by the magnetic field and rotation of the elastic sphere.

In-situ changes in the elastic wave velocity of rock with increasing temperature using high-resolution coda wave interferometry

NASA Astrophysics Data System (ADS)

Griffiths, Luke; Heap, Michael; Lengliné, Olivier; Schmittbuhl, Jean; Baud, Patrick

2017-04-01

Rock undergoes fluctuations in temperature in various settings in Earth's crust, including areas of volcanic or geothermal activity, or industrial environments such as hydrocarbon or geothermal reservoirs. Changes in temperature can cause thermal stresses that can result in the formation of microcracks, which affect the mechanical, physical, and transport properties of rocks. Of the affected physical properties, the elastic wave velocity of rock is particularly sensitive to microcracking. Monitoring the evolution of elastic wave velocity during the thermal stressing of rock therefore provides valuable insight into thermal cracking processes. One monitoring technique is Coda Wave Interferometry (CWI), which infers high-resolution changes in the medium from changes in multiple-scattered elastic waves. We have designed a new experimental setup to perform CWI whilst cyclically heating and cooling samples of granite (cylinders of 20 mm diameter and 40 mm length). In our setup, the samples are held between two pistons within a tube furnace and are heated and cooled at a rate of 1 °C/min to temperatures of up to 300 °C. Two high temperature piezo-transducers are each in contact with an opposing face of the rock sample. The servo-controlled uniaxial press compensates for the thermal expansion and contraction of the pistons and the sample, keeping the coupling between the transducers and the sample, and the axial force acting on the sample, constant throughout. Our setup is designed for simultaneous acoustic emission monitoring (AE is commonly used as a proxy for microcracking), and so we can follow thermal microcracking precisely by combining the AE and CWI techniques. We find that during the first heating/cooling cycle, the onset of thermal microcracking occurs at a relatively low temperature of around 65 °C. The CWI shows that elastic wave velocity decreases with increasing temperature and increases during cooling. Upon cooling, back to room temperature, there is an irreversible relative decrease in velocity of several percent associated with the presence of new thermal microcracks. Our data suggest that few new microcracks were formed when the same sample was subject to subsequent identical heating/cooling cycles as changes in the elastic wave velocity are near-reversible. Our results shed light on the temperature conditions required for thermal microcracking and the influence of temperature on elastic wave velocity with applications to a wide variety of geoscientific disciplines.

Quasi-periodic Fibonacci and periodic one-dimensional hypersonic phononic crystals of porous silicon: Experiment and simulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aliev, Gazi N., E-mail: g.aliev@bath.ac.uk; Goller, Bernhard

2014-09-07

A one-dimensional Fibonacci phononic crystal and a distributed Bragg reflector were constructed from porous silicon. The structures had the same number of layers and similar acoustic impedance mismatch, and were electrochemically etched in highly boron doped silicon wafers. The thickness of the individual layers in the stacks was approximately 2 μm. Both types of hypersonic band gap structure were studied by direct measurement of the transmittance of longitudinal acoustic waves in the 0.1–2.6 GHz range. Acoustic band gaps deeper than 50 dB were detected in both structures. The experimental results were compared with model calculations employing the transfer matrix method. The acoustic propertiesmore » of periodic and quasi-periodic structures in which half-wave retarding bi-layers do not consist of two quarter-wave retarding layers are discussed. The strong correlation between width and depth of gaps in the transmission spectra is demonstrated. The dominant mechanisms of acoustic losses in porous multilayer structures are discussed. The elastic constants remain proportional over our range of porosity, and hence, the Grüneisen parameter is constant. This simplifies the expression for the porosity dependence of the Akhiezer damping.« less

Use of shear wave elastography to differentiate benign and malignant breast lesions

PubMed Central

Olgun, Deniz Çebi; Korkmazer, Bora; Kılıç, Fahrettin; Dikici, Atilla Süleyman; Velidedeoğlu, Mehmet; Aydoğan, Fatih; Kantarcı, Fatih; Yılmaz, Mehmet Halit

2014-01-01

PURPOSE We aimed to determine the correlations between the elasticity values of solid breast masses and histopathological findings to define cutoff elasticity values differentiating malignant from benign lesions. MATERIALS and METHODS A total of 115 solid breast lesions of 109 consecutive patients were evaluated prospectively using shear wave elastography (SWE). Two orthogonal elastographic images of each lesion were obtained. Minimum, mean, and maximum elasticity values were calculated in regions of interest placed over the stiffest areas on the two images; we also calculated mass/fat elasticity ratios. Correlation of elastographic measurements with histopathological results were studied. RESULTS Eighty-three benign and thirty-two malignant lesions were histopathologically diagnosed. The minimum, mean, and maximum elasticity values, and the mass/fat elasticity ratios of malignant lesions, were significantly higher than those of benign lesions. The cutoff value was 45.7 kPa for mean elasticity (sensitivity, 96%; specificity, 95%), 54.3 kPa for maximum elasticity (sensitivity, 95%; specificity, 94%), 37.1 kPa for minimum elasticity (sensitivity, 96%; specificity, 95%), and 4.6 for the mass/fat elasticity ratio (sensitivity, 97%; specificity, 95%). CONCLUSION SWE yields additional valuable quantitative data to ultrasonographic examination on solid breast lesions. SWE may serve as a complementary tool for diagnosis of breast lesions. Long-term clinical studies are required to accurately select lesions requiring biopsy. PMID:24509183

Observation of band gaps in the gigahertz range and deaf bands in a hypersonic aluminum nitride phononic crystal slab

NASA Astrophysics Data System (ADS)

Gorisse, M.; Benchabane, S.; Teissier, G.; Billard, C.; Reinhardt, A.; Laude, V.; Defaÿ, E.; Aïd, M.

2011-06-01

We report on the observation of elastic waves propagating in a two-dimensional phononic crystal composed of air holes drilled in an aluminum nitride membrane. The theoretical band structure indicates the existence of an acoustic band gap centered around 800 MHz with a relative bandwidth of 6.5% that is confirmed by gigahertz optical images of the surface displacement. Further electrical measurements and computation of the transmission reveal a much wider attenuation band that is explained by the deaf character of certain bands resulting from the orthogonality of their polarization with that of the source.

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

An Experimental Study on the Impact of Different-frequency Elastic Waves on Water Retention Curve

NASA Astrophysics Data System (ADS)

Deng, J. H.; Dai, J. Y.; Lee, J. W.; Lo, W. C.

2017-12-01

ABSTEACTOver the past few decades, theoretical and experimental studies on the connection between elastic wave attributes and the physical properties of a fluid-bearing porous medium have attracted the attention of many scholars in fields of porous medium flow and hydrogeology. It has been previously determined that the transmission of elastic waves in a porous medium containing two immiscible fluids will have an effect on the water retention curve, but it has not been found that the water retention curve will be affected by the frequency of elastic vibration waves or whether the effect on the soil is temporary or permanent. This research is based on a sand box test in which the soil is divided into three layers (a lower, middle, and upper layer). In this case, we discuss different impacts on the water retention curve during the drying process under sound waves (elastic waves) subject to three frequencies (150Hz, 300Hz, and 450Hz), respectively. The change in the water retention curve before and after the effect is then discussed. In addition, how sound waves affect the water retention curve at different depths is also observed. According to the experimental results, we discover that sound waves can cause soil either to expand or to contract. When the soil is induced to expand due to sound waves, it can contract naturally and return to the condition it was in before the influence of the sound waves. On the contrary, when the soil is induced to contract, it is unable to return to its initial condition. Due to the results discussed above, it is suggested that sound waves causing soil to expand have a temporary impact while those causing soil to contract have a permanent impact. In addition, our experimental results show how sound waves affect the water retention curve at different depths. The degree of soil expansion and contraction caused by the sound waves will differ at various soil depths. Nevertheless, the expanding or contracting of soil is only subject to the frequency of sound waves. Key words: Elastic waves, Water retention curve, Sand box test.

Rogue Waves and Lump Solitons of the (3+1)-Dimensional Generalized B-type Kadomtsev-Petviashvili Equation for Water Waves

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Liu, Lei; Chai, Han-Peng; Yuan, Yu-Qiang

2017-12-01

In this paper, the (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev-Petviashvili hierarchy reduction, we obtain the first-order, higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, and 11471050, by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and by the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02

Elastic parabolic equation solutions for oceanic T-wave generation and propagation from deep seismic sources.

PubMed

Frank, Scott D; Collis, Jon M; Odom, Robert I

2015-06-01

Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.

Thermophysical and Mechanical Properties of Granite and Its Effects on Borehole Stability in High Temperature and Three-Dimensional Stress

PubMed Central

Bao-lin, Liu; Hai-yan, Zhu; Chuan-liang, Yan; Zhi-jun, Li; Zhi-qiao, Wang

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200°C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations. PMID:24778592

Thermophysical and mechanical properties of granite and its effects on borehole stability in high temperature and three-dimensional stress.

PubMed

Wang, Yu; Liu, Bao-lin; Zhu, Hai-yan; Yan, Chuan-liang; Li, Zhi-jun; Wang, Zhi-qiao

2014-01-01

When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite's stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200 °C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations.

High-pressure elastic properties of major materials of Earth's mantle from first principles

NASA Astrophysics Data System (ADS)

Karki, Bijaya B.; Stixrude, Lars; Wentzcovitch, Renata M.

2001-11-01

The elasticity of materials is important for our understanding of processes ranging from brittle failure, to flexure, to the propagation of elastic waves. Seismologically revealed structure of the Earth's mantle, including the radial (one-dimensional) profile, lateral heterogeneity, and anisotropy are determined largely by the elasticity of the materials that make up this region. Despite its importance to geophysics, our knowledge of the elasticity of potentially relevant mineral phases at conditions typical of the Earth's mantle is still limited: Measuring the elastic constants at elevated pressure-temperature conditions in the laboratory remains a major challenge. Over the past several years, another approach has been developed based on first-principles quantum mechanical theory. First-principles calculations provide the ideal complement to the laboratory approach because they require no input from experiment; that is, there are no free parameters in the theory. Such calculations have true predictive power and can supply critical information including that which is difficult to measure experimentally. A review of high-pressure theoretical studies of major mantle phases shows a wide diversity of elastic behavior among important tetrahedrally and octahedrally coordinated Mg and Ca silicates and Mg, Ca, Al, and Si oxides. This is particularly apparent in the acoustic anisotropy, which is essential for understanding the relationship between seismically observed anisotropy and mantle flow. The acoustic anisotropy of the phases studied varies from zero to more than 50% and is found to depend on pressure strongly, and in some cases nonmonotonically. For example, the anisotropy in MgO decreases with pressure up to 15 GPa before increasing upon further compression, reaching 50% at a pressure of 130 GPa. Compression also has a strong effect on the elasticity through pressure-induced phase transitions in several systems. For example, the transition from stishovite to CaCl2 structure in silica is accompanied by a discontinuous change in the shear (S) wave velocity that is so large (60%) that it may be observable seismologically. Unifying patterns emerge as well: Eulerian finite strain theory is found to provide a good description of the pressure dependence of the elastic constants for most phases. This is in contrast to an evaluation of Birch's law, which shows that this systematic accounts only roughly for the effect of pressure, composition, and structure on the longitudinal (P) wave velocity. The growing body of theoretical work now allows a detailed comparison with seismological observations. The athermal elastic wave velocities of most important mantle phases are found to be higher than the seismic wave velocities of the mantle by amounts that are consistent with the anticipated effects of temperature and iron content on the P and S wave velocities of the phases studied. An examination of future directions focuses on strategies for extending first-principles studies to more challenging but geophysically relevant situations such as solid solutions, high-temperature conditions, and mineral composites.

Diagnostic performance of shear wave elastography of the breast according to scanning orientation.

PubMed

Kim, Solip; Choi, SeonHyeong; Choi, Yoonjung; Kook, Shin-Ho; Park, Hee Jin; Chung, Eun Chul

2014-10-01

To evaluate the influence of the scanning orientation on diagnostic performance measured by the mean elasticity, maximum elasticity, and fat-to-lesion elasticity ratio on ultrasound-based shear wave elastography in differentiating breast cancers from benign lesions. In this study, a total of 260 breast masses from 235 consecutive patients were observed from March 2012 to November 2012. For each lesion, the mean elasticity value, maximum elasticity value, and fat-to-lesion ratio were measured along two orthogonal directions, and all values were compared with pathologic results. There were 59 malignant and 201 benign lesions. Malignant masses showed higher mean elasticity, maximum elasticity, and fat-to-lesion ratio values than benign lesions (P < .0001). The areas under the receiver operating characteristic curves were as follows: average mean elasticity on both views, 0.870; mean elasticity on the transverse view, 0.866; maximum elasticity on both views, 0.865; maximum elasticity on the transverse view, 0.864; mean elasticity on the longitudinal view, 0.849; fat-to-lesion ratio on both views, 0.849; maximum elasticity on the longitudinal view, 0.845; fat-to-lesion ratio on the transverse view, 0.841; and fat-to-lesion ratio on the longitudinal view, 0.814. Intraclass correlation coefficients for agreement between the scanning directions were as follows: mean elasticity, 0.852; maximum elasticity, 0.842; fat-to-lesion ratio, 0.746, for masses; and mean elasticity, 0.392, for anterior mammary fat. Mean elasticity, maximum elasticity, and fat-to-lesion elasticity ratio values were helpful in differentiating benign and malignant breast masses. The scanning orientation did not significantly affect the diagnostic performance of shear wave elastography for breast masses. © 2014 by the American Institute of Ultrasound in Medicine.

Solitary wave solutions of two-dimensional nonlinear Kadomtsev-Petviashvili dynamic equation in dust-acoustic plasmas

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-09-01

Nonlinear two-dimensional Kadomtsev-Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech-tanh, sinh-cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of Mathematica program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.

Sound waves and flexural mode dynamics in two-dimensional crystals

NASA Astrophysics Data System (ADS)

Michel, K. H.; Scuracchio, P.; Peeters, F. M.

2017-09-01

Starting from a Hamiltonian with anharmonic coupling between in-plane acoustic displacements and out-of-plane (flexural) modes, we derived coupled equations of motion for in-plane displacements correlations and flexural mode density fluctuations. Linear response theory and time-dependent thermal Green's functions techniques are applied in order to obtain different response functions. As external perturbations we allow for stresses and thermal heat sources. The displacement correlations are described by a Dyson equation where the flexural density distribution enters as an additional perturbation. The flexural density distribution satisfies a kinetic equation where the in-plane lattice displacements act as a perturbation. In the hydrodynamic limit this system of coupled equations is at the basis of a unified description of elastic and thermal phenomena, such as isothermal versus adiabatic sound motion and thermal conductivity versus second sound. The general theory is formulated in view of application to graphene, two-dimensional h-BN, and 2H-transition metal dichalcogenides and oxides.

Quantitative shear wave ultrasound elastography: initial experience in solid breast masses

PubMed Central

2010-01-01

Introduction Shear wave elastography is a new method of obtaining quantitative tissue elasticity data during breast ultrasound examinations. The aims of this study were (1) to determine the reproducibility of shear wave elastography (2) to correlate the elasticity values of a series of solid breast masses with histological findings and (3) to compare shear wave elastography with greyscale ultrasound for benign/malignant classification. Methods Using the Aixplorer® ultrasound system (SuperSonic Imagine, Aix en Provence, France), 53 solid breast lesions were identified in 52 consecutive patients. Two orthogonal elastography images were obtained of each lesion. Observers noted the mean elasticity values in regions of interest (ROI) placed over the stiffest areas on the two elastography images and a mean value was calculated for each lesion. A sub-set of 15 patients had two elastography images obtained by an additional operator. Reproducibility of observations was assessed between (1) two observers analysing the same pair of images and (2) findings from two pairs of images of the same lesion taken by two different operators. All lesions were subjected to percutaneous biopsy. Elastography measurements were correlated with histology results. After preliminary experience with 10 patients a mean elasticity cut off value of 50 kilopascals (kPa) was selected for benign/malignant differentiation. Greyscale images were classified according to the American College of Radiology (ACR) Breast Imaging Reporting and Data System (BI-RADS). BI-RADS categories 1-3 were taken as benign while BI-RADS categories 4 and 5 were classified as malignant. Results Twenty-three benign lesions and 30 cancers were diagnosed on histology. Measurement of mean elasticity yielded an intraclass correlation coefficient of 0.99 for two observers assessing the same pairs of elastography images. Analysis of images taken by two independent operators gave an intraclass correlation coefficient of 0.80. Shear wave elastography versus greyscale BI-RADS performance figures were sensitivity: 97% vs 87%, specificity: 83% vs 78%, positive predictive value (PPV): 88% vs 84%, negative predictive value (NPV): 95% vs 82% and accuracy: 91% vs 83% respectively. These differences were not statistically significant. Conclusions Shear wave elastography gives quantitative and reproducible information on solid breast lesions with diagnostic accuracy at least as good as greyscale ultrasound with BI-RADS classification. PMID:21122101

Quantitative shear wave ultrasound elastography: initial experience in solid breast masses.

PubMed

Evans, Andrew; Whelehan, Patsy; Thomson, Kim; McLean, Denis; Brauer, Katrin; Purdie, Colin; Jordan, Lee; Baker, Lee; Thompson, Alastair

2010-01-01

Shear wave elastography is a new method of obtaining quantitative tissue elasticity data during breast ultrasound examinations. The aims of this study were (1) to determine the reproducibility of shear wave elastography (2) to correlate the elasticity values of a series of solid breast masses with histological findings and (3) to compare shear wave elastography with greyscale ultrasound for benign/malignant classification. Using the Aixplorer® ultrasound system (SuperSonic Imagine, Aix en Provence, France), 53 solid breast lesions were identified in 52 consecutive patients. Two orthogonal elastography images were obtained of each lesion. Observers noted the mean elasticity values in regions of interest (ROI) placed over the stiffest areas on the two elastography images and a mean value was calculated for each lesion. A sub-set of 15 patients had two elastography images obtained by an additional operator. Reproducibility of observations was assessed between (1) two observers analysing the same pair of images and (2) findings from two pairs of images of the same lesion taken by two different operators. All lesions were subjected to percutaneous biopsy. Elastography measurements were correlated with histology results. After preliminary experience with 10 patients a mean elasticity cut off value of 50 kilopascals (kPa) was selected for benign/malignant differentiation. Greyscale images were classified according to the American College of Radiology (ACR) Breast Imaging Reporting and Data System (BI-RADS). BI-RADS categories 1-3 were taken as benign while BI-RADS categories 4 and 5 were classified as malignant. Twenty-three benign lesions and 30 cancers were diagnosed on histology. Measurement of mean elasticity yielded an intraclass correlation coefficient of 0.99 for two observers assessing the same pairs of elastography images. Analysis of images taken by two independent operators gave an intraclass correlation coefficient of 0.80. Shear wave elastography versus greyscale BI-RADS performance figures were sensitivity: 97% vs 87%, specificity: 83% vs 78%, positive predictive value (PPV): 88% vs 84%, negative predictive value (NPV): 95% vs 82% and accuracy: 91% vs 83% respectively. These differences were not statistically significant. Shear wave elastography gives quantitative and reproducible information on solid breast lesions with diagnostic accuracy at least as good as greyscale ultrasound with BI-RADS classification.

A combined application of boundary-element and Runge-Kutta methods in three-dimensional elasticity and poroelasticity

NASA Astrophysics Data System (ADS)

Igumnov, Leonid; Ipatov, Aleksandr; Belov, Aleksandr; Petrov, Andrey

2015-09-01

The report presents the development of the time-boundary element methodology and a description of the related software based on a stepped method of numerical inversion of the integral Laplace transform in combination with a family of Runge-Kutta methods for analyzing 3-D mixed initial boundary-value problems of the dynamics of inhomogeneous elastic and poro-elastic bodies. The results of the numerical investigation are presented. The investigation methodology is based on direct-approach boundary integral equations of 3-D isotropic linear theories of elasticity and poroelasticity in Laplace transforms. Poroelastic media are described using Biot models with four and five base functions. With the help of the boundary-element method, solutions in time are obtained, using the stepped method of numerically inverting Laplace transform on the nodes of Runge-Kutta methods. The boundary-element method is used in combination with the collocation method, local element-by-element approximation based on the matched interpolation model. The results of analyzing wave problems of the effect of a non-stationary force on elastic and poroelastic finite bodies, a poroelastic half-space (also with a fictitious boundary) and a layered half-space weakened by a cavity, and a half-space with a trench are presented. Excitation of a slow wave in a poroelastic medium is studied, using the stepped BEM-scheme on the nodes of Runge-Kutta methods.

Real-time 1-D/2-D transient elastography on a standard ultrasound scanner using mechanically induced vibration.

PubMed

Azar, Reza Zahiri; Dickie, Kris; Pelissier, Laurent

2012-10-01

Transient elastography has been well established in the literature as a means of assessing the elasticity of soft tissue. In this technique, tissue elasticity is estimated from the study of the propagation of the transient shear waves induced by an external or internal source of vibration. Previous studies have focused mainly on custom single-element transducers and ultrafast scanners which are not available in a typical clinical setup. In this work, we report the design and implementation of a transient elastography system on a standard ultrasound scanner that enables quantitative assessment of tissue elasticity in real-time. Two new custom imaging modes are introduced that enable the system to image the axial component of the transient shear wave, in response to an externally induced vibration, in both 1-D and 2-D. Elasticity reconstruction algorithms that estimate the tissue elasticity from these transient waves are also presented. Simulation results are provided to show the advantages and limitations of the proposed system. The performance of the system is also validated experimentally using a commercial elasticity phantom.

The role of viscosity estimation for oil-in-gelatin phantom in shear wave based ultrasound elastography.

PubMed

Zhu, Ying; Dong, Changfeng; Yin, Yin; Chen, Xin; Guo, Yanrong; Zheng, Yi; Shen, Yuanyuan; Wang, Tianfu; Zhang, Xinyu; Chen, Siping

2015-02-01

Shear wave based ultrasound elastography utilizes mechanical excitation or acoustic radiation force to induce shear waves in deep tissue. The tissue response is monitored to obtain elasticity information about the tissue. During the past two decades, tissue elasticity has been extensively studied and has been used in clinical disease diagnosis. However, biological soft tissues are viscoelastic in nature. Therefore, they should be simultaneously characterized in terms of elasticity and viscosity. In this study, two shear wave-based elasticity imaging methods, shear wave dispersion ultrasound vibrometry (SDUV) and acoustic radiation force impulsive (ARFI) imaging, were compared. The discrepancy between the measurements obtained by the two methods was analyzed, and the role of viscosity was investigated. To this end, four types of gelatin phantoms containing 0%, 20%, 30% and 40% castor oil were fabricated to mimic different viscosities of soft tissue. For the SDUV method, the shear elasticity μ1 was 3.90 ± 0.27 kPa, 4.49 ± 0.16 kPa, 2.41 ± 0.33 kPa and 1.31 ± 0.09 kPa; and the shear viscosity μ2 was 1.82 ± 0.31 Pa•s, 2.41 ± 0.35 Pa•s, 2.65 ± 0.13 Pa•s and 2.89 ± 0.14 Pa•s for 0%, 20%, 30% and 40% oil, respectively in both cases. For the ARFI measurements, the shear elasticity μ was 7.30 ± 0.20 kPa, 8.20 ± 0.31 kPa, 7.42 ± 0.21 kPa and 5.90 ± 0.36 kPa for 0%, 20%, 30% and 40% oil, respectively. The SDUV results demonstrated that the elasticity first increased from 0% to 20% oil and then decreased for the 30% and 40% oil. The viscosity decreased consistently as the concentration of castor oil increased from 0% to 40%. The elasticity measured by ARFI showed the same trend as that of the SDUV but exceeded the results measured by SDUV. To clearly validate the impact of viscosity on the elasticity estimation, an independent measurement of the elasticity and viscosity by dynamic mechanical analysis (DMA) was conducted on these four types of gelatin phantoms and then compared with SDUV and ARFI results. The shear elasticities obtained by DMA (3.44 ± 0.31 kPa, 4.29 ± 0.13 kPa, 2.05 ± 0.29 kPa and 1.06 ± 0.18 kPa for 0%, 20%, 30% and 40% oil, respectively) were lower than those by SDUV, whereas the shear viscosities obtained by DMA (2.52 ± 0.32 Pa·s, 3.18 ± 0.12 Pa·s, 3.98 ± 0.19 Pa·s and 4.90 ± 0.20 Pa·s for 0%, 20%, 30% and 40% oil, respectively) were greater than those obtained by SDUV. However, the DMA results showed that the trend in the elasticity and viscosity data was the same as that obtained from the SDUV and ARFI. The SDUV results demonstrated that adding castor oil changed the viscoelastic properties of the phantoms and resulted in increased dispersion of the shear waves. Viscosity can provide important and independent information about the inner state of the phantoms, in addition to the elasticity. Because the ARFI method ignores the dispersion of the shear waves, namely viscosity, it may bias the estimation of the true elasticity. This study sheds further light on the significance of the viscosity measurements in shear wave based elasticity imaging methods. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Three-dimensional instability of standing waves

NASA Astrophysics Data System (ADS)

Zhu, Qiang; Liu, Yuming; Yue, Dick K. P.

2003-12-01

We investigate the three-dimensional instability of finite-amplitude standing surface waves under the influence of gravity. The analysis employs the transition matrix (TM) approach and uses a new high-order spectral element (HOSE) method for computation of the nonlinear wave dynamics. HOSE is an extension of the original high-order spectral method (HOS) wherein nonlinear wave wave and wave body interactions are retained up to high order in wave steepness. Instead of global basis functions in HOS, however, HOSE employs spectral elements to allow for complex free-surface geometries and surface-piercing bodies. Exponential convergence of HOS with respect to the total number of spectral modes (for a fixed number of elements) and interaction order is retained in HOSE. In this study, we use TM-HOSE to obtain the stability of general three-dimensional perturbations (on a two-dimensional surface) on two classes of standing waves: plane standing waves in a rectangular tank; and radial/azimuthal standing waves in a circular basin. For plane standing waves, we confirm the known result of two-dimensional side-bandlike instability. In addition, we find a novel three-dimensional instability for base flow of any amplitude. The dominant component of the unstable disturbance is an oblique (standing) wave oriented at an arbitrary angle whose frequency is close to the (nonlinear) frequency of the original standing wave. This finding is confirmed by direct long-time simulations using HOSE which show that the nonlinear evolution leads to classical Fermi Pasta Ulam recurrence. For the circular basin, we find that, beyond a threshold wave steepness, a standing wave (of nonlinear frequency Omega) is unstable to three-dimensional perturbations. The unstable perturbation contains two dominant (standing-wave) components, the sum of whose frequencies is close to 2Omega. From the cases we consider, the critical wave steepness is found to generally decrease/increase with increasing radial/azimuthal mode number of the base standing wave. Finally, we show that the instability we find for both two- and three-dimensional standing waves is a result of third-order (quartet) resonance.

An electrical analogy to Mie scattering

PubMed Central

Caridad, José M.; Connaughton, Stephen; Ott, Christian; Weber, Heiko B.; Krstić, Vojislav

2016-01-01

Mie scattering is an optical phenomenon that appears when electromagnetic waves, in particular light, are elastically scattered at a spherical or cylindrical object. A transfer of this phenomenon onto electron states in ballistic graphene has been proposed theoretically, assuming a well-defined incident wave scattered by a perfectly cylindrical nanometer scaled potential, but experimental fingerprints are lacking. We present an experimental demonstration of an electrical analogue to Mie scattering by using graphene as a conductor, and circular potentials arranged in a square two-dimensional array. The tabletop experiment is carried out under seemingly unfavourable conditions of diffusive transport at room-temperature. Nonetheless, when a canted arrangement of the array with respect to the incident current is chosen, cascaded Mie scattering results robustly in a transverse voltage. Its response on electrostatic gating and variation of potentials convincingly underscores Mie scattering as underlying mechanism. The findings presented here encourage the design of functional electronic metamaterials. PMID:27671003

Three-dimensional shear wave elastography for differentiation of breast lesions: An initial study with quantitative analysis using three orthogonal planes.

PubMed

Wang, Qiao

2018-05-25

To prospectively evaluate the diagnostic performance of three-dimensional (3D) shear wave elastography (SWE) for breast lesions with quantitative stiffness information from transverse, sagittal and coronal planes. Conventional ultrasound (US), two-dimensional (2D)-SWE and 3D-SWE were performed for 122 consecutive patients with 122 breast lesions before biopsy or surgical excision. Maximum elasticity values of Young's modulus (Emax) were recorded on 2D-SWE and three planes of 3D-SWE. Area under the receiver operating characteristic curve (AUC), sensitivity and specificity of US, 2D-SWE and 3D-SWE were evaluated. Two combined sets (i.e., BI-RADS and 2D-SWE; BI-RADS and 3D-SWE) were compared in AUC. Observer consistency was also evaluated. On 3D-SWE, the AUC and sensitivity of sagittal plane were significantly higher than those of transverse and coronal planes (both P < 0.05). Compared with BI-RADS alone, both combined sets had significantly (P < 0.05) higher AUCs and specificities, whereas, the two combined sets showed no significant difference in AUC (P > 0.05). However, the combined set of BI-RADS and sagittal plane of 3D-SWE had significantly higher sensitivity than the combined set of BI-RADS and 2D-SWE. The sagittal plane shows the best diagnostic performance among 3D-SWE. The combination of BI-RADS and 3D-SWE is a useful tool for predicting breast malignant lesions in comparison with BI-RADS alone.

3D Ultrasonic Wave Simulations for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Campbell, Leckey Cara A/; Miler, Corey A.; Hinders, Mark K.

2011-01-01

Structural health monitoring (SHM) for the detection of damage in aerospace materials is an important area of research at NASA. Ultrasonic guided Lamb waves are a promising SHM damage detection technique since the waves can propagate long distances. For complicated flaw geometries experimental signals can be difficult to interpret. High performance computing can now handle full 3-dimensional (3D) simulations of elastic wave propagation in materials. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate ultrasound scattering from flaws in materials. EFIT results have been compared to experimental data and the simulations provide unique insight into details of the wave behavior. This type of insight is useful for developing optimized experimental SHM techniques. 3D EFIT can also be expanded to model wave propagation and scattering in anisotropic composite materials.

The relationship between elastic constants and structure of shock waves in a zinc single crystal

NASA Astrophysics Data System (ADS)

Krivosheina, M. N.; Kobenko, S. V.; Tuch, E. V.

2017-12-01

The paper provides a 3D finite element simulation of shock-loaded anisotropic single crystals on the example of a Zn plate under impact using a mathematical model, which allows for anisotropy in hydrostatic stress and wave velocities in elastic and plastic ranges. The simulation results agree with experimental data, showing the absence of shock wave splitting into an elastic precursor and a plastic wave in Zn single crystals impacted in the [0001] direction. It is assumed that the absence of an elastic precursor under impact loading of a zinc single crystal along the [0001] direction is determined by the anomalously large ratio of the c/a-axes and close values of the propagation velocities of longitudinal and bulk elastic waves. It is shown that an increase in only one elastic constant along the [0001] direction results in shock wave splitting into an elastic precursor and a shock wave of "plastic" compression.

Lamb Wave Assessment of Fatigue and Thermal Damage in Composites

NASA Technical Reports Server (NTRS)

Seale, Michael D.; Smith, Barry T.; Prosser, W. H.

2004-01-01

Among the various techniques available, ultrasonic Lamb waves offer a convenient method of evaluating composite materials. Since the Lamb wave velocity depends on the elastic properties of a structure, an effective tool exists to monitor damage in composites by measuring the velocity of these waves. Lamb wave measurements can propagate over long distances and are sensitive to the desired in-plane elastic properties of the material. This paper describes two studies which monitor fatigue damage and two studies which monitor thermal damage in composites using Lamb waves. In the fatigue studies, the Lamb wave velocity is compared to modulus measurements obtained using strain gage measurements in the first experiment and the velocity is monitored along with the crack density in the second. In the thermal damage studies, one examines samples which were exposed to varying temperatures for a three minute duration and the second includes rapid thermal damage in composites by intense laser beams. In all studies, the Lamb wave velocity is demonstrated to be an excellent method to monitor damage in composites.

Non-collinear interaction of guided elastic waves in an isotropic plate

NASA Astrophysics Data System (ADS)

Ishii, Yosuke; Biwa, Shiro; Adachi, Tadaharu

2018-04-01

The nonlinear wave propagation in a homogeneous and isotropic elastic plate is analyzed theoretically to investigate the non-collinear interaction of plate wave modes. In the presence of two primary plate waves (Rayleigh-Lamb or shear horizontal modes) propagating in arbitrary directions, an explicit expression for the modal amplitude of nonlinearly generated wave fields with the sum or difference frequency of the primary modes is derived by using the perturbation analysis. The modal amplitude is shown to grow in proportion with the propagation distance when the resonance condition is satisfied, i.e., when the wavevector of secondary wave coincides with the sum or difference of those of primary modes. Furthermore, the non-collinear interaction of two symmetric or two antisymmetric modes is shown to produce the secondary wave fields consisting only of the symmetric modes, while a pair of symmetric and antisymmetric primary modes is shown to produce only the antisymmetric modes. The influence of the intersection angle, the primary frequencies, and the mode combinations on the modal amplitude of secondary wave is examined for a low-frequency range where the lowest-order symmetric and antisymmetric Rayleigh-Lamb waves and the lowest-order symmetric shear horizontal wave are the only propagating modes.

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

NASA Astrophysics Data System (ADS)

Kanel, G. I.; Savinykh, A. S.; Garkushin, G. V.; Razorenov, S. V.; Ashitkov, S. I.; Zaretsky, E. B.

2016-11-01

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface.

Manipulating sonic band gaps at will: vibrational density of states in three-dimensional acoustic metamaterial composites

NASA Astrophysics Data System (ADS)

Terao, Takamichi

2018-04-01

Vibrational properties of elastic composites containing a mass-in-mass microstructure embedded in a solid matrix are numerically studied. Using a lattice model, we investigate the vibrational density of states in three-dimensional composite structures where resonant particles are randomly dispersed. By dispersing such particles in the system, a sonic band gap appears. It is confirmed that this band gap can be introduced in a desired frequency regime by changing the parameters of resonant particles and the frequency width of this band gap can be controlled by varying the concentration of the resonant particles to be dispersed. In addition, multiple sonic band gaps can be realized using different species of resonant particles. These results enable us to suggest an alternative method to fabricate devices that can inhibit the propagation of elastic waves with specific frequencies using acoustic metamaterials.

Elastic-wave velocity in marine sediments with gas hydrates: Effective medium modeling

USGS Publications Warehouse

Helgerud, M.B.; Dvorkin, J.; Nur, A.; Sakai, A.; Collett, T.

1999-01-01

We offer a first-principle-based effective medium model for elastic-wave velocity in unconsolidated, high porosity, ocean bottom sediments containing gas hydrate. The dry sediment frame elastic constants depend on porosity, elastic moduli of the solid phase, and effective pressure. Elastic moduli of saturated sediment are calculated from those of the dry frame using Gassmann's equation. To model the effect of gas hydrate on sediment elastic moduli we use two separate assumptions: (a) hydrate modifies the pore fluid elastic properties without affecting the frame; (b) hydrate becomes a component of the solid phase, modifying the elasticity of the frame. The goal of the modeling is to predict the amount of hydrate in sediments from sonic or seismic velocity data. We apply the model to sonic and VSP data from ODP Hole 995 and obtain hydrate concentration estimates from assumption (b) consistent with estimates obtained from resistivity, chlorinity and evolved gas data. Copyright 1999 by the American Geophysical Union.

Development of an intravascular ultrasound elastography based on a dual-element transducer

NASA Astrophysics Data System (ADS)

Shih, Cho-Chiang; Chen, Pei-Yu; Ma, Teng; Zhou, Qifa; Shung, K. Kirk; Huang, Chih-Chung

2018-04-01

The ability to measure the elastic properties of plaques and vessels would be useful in clinical diagnoses, particularly for detecting a vulnerable plaque. This study demonstrates the feasibility of the combination of intravascular ultrasound (IVUS) and acoustic radiation force elasticity imaging for detecting the distribution of stiffness within atherosclerotic arteries ex vivo. A dual-frequency IVUS transducer with two elements was used to induce the propagation of the shear wave (by the 8.5 MHz pushing element) which could be simultaneously monitored by the 31 MHz imaging element. The wave-amplitude image and the wave-velocity image were reconstructed by measuring the peak displacement and wave velocity of shear wave propagation, respectively. System performance was verified using gelatin phantoms. The phantom results demonstrate that the stiffness differences of shear modulus of 1.6 kPa can be distinguished through the wave-amplitude and wave-velocity images. The stiffness distributions of the atherosclerotic aorta from a rabbit were obtained, for which the values of peak displacement and the shear wave velocity were 3.7 ± 1.2 µm and 0.38 ± 0.19 m s-1 for the lipid-rich plaques, and 1.0 ± 0.2 µm and 3.45 ± 0.45 m s-1 for the arterial walls, respectively. These results indicate that IVUS elasticity imaging can be used to distinguish the elastic properties of plaques and vessels.

Three-dimensional separation for interaction of shock waves with turbulent boundary layers

NASA Technical Reports Server (NTRS)

Goldberg, T. J.

1973-01-01

For the interaction of shock waves with turbulent boundary layers, obtained experimental three-dimensional separation results and correlations with earlier two-dimensional and three-dimensional data are presented. It is shown that separation occurs much earlier for turbulent three-dimensional than for two-dimensional flow at hypersonic speeds.

Resonance fluorescence based two- and three-dimensional atom localization

NASA Astrophysics Data System (ADS)

Wahab, Abdul; Rahmatullah; Qamar, Sajid

2016-06-01

Two- and three-dimensional atom localization in a two-level atom-field system via resonance fluorescence is suggested. For the two-dimensional localization, the atom interacts with two orthogonal standing-wave fields, whereas for the three-dimensional atom localization, the atom interacts with three orthogonal standing-wave fields. The effect of the detuning and phase shifts associated with the corresponding standing-wave fields is investigated. A precision enhancement in position measurement of the single atom can be noticed via the control of the detuning and phase shifts.

Macroscopic Lagrangian description of warm plasmas. II Nonlinear wave interactions

NASA Technical Reports Server (NTRS)

Kim, H.; Crawford, F. W.

1983-01-01

A macroscopic Lagrangian is simplified to the adiabatic limit and expanded about equilibrium, to third order in perturbation, for three illustrative cases: one-dimensional compression parallel to the static magnetic field, two-dimensional compression perpendicular to the static magnetic field, and three-dimensional compression. As examples of the averaged-Lagrangian method applied to nonlinear wave interactions, coupling coefficients are derived for interactions between two electron plasma waves and an ion acoustic wave, and between an ordinary wave, an electron plasma wave, and an ion acoustic wave.

Sound transmission through double panel constructions lined with elastic porous materials

NASA Astrophysics Data System (ADS)

Bolton, J. S.; Green, E. R.

1986-07-01

Attention is given to a theory governing one-dimensional wave motion in elastic porous materials which is capable of reproducing experimental transmission measurements for unfaced polyurethane foam layers. Calculations of the transmission loss of fuselage-like foam-lined double panels are presented and it is shown that the foam/panel boundary conditions have a large effect on the panel performance; a hybrid arrangement whereby the foam is bonded directly to one panel and separated from the other by a thin air gap appears to be the most advantageous under practical circumstances. With this configuratiom, the mass-air-mass resonance is minimized and increased low-frequency performance is offered.

Viscoelastic effect on acoustic band gaps in polymer-fluid composites

NASA Astrophysics Data System (ADS)

Merheb, B.; Deymier, P. A.; Muralidharan, K.; Bucay, J.; Jain, M.; Aloshyna-Lesuffleur, M.; Greger, R. W.; Mohanty, S.; Berker, A.

2009-10-01

In this paper, we present a theoretical analysis of the propagation of acoustic waves through elastic and viscoelastic two-dimensional phononic crystal structures. Numerical calculations of transmission spectra are conducted by extending the finite-difference-time-domain method to account for linear viscoelastic materials with time-dependent moduli. We study a phononic crystal constituted of a square array of cylindrical air inclusions in a solid viscoelastic matrix. The elastic properties of the solid are those of a silicone rubber. This system exhibits very wide band gaps in its transmission spectrum that extend to frequencies in the audible range of the spectrum. These gaps are characteristic of fluid matrix/air inclusion systems and result from the very large contrast between the longitudinal and transverse speeds of sound in rubber. By treating the matrix as a viscoelastic medium within the standard linear solid (SLS) model, we demonstrate that viscoelasticity impacts the transmission properties of the rubber/air phononic crystal not only by attenuating the transmitted acoustic waves but also by shifting the passing bands frequencies toward lower values. The ranges of frequencies exhibiting attenuation or frequency shift are determined by the value of the relaxation time in the SLS model. We show that viscoelasticity can be used to decrease the frequency of pass bands (and consequently stop bands) in viscoelastic/air phononic crystals.

Ultrasonic surface measurements at the Porta Nigra, Trier, and the Neptungrotte, Park Sanssouci Potsdam

NASA Astrophysics Data System (ADS)

Meier, Thomas; Auras, Michael; Fehr, Moritz; Köhn, Daniel

2015-04-01

Ultrasonic measurements along profiles at the surface of an object are well suited to characterize non-destructively weathering of natural stone near the surface. Ultrasonic waveforms of surface measurements in the frequency range between 10 kHz and 300 kHz are often dominated by the Rayleigh wave - a surface wave that is mainly sensitive to the velocity and attenuation of S-waves in the upper 0.3 cm to 3 cm. The frequency dependence of the Rayleigh wave velocity may be used to analyze variations of the material properties with depth. Applications of ultrasonic surface measurements are shown for two buildings: the Roman Porta Nigra in Trier from the 3rd century AD and the Neptungrotte at Park Sanssouci in Potsdam designed by von Knobelsdorff in the 18th century. Both buildings belong to the world cultural heritage and restorations are planned for the near future. It is interesting to compare measurements at these two buildings because they show the applicability of ultrasonic surface measurements to different natural stones. The Porta Nigra is made of local sandstones whereas the facades of the Neptungrotte are made of Carrara and Kauffunger marble. 71 and 46 surface measurements have been carried out, respectively. At both buildings, Rayleigh-wave group velocities show huge variations. At the Porta Nigra they vary between ca. 0.4 km/s and 1.8 km/s and at the Neptungrotte between ca. 0.7 km/s and 3.0 km/s pointing to alterations in the Rayleigh- and S-wave velocities of more than 50 % due to weathering. Note that velocities of elastic waves may increase e.g. because of the formation of black crusts like at the Porta Nigra or they may be strongly reduced due to weathering. The accuracy of the ultrasonic surface measurements, its reproducibility, and the influence of varying water saturation are discussed. Options for the analysis of ultrasonic waveforms are presented ranging from dispersion analysis to full waveform inversions for one-dimensional and two-dimensional models of the outermost layers of the object under investigation. Furthermore, results of non-destructive ultrasonic surface measurements are compared to results of destructive investigation techniques.

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

NASA Astrophysics Data System (ADS)

Herbold, Eric B.

New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one-dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero (sonic vacuum), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The acoustic diode effect will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed powder samples in simulated drop-weight tests. The calculations indicate that the dynamic formation of mesoscale force chains increase the strength of the sample. This is also apparent in three-dimensional finite element calculations of drop-weight test simulations using LS-Dyna despite a higher granular bulk coordination number, and an increased mobility of individual grains.

Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Y.; Rizzo, F.J.

1997-08-01

In this paper, the composite boundary integral equation (BIE) formulation is applied to scattering of elastic waves from thin shapes with small but {ital finite} thickness (open cracks or thin voids, thin inclusions, thin-layer interfaces, etc.), which are modeled with {ital two surfaces}. This composite BIE formulation, which is an extension of the Burton and Miller{close_quote}s formulation for acoustic waves, uses a linear combination of the conventional BIE and the hypersingular BIE. For thin shapes, the conventional BIE, as well as the hypersingular BIE, will degenerate (or nearly degenerate) if they are applied {ital individually} on the two surfaces. Themore » composite BIE formulation, however, will not degenerate for such problems, as demonstrated in this paper. Nearly singular and hypersingular integrals, which arise in problems involving thin shapes modeled with two surfaces, are transformed into sums of weakly singular integrals and nonsingular line integrals. Thus, no finer mesh is needed to compute these nearly singular integrals. Numerical examples of elastic waves scattered from penny-shaped cracks with varying openings are presented to demonstrate the effectiveness of the composite BIE formulation. {copyright} {ital 1997 Acoustical Society of America.}« less

Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

NASA Astrophysics Data System (ADS)

Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

2017-11-01

In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

Travelling-wave solutions of a weakly nonlinear two-dimensional higher-order Kadomtsev-Petviashvili dynamical equation for dispersive shallow-water waves

NASA Astrophysics Data System (ADS)

Seadawy, Aly R.

2017-01-01

The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics.

PubMed

Meziane, A; Norris, A N; Shuvalov, A L

2011-10-01

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface. © 2011 Acoustical Society of America

Elastic Wave Propagation Mechanisms in Underwater Acoustic Environments

DTIC Science & Technology

2015-09-30

Elastic wave propagation mechanisms in underwater acoustic environments Scott D. Frank Marist College Department of Mathematics Poughkeepsie...conversion from elastic propagation to acoustic propagation, and intense interface waves on underwater acoustic environments with elastic bottoms...acoustic propagation will be considered as a means to predict the presence of elastic ice layers. APPROACH In a cylindrically symmetric environment

Simplified computational methods for elastic and elastic-plastic fracture problems

NASA Technical Reports Server (NTRS)

Atluri, Satya N.

1992-01-01

An overview is given of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fractures. Topics covered include analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids, with crack faces being subjected to arbitrary tractions; finite element or boundary element alternating methods for two or three dimensional crack problems; a 'direct stiffness' method for stiffened panels with flexible fasteners and with multiple cracks; multiple site damage near a row of fastener holes; an analysis of cracks with bonded repair patches; methods for the generation of weight functions for two and three dimensional crack problems; and domain-integral methods for elastic-plastic or inelastic crack mechanics.

Optical theorem for two-dimensional (2D) scalar monochromatic acoustical beams in cylindrical coordinates.

PubMed

Mitri, F G

2015-09-01

The optical theorem for plane waves is recognized as one of the fundamental theorems in optical, acoustical and quantum wave scattering theory as it relates the extinction cross-section to the forward scattering complex amplitude function. Here, the optical theorem is extended and generalized in a cylindrical coordinates system for the case of 2D beams of arbitrary character as opposed to plane waves of infinite extent. The case of scalar monochromatic acoustical wavefronts is considered, and generalized analytical expressions for the extinction, absorption and scattering cross-sections are derived and extended in the framework of the scalar resonance scattering theory. The analysis reveals the presence of an interference scattering cross-section term describing the interaction between the diffracted Franz waves with the resonance elastic waves. The extended optical theorem in cylindrical coordinates is applicable to any object of arbitrary geometry in 2D located arbitrarily in the beam's path. Related investigations in optics, acoustics and quantum mechanics will benefit from this analysis in the context of wave scattering theory and other phenomena closely connected to it, such as the multiple scattering by a cloud of particles, as well as the resulting radiation force and torque. Copyright © 2015 Elsevier B.V. All rights reserved.

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles.

PubMed

Weinberg, Kerstin; Ortiz, Michael

2009-08-01

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

Reconciling experimental and static-dynamic numerical estimations of seismic anisotropy in Alpine Fault mylonites

NASA Astrophysics Data System (ADS)

Adam, L.; Frehner, M.; Sauer, K. M.; Toy, V.; Guerin-Marthe, S.; Boulton, C. J.

2017-12-01

Reconciling experimental and static-dynamic numerical estimations of seismic anisotropy in Alpine Fault mylonitesLudmila Adam1, Marcel Frehner2, Katrina Sauer3, Virginia Toy3, Simon Guerin-Marthe4, Carolyn Boulton5(1) University of Auckland, New Zealand, (2) ETH Zurich, Switzerland, (3) University of Otago, New Zealand (4) Durham University, Earth Sciences, United Kingdom (5) Victoria University of Wellington, New Zealand Quartzo-feldspathic mylonites and schists are the main contributors to seismic wave anisotropy in the vicinity of the Alpine Fault (New Zealand). We must determine how the physical properties of rocks like these influence elastic wave anisotropy if we want to unravel both the reasons for heterogeneous seismic wave propagation, and interpret deformation processes in fault zones. To study such controls on velocity anisotropy we can: 1) experimentally measure elastic wave anisotropy on cores at in-situ conditions or 2) estimate wave velocities by static (effective medium averaging) or dynamic (finite element) modelling based on EBSD data or photomicrographs. Here we compare all three approaches in study of schist and mylonite samples from the Alpine Fault. Volumetric proportions of intrinsically anisotropic micas in cleavage domains and comparatively isotropic quartz+feldspar in microlithons commonly vary significantly within one sample. Our analysis examines the effects of these phases and their arrangement, and further addresses how heterogeneity influences elastic wave anisotropy. We compare P-wave seismic anisotropy estimates based on millimetres-scale ultrasonic waves under in situ conditions, with simulations that account for micrometre-scale variations in elastic properties of constitutent minerals with the MTEX toolbox and finite-element wave propagation on EBSD images. We observe that the sorts of variations in the distribution of micas and quartz+feldspar within any one of our real core samples can change the elastic wave anisotropy by 10%. In addition, at 60 MPa confining pressure, experimental elastic anisotropy is greater than modelled anisotropy, which could indicate that open microfractures dramatically influence seismic wave anisotropy in the top 3 to 4 km of the crust, or be related to the different resolutions of the two methods.

New Patterns of the Two-Dimensional Rogue Waves: (2+1)-Dimensional Maccari System

NASA Astrophysics Data System (ADS)

Wang, Gai-Hua; Wang, Li-Hong; Rao, Ji-Guang; He, Jing-Song

2017-06-01

The ocean rogue wave is one kind of puzzled destructive phenomenon that has not been understood thoroughly so far. The two-dimensional nature of this wave has inspired the vast endeavors on the recognizing new patterns of the rogue waves based on the dynamical equations with two-spatial variables and one-temporal variable, which is a very crucial step to prevent this disaster event at the earliest stage. Along this issue, we present twelve new patterns of the two-dimensional rogue waves, which are reduced from a rational and explicit formula of the solutions for a (2+1)-dimensional Maccari system. The extreme points (lines) of the first-order lumps (rogue waves) are discussed according to their analytical formulas. For the lower-order rogue waves, we show clearly in formula that parameter b 2 plays a significant role to control these patterns. Supported by the National Natural Science Foundation of China under Grant No. 11671219, the K. C. Wong Magna Fund in Ningbo University, Gai-Hua Wang is also supported by the Scientific Research Foundation of Graduate School of Ningbo University

Characterizing crustal and uppermost mantle anisotropy with a depth-dependent tilted hexagonally symmetric elastic tensor: theory and examples

NASA Astrophysics Data System (ADS)

Feng, L.; Xie, J.; Ritzwoller, M. H.

2017-12-01

Two major types of surface wave anisotropy are commonly observed by seismologists but are only rarely interpreted jointly: apparent radial anisotropy, which is the difference in propagation speed between horizontally and vertically polarized waves inferred from Love and Rayleigh waves, and apparent azimuthal anisotropy, which is the directional dependence of surface wave speeds (usually Rayleigh waves). We describe a method of inversion that interprets simultaneous observations of radial and azimuthal anisotropy under the assumption of a hexagonally symmetric elastic tensor with a tilted symmetry axis defined by dip and strike angles. With a full-waveform numerical solver based on the spectral element method (SEM), we verify the validity of the forward theory used for the inversion. We also present two examples, in the US and Tibet, in which we have successfully applied the tomographic method to demonstrate that the two types of apparent anisotropy can be interpreted jointly as a tilted hexagonally symmetric medium.

Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid

PubMed Central

Sapozhnikov, Oleg A.; Bailey, Michael R.

2013-01-01

A theoretical approach is developed to calculate the radiation force of an arbitrary acoustic beam on an elastic sphere in a liquid or gas medium. First, the incident beam is described as a sum of plane waves by employing conventional angular spectrum decomposition. Then, the classical solution for the scattering of a plane wave from an elastic sphere is applied for each plane-wave component of the incident field. The net scattered field is expressed as a superposition of the scattered fields from all angular spectrum components of the incident beam. With this formulation, the incident and scattered waves are superposed in the far field to derive expressions for components of the radiation stress tensor. These expressions are then integrated over a spherical surface to analytically describe the radiation force on an elastic sphere. Limiting cases for particular types of incident beams are presented and are shown to agree with known results. Finally, the analytical expressions are used to calculate radiation forces associated with two specific focusing transducers. PMID:23363086

Interaction for solitary waves in coasting charged particle beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Shi-Wei; Hong, Xue-Ren; Shi, Yu-Ren

2014-03-15

By using the extended Poincare-Lighthill-Kuo perturbation method, the collision of solitary waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves, which move in opposite directions and can be described by two Korteweg-deVries equation in small-amplitude limit. The collision of two solitary waves is elastic, and after the interaction they preserve their original properties. Then the weak phase shift in traveling direction of collision between two solitary waves is derived explicitly.

On the response of rubbers at high strain rates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Niemczura, Johnathan Greenberg

In this report, we examine the propagation of tensile waves of finite deformation in rubbers through experiments and analysis. Attention is focused on the propagation of one-dimensional dispersive and shock waves in strips of latex and nitrile rubber. Tensile wave propagation experiments were conducted at high strain-rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in the rubber strips. Analysis of the response through the theory of finite waves and quantitative matching between themore » experimental observations and analytical predictions was used to determine an appropriate instantaneous elastic response for the rubbers. This analysis also yields the tensile shock adiabat for rubber. Dispersive waves as well as shock waves are also observed in free-retraction experiments; these are used to quantify hysteretic effects in rubber.« less

The price sensitivity of cigarette consumption in Bangladesh: evidence from the International Tobacco Control (ITC) Bangladesh Wave 1 (2009) and Wave 2 (2010) Surveys.

PubMed

Nargis, Nigar; Ruthbah, Ummul H; Hussain, A K M Ghulam; Fong, Geoffrey T; Huq, Iftekharul; Ashiquzzaman, S M

2014-03-01

In Bangladesh, the average excise tax on cigarettes accounted for just 38% of the average retail price of cigarettes in 2009, and 45% in 2010. Both these rates are well below the WHO recommended share of 70% of the retail price at a minimum. There is thus ample room for raising taxes on cigarettes in Bangladesh. The objective of the present work was therefore to estimate the price elasticity of demand for cigarettes and the effect of tax increases on the consumption of cigarettes and on tax revenue in Bangladesh. Based on data from Wave 1 (2009) and Wave 2 (2010) of the International Tobacco Control Bangladesh Survey, we estimated the overall impact of a price change on cigarette demand using a two-part model. The total price elasticity of cigarettes was measured by the sum of the elasticity of smoking prevalence and the elasticity of average daily consumption conditional on smoking participation. The price elasticity estimates were used in a simulation model to predict changes in cigarette consumption and tax revenue from tax and price increases. The total price elasticity of demand for cigarettes was estimated at -0.49. The elasticity of smoking prevalence accounted for 59% of the total price elasticity. The price elasticity of cigarette consumption is higher for people belonging to lower socioeconomic status. Increases in taxes would result in a significant reduction in cigarette consumption while increasing tax revenue. Raising cigarette prices through increased taxation could lead to a win-win-win situation in Bangladesh: it would reduce cigarette consumption, increase tobacco tax revenue and potentially decrease socioeconomic inequities.

The Price Sensitivity of Cigarette Consumption in Bangladesh: Evidence from the International Tobacco Control (ITC) Bangladesh Wave 1 (2009) and Wave 2 (2010) Surveys

PubMed Central

Nargis, Nigar; Ruthbah, Ummul H.; Hussain, AKM Ghulam; Fong, Geoffrey T.; Huq, Iftekharul; Ashiquzzaman, SM

2014-01-01

Background In Bangladesh, the average excise tax on cigarettes accounted for merely 38% in 2009 and 45% in 2010 of the average retail price of cigarettes. It is well below the WHO recommended share of 70% of the retail price at a minimum. There is thus ample room for raising taxes on cigarettes in Bangladesh. Objective The objective of the paper is to estimate the price elasticity of demand for cigarettes and the effect of tax increases on the consumption of cigarettes and on tax revenue in Bangladesh. Methods Based on data from Wave 1 (2009) and Wave 2 (2010) of the International Tobacco Control Bangladesh Survey, we estimate the overall impact of a price change on cigarette demand using a two-part model. The total price elasticity of cigarettes is measured by the sum of the elasticity of smoking prevalence and the elasticity of average daily consumption conditional on smoking participation. The price elasticity estimates are used in a simulation model to predict changes in cigarette consumption and tax revenue from tax and price increases. Findings The total price elasticity of demand for cigarettes is estimated at −0.49. The elasticity of smoking prevalence accounts for 59% of the total price elasticity. The price elasticity of cigarette consumption is higher for people belonging to lower socio-economic status. Increases in taxes would result in significant reduction in cigarette consumption while tax revenue increases. Conclusion Raising cigarette price through increased taxation can lead to a win-win-win situation in Bangladesh—it will reduce cigarette consumption, increase tobacco tax revenue and potentially decrease socio-economic inequities. PMID:24105828

In Vivo Determination of the Complex Elastic Moduli of Cetacean Head Tissue

DTIC Science & Technology

2009-09-30

remotely generated elastic waves can be detected remotely using a modified version of an ultrasonic Doppler vibration measurement system called NIVMS...developed at Georgia Techiii. Algorithms are being developed to enable the magnitude and phase of vibration to be determined, as well as the range (tissue...depth) along the ultrasonic beam at which the vibration is being measured. By measuring the amplitude and arrival time of the shear wave at two

Molecular Dynamics Simulation Studies of Fracture in Two Dimensions

DTIC Science & Technology

1980-05-01

reversibility of trajectories. The microscopic elastic constants, dispersion relation and phonon spectrum of the system were determined by lattice dynamics. These... linear elasticity theory of a two-dimensional crack embedded in an infinite medium. System con- sists of 436 particles arranged in a tri- angular lattice ...satisfying these demands. In evaluating the mechanical energy of his model, Griffith used a result from linear elasticity theory, namely that for any body

Analysis of the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium

NASA Astrophysics Data System (ADS)

Chai, Han-Peng; Tian, Bo; Zhen, Hui-Ling; Chai, Jun; Guan, Yue-Yang

2017-08-01

Korteweg-de Vries (KdV)-type equations are seen to describe the shallow-water waves, lattice structures and ion-acoustic waves in plasmas. Hereby, we consider an extension of the KdV-type equations called the generalized (2+1)-dimensional Nizhnik-Novikov-Veselov equations with variable coefficients in an inhomogeneous medium. Via the Hirota bilinear method and symbolic computation, we derive the bilinear forms, N-soliton solutions and Bäcklund transformation. Effects of the first- and higher-order dispersion terms are investigated. Soliton evolution and interaction are graphically presented and analyzed: Both the propagation velocity and direction of the soliton change when the dispersion terms are time-dependent; The interactions between/among the solitons are elastic, independent of the forms of the coefficients in the equations.

Rotational elasticity

NASA Astrophysics Data System (ADS)

Vassiliev, Dmitri

2017-04-01

We consider an infinite three-dimensional elastic continuum whose material points experience no displacements, only rotations. This framework is a special case of the Cosserat theory of elasticity. Rotations of material points are described mathematically by attaching to each geometric point an orthonormal basis that gives a field of orthonormal bases called the coframe. As the dynamical variables (unknowns) of our theory, we choose the coframe and a density. We write down the general dynamic variational functional for our rotational theory of elasticity, assuming our material to be physically linear but the kinematic model geometrically nonlinear. Allowing geometric nonlinearity is natural when dealing with rotations because rotations in dimension three are inherently nonlinear (rotations about different axes do not commute) and because there is no reason to exclude from our study large rotations such as full turns. The main result of the talk is an explicit construction of a class of time-dependent solutions that we call plane wave solutions; these are travelling waves of rotations. The existence of such explicit closed-form solutions is a non-trivial fact given that our system of Euler-Lagrange equations is highly nonlinear. We also consider a special case of our rotational theory of elasticity which in the stationary setting (harmonic time dependence and arbitrary dependence on spatial coordinates) turns out to be equivalent to a pair of massless Dirac equations. The talk is based on the paper [1]. [1] C.G.Boehmer, R.J.Downes and D.Vassiliev, Rotational elasticity, Quarterly Journal of Mechanics and Applied Mathematics, 2011, vol. 64, p. 415-439. The paper is a heavily revised version of preprint https://arxiv.org/abs/1008.3833

Laser probe for measuring 2-D wave slope spectra of ocean capillary waves

NASA Technical Reports Server (NTRS)

Palm, C. S.; Anderson, R. C.; Reece, A. M.

1977-01-01

A laser-optical instrument for use in determining the two-dimensional wave-slope spectrum of ocean capillary waves is described. The instrument measures up to a 35-deg tip angle of the surface normal by measuring the position of a refracted laser beam directed vertically upward through a water surface. A telescope, a continuous two-dimensional Schottky barrier photodiode, and a pair of analog dividers render the signals independent of water height and insensitive to laser-beam intensity fluctuations. Calibration is performed entirely in the laboratory before field use. Sample records and wave-slope spectra are shown for one-dimensional wave-tank tests and for two-dimensional ocean tests. These are presented along with comparison spectra for calm and choppy water conditions. A mechanical wave follower was used to adjust the instrument position in the presence of large ocean swell and tides.

Combined distributed and concentrated transducer network for failure indication

NASA Astrophysics Data System (ADS)

Ostachowicz, Wieslaw; Wandowski, Tomasz; Malinowski, Pawel

2010-03-01

In this paper algorithm for discontinuities localisation in thin panels made of aluminium alloy is presented. Mentioned algorithm uses Lamb wave propagation methods for discontinuities localisation. Elastic waves were generated and received using piezoelectric transducers. They were arranged in concentrated arrays distributed on the specimen surface. In this way almost whole specimen could be monitored using this combined distributed-concentrated transducer network. Excited elastic waves propagate and reflect from panel boundaries and discontinuities existing in the panel. Wave reflection were registered through the piezoelectric transducers and used in signal processing algorithm. Proposed processing algorithm consists of two parts: signal filtering and extraction of obstacles location. The first part was used in order to enhance signals by removing noise from them. Second part allowed to extract features connected with wave reflections from discontinuities. Extracted features damage influence maps were a basis to create damage influence maps. Damage maps indicated intensity of elastic wave reflections which corresponds to obstacles coordinates. Described signal processing algorithms were implemented in the MATLAB environment. It should be underlined that in this work results based only on experimental signals were presented.

Computational investigation of feedback loop as a potential source of neuromechanical wave speed discrepancy in swimming animals

NASA Astrophysics Data System (ADS)

Patel, Namu; Patankar, Neelesh A.

2017-11-01

Aquatic locomotion relies on feedback loops to generate the flexural muscle moment needed to attain the reference shape. Experimentalists have consistently reported a difference between the electromyogram (EMG) and curvature wave speeds. The EMG wave speed has been found to correlate with the cross-sectional moment wave. The correlation, however, remains unexplained. Using feedback dependent controller models, we demonstrate two scenarios - one at higher passive elastic stiffness and another at lower passive elastic stiffness of the body. The former case becomes equivalent to the penalty type mathematical model for swimming used in prior literature and it does not reproduce neuromechanical wave speed discrepancy. The latter case at lower elastic stiffness does reproduce the wave speed discrepancy and appears to be biologically most relevant. These findings are applied to develop testable hypotheses about control mechanisms that animals might be using at during low and high Reynolds number swimming. This work is supported by NSF Grants DMS-1547394, CBET-1066575, ACI-1460334, and IOS-1456830. Travel for NP is supported by Institute for Defense Analyses.

Elastic versus acoustic inversion for marine surveys

NASA Astrophysics Data System (ADS)

Mora, Peter; Wu, Zedong

2018-04-01

Full Wavefield Inversion (FWI) is a powerful and elegant approach for seismic imaging that is on the way to becoming the method of choice when processing exploration or global seismic data. In the case of processing marine survey data, one may be tempted to assume acoustic FWI is sufficient given that only pressure waves exist in the water layer. In this paper, we pose the question as to whether or not in theory - at least for a hard water bottom case - it should be possible to resolve the shear modulus or S-wave velocity in a marine setting using large offset data. We therefore conduct numerical experiments with idealized marine data calculated with the elastic wave equation. We study two cases, FWI of data due to a diffractor model, and FWI of data due to a fault model. We find that at least in idealized situation, elastic FWI of hard waterbottom data is capable of resolving between the two Lamé parameters λ and μ. Another numerical experiment with a soft waterbottom layer gives the same result. In contrast, acoustic FWI of the synthetic elastic data results in a single image of the first Lamé parameter λ which contains severe artefacts for diffraction data and noticable artefacts for layer reflection data. Based on these results, it would appear that at least, inversions of large offset marine data should be fully elastic rather than acoustic unless it has been demonstrated that for the specific case in question (offsets, model and water depth, practical issues such as soft sediment attenuation of shear waves or computational time), that an acoustic only inversion provides a reasonably good quality of image comparable to that of an elastic inversion. Further research with real data is required to determine the degree to which practical issues such as shear wave attenuation in soft sediments may affect this result.

Elastic versus acoustic inversion for marine surveys

NASA Astrophysics Data System (ADS)

Mora, Peter; Wu, Zedong

2018-07-01

Full wavefield inversion (FWI) is a powerful and elegant approach for seismic imaging that is on the way to becoming the method of choice when processing exploration or global seismic data. In the case of processing marine survey data, one may be tempted to assume that acoustic FWI is sufficient given that only pressure waves exist in the water layer. In this paper, we pose the question as to whether or not in theory—at least for a hard waterbottom case—it should be possible to resolve the shear modulus or S-wave velocity in a marine setting using large offset data. We, therefore, conduct numerical experiments with idealized marine data calculated with the elastic wave equation. We study two cases, FWI of data due to a diffractor model, and FWI of data due to a fault model. We find that at least in idealized situation, elastic FWI of hard waterbottom data is capable of resolving between the two Lamé parameters λ and μ. Another numerical experiment with a soft waterbottom layer gives the same result. In contrast, acoustic FWI of the synthetic elastic data results in a single image of the first Lamé parameter λ which contains severe artefacts for diffraction data and notable artefacts for layer reflection data. Based on these results, it would appear that at least the inversions of large offset marine data should be fully elastic rather than acoustic, unless it has been demonstrated that for the specific case in question (offsets, model and water depth, practical issues such as soft sediment attenuation of shear waves or computational time), an acoustic-only inversion provides a reasonably good quality of image comparable to that of an elastic inversion. Further research with real data is required to determine the degree to which practical issues such as shear wave attenuation in soft sediments may affect this result.

Shear wave elasticity imaging based on acoustic radiation force and optical detection.

PubMed

Cheng, Yi; Li, Rui; Li, Sinan; Dunsby, Christopher; Eckersley, Robert J; Elson, Daniel S; Tang, Meng-Xing

2012-09-01

Tissue elasticity is closely related to the velocity of shear waves within biologic tissue. Shear waves can be generated by an acoustic radiation force and tracked by, e.g., ultrasound or magnetic resonance imaging (MRI) measurements. This has been shown to be able to noninvasively map tissue elasticity in depth and has great potential in a wide range of clinical applications including cancer and cardiovascular diseases. In this study, a highly sensitive optical measurement technique is proposed as an alternative way to track shear waves generated by the acoustic radiation force. A charge coupled device (CCD) camera was used to capture diffuse photons from tissue mimicking phantoms illuminated by a laser source at 532 nm. CCD images were recorded at different delays after the transmission of an ultrasound burst and were processed to obtain the time of flight for the shear wave. A differential measurement scheme involving generation of shear waves at two different positions was used to improve the accuracy and spatial resolution of the system. The results from measurements on both homogeneous and heterogeneous phantoms were compared with measurements from other instruments and demonstrate the feasibility and accuracy of the technique for imaging and quantifying elasticity. The relative error in estimation of shear wave velocity can be as low as 3.3% with a spatial resolution of 2 mm, and increases to 8.8% with a spatial resolution of 1 mm for the medium stiffness phantom. The system is shown to be highly sensitive and is able to track shear waves propagating over several centimetres given the ultrasound excitation amplitude and the phantom material used in this study. It was also found that the reflection of shear waves from boundaries between regions with different elastic properties can cause significant bias in the estimation of elasticity, which also applies to other shear wave tracking techniques. This bias can be reduced at the expense of reduced spatial resolution. Copyright © 2012 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity

NASA Astrophysics Data System (ADS)

Korepanov, V. V.; Matveenko, V. P.; Fedorov, A. Yu.; Shardakov, I. N.

2013-07-01

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

Green’s functions for a volume source in an elastic half-space

PubMed Central

Zabolotskaya, Evgenia A.; Ilinskii, Yurii A.; Hay, Todd A.; Hamilton, Mark F.

2012-01-01

Green’s functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Green’s function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Green’s function obtained following the first approach. The Green’s function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects. PMID:22423682

A computer program to trace seismic ray distribution in complex two-dimensional geological models

USGS Publications Warehouse

Yacoub, Nazieh K.; Scott, James H.

1970-01-01

A computer program has been developed to trace seismic rays and their amplitudes and energies through complex two-dimensional geological models, for which boundaries between elastic units are defined by a series of digitized X-, Y-coordinate values. Input data for the program includes problem identification, control parameters, model coordinates and elastic parameter for the elastic units. The program evaluates the partitioning of ray amplitude and energy at elastic boundaries, computes the total travel time, total travel distance and other parameters for rays arising at the earth's surface. Instructions are given for punching program control cards and data cards, and for arranging input card decks. An example of printer output for a simple problem is presented. The program is written in FORTRAN IV language. The listing of the program is shown in the Appendix, with an example output from a CDC-6600 computer.

Propagating elastic vibrations dominate thermal conduction in amorphous silicon

NASA Astrophysics Data System (ADS)

Moon, Jaeyun; Latour, Benoit; Minnich, Austin J.

2018-01-01

The thermal atomic vibrations of amorphous solids can be distinguished by whether they propagate as elastic waves or do not propagate due to lack of atomic periodicity. In a -Si, prior works concluded that nonpropagating waves are the dominant contributors to heat transport, with propagating waves being restricted to frequencies less than a few THz and scattered by anharmonicity. Here, we present a lattice and molecular dynamics analysis of vibrations in a -Si that supports a qualitatively different picture in which propagating elastic waves dominate the thermal conduction and are scattered by local fluctuations of elastic modulus rather than anharmonicity. We explicitly demonstrate the propagating nature of waves up to around 10 THz, and further show that pseudoperiodic structures with homogeneous elastic properties exhibit a marked temperature dependence characteristic of anharmonic interactions. Our work suggests that most heat is carried by propagating elastic waves in a -Si and demonstrates that manipulating local elastic modulus variations is a promising route to realize amorphous materials with extreme thermal properties.

Direct Calculation of the Scattering Amplitude Without Partial Wave Decomposition. III; Inclusion of Correlation Effects

NASA Technical Reports Server (NTRS)

Shertzer, Janine; Temkin, Aaron

2007-01-01

In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.

Elastic Bottom Propagation Mechanisms Investigated by Parabolic Equation Methods

DTIC Science & Technology

2014-09-30

channel propagation of oceanic T waves from seismic sources in the presence of intervening seamounts or coral reef barriers is established using elastic PE...environments in the form of scattering at an elastic interface, oceanic T - waves , and Scholte waves . OBJECTIVES To implement explosive and earthquake...oceanic T - waves , which are acoustic waves that result from earthquake or buried explosive sources, and Rayleigh-type waves along the ocean floor, whose

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

Elastic solitons in delaminated bars: splitting leads to fission

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Khusnutdinova, K. R.; Semenova, I. V.

2008-06-01

Recent theoretical and successful experimental studies confirmed existence and demonstrated main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Our current research is devoted to nonlinear wave processes in layered elastic wave guides with inhomogeneities modelling delamination. We present first theoretical and experimental results showing the influence of delamination on the parameters of the longitudinal strain solitary wave.

Room temperature elastic properties of Rh-based alloys studied by surface Brillouin scattering

NASA Astrophysics Data System (ADS)

Sumanya, C.; Mathe, B. A.; Comins, J. D.; Every, A. G.; Osawa, M.; Harada, H.

2014-10-01

Platinum metal group alloys are promising materials for use in a new generation of gas turbine engines owing to their excellent high-temperature properties. In the present work, room temperature elastic properties of single crystals of Rh3Nb and Rh3Zr are investigated. Surface Brillouin scattering spectra for a range of wave vector directions on the (001) surface have been acquired in order to determine the angular variation of the velocities of the Rayleigh and pseudo-surface acoustic waves and that of the longitudinal lateral wave (LLW) threshold within the Lamb shoulder. The elastic stiffness constants C11, C12, and C44 of these cubic crystal specimens have been derived using two approaches: the first involving the least-squares fit of the combined measured wave velocity data to calculated values and the second an analytical approach using the Rayleigh velocities in the [100] and [110] directions and LLW velocity in the [100] direction, and extracting the elastic stiffness constants from the secular equations for these velocities. Results from the two methods are in good agreement and are for Rh3Nb, C11 = 368 ± 3, C12 = 186 ± 5, and C44 = 161 ± 3 in GPa; and for Rh3Zr, C11 = 329 ± 4, C12 = 185 ± 6, and C44 = 145 ± 4 in GPa.

Analytic Simulation of the Elastic Waves Propagation in the Neighborhood of Fluid Filled Wells with Monopole Sources

NASA Astrophysics Data System (ADS)

Ávila-Carrera, R.; Sánchez-Sesma, F. J.; Spurlin, James H.; Valle-Molina, C.; Rodríguez-Castellanos, A.

2014-09-01

An analytic formulation to understand the scattering, diffraction and attenuation of elastic waves at the neighborhood of fluid filled wells is presented. An important, and not widely exploited, technique to carefully investigate the wave propagation in exploration wells is the logging of sonic waveforms. Fundamental decisions and production planning in petroleum reservoirs are made by interpretation of such recordings. Nowadays, geophysicists and engineers face problems related to the acquisition and interpretation under complex conditions associated with conducting open-hole measurements. A crucial problem that directly affects the response of sonic logs is the eccentricity of the measuring tool with respect to the center of the borehole. Even with the employment of centralizers, this simple variation, dramatically changes the physical conditions on the wave propagation around the well. Recent works in the numerical field reported advanced studies in modeling and simulation of acoustic wave propagation around wells, including complex heterogeneities and anisotropy. However, no analytical efforts have been made to formally understand the wireline sonic logging measurements acquired with borehole-eccentered tools. In this paper, the Graf's addition theorem was used to describe monopole sources in terms of solutions of the wave equation. The formulation was developed from the three-dimensional discrete wave-number method in the frequency domain. The cylindrical Bessel functions of the third kind and order zero were re-derived to obtain a simplified set of equations projected into a bi-dimensional plane-space for displacements and stresses. This new and condensed analytic formulation allows the straightforward calculation of all converted modes and their visualization in the time domain via Fourier synthesis. The main aim was to obtain spectral surfaces of transfer functions and synthetic seismograms that might be useful to understand the wave motion produced by the eccentricity of the source and explain in detail the new arising borehole propagation modes. Finally, time histories and amplitude spectra for relevant examples are presented and the validation of time traces using the spectral element method is reported.

Toward soft-tissue elastography using digital holography to monitor surface acoustic waves

NASA Astrophysics Data System (ADS)

Li, Shiguang; Mohan, Karan D.; Sanders, William W.; Oldenburg, Amy L.

2011-11-01

Measuring the elasticity distribution inside the human body is of great interest because elastic abnormalities can serve as indicators of several diseases. We present a method for mapping elasticity inside soft tissues by imaging surface acoustic waves (SAWs) with digital holographic interferometry. With this method, we show that SAWs are consistent with Rayleigh waves, with velocities proportional to the square root of the elastic modulus greater than 2-40 kPa in homogeneous tissue phantoms. In two-layer phantoms, the SAW velocity transitions approximately from that of the lower layer to that of the upper layer as frequency is increased in agreement with the theoretical relationship between SAW dispersion and the depth-dependent stiffness profile. We also observed deformation in the propagation direction of SAWs above a stiff inclusion placed 8 mm below the surface. These findings demonstrate the potential for quantitative digital holography-based elastography of soft tissues as a noninvasive method for disease detection.

Longitudinal shear wave imaging for elasticity mapping using optical coherence elastography

NASA Astrophysics Data System (ADS)

Zhu, Jiang; Miao, Yusi; Qi, Li; Qu, Yueqiao; He, Youmin; Yang, Qiang; Chen, Zhongping

2017-05-01

Shear wave measurements for the determination of tissue elastic properties have been used in clinical diagnosis and soft tissue assessment. A shear wave propagates as a transverse wave where vibration is perpendicular to the wave propagation direction. Previous transverse shear wave measurements could detect the shear modulus in the lateral region of the force; however, they could not provide the elastic information in the axial region of the force. In this study, we report the imaging and quantification of longitudinal shear wave propagation using optical coherence tomography to measure the elastic properties along the force direction. The experimental validation and finite element simulations show that the longitudinal shear wave propagates along the vibration direction as a plane wave in the near field of a planar source. The wave velocity measurement can quantify the shear moduli in a homogeneous phantom and a side-by-side phantom. Combining the transverse shear wave and longitudinal shear wave measurements, this system has great potential to detect the directionally dependent elastic properties in tissues without a change in the force direction.

Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling

PubMed Central

Aoki, Michio

2018-01-01

Conventional manufacturing techniques—moulding, machining and casting—exist to produce three-dimensional (3D) shapes. However, these industrial processes are typically geared for mass production and are not directly applicable to residential settings, where inexpensive and versatile tools are desirable. Moreover, those techniques are, in general, not adequate to process soft elastic materials. Here, we introduce a new concept of forming 3D closed hollow shapes from two-dimensional (2D) elastic ribbons by controlled buckling. We numerically and experimentally characterize how the profile and thickness of the ribbon determine its buckled shape. We find a 2D master profile with which various elliptical 3D shapes can be formed. More complex natural and artificial hollow shapes, such as strawberry, hourglass and wheel, can also be achieved via strategic design and pattern engraving on the ribbons. The nonlinear response of the post-buckling regime is rationalized through finite-element analysis, which shows good quantitative agreement with experiments. This robust fabrication should complement conventional techniques and provide a rich arena for future studies on the mechanics and new applications of elastic hollow structures. PMID:29515894

Forming three-dimensional closed shapes from two-dimensional soft ribbons by controlled buckling

NASA Astrophysics Data System (ADS)

Aoki, Michio; Juang, Jia-Yang

2018-02-01

Conventional manufacturing techniques-moulding, machining and casting-exist to produce three-dimensional (3D) shapes. However, these industrial processes are typically geared for mass production and are not directly applicable to residential settings, where inexpensive and versatile tools are desirable. Moreover, those techniques are, in general, not adequate to process soft elastic materials. Here, we introduce a new concept of forming 3D closed hollow shapes from two-dimensional (2D) elastic ribbons by controlled buckling. We numerically and experimentally characterize how the profile and thickness of the ribbon determine its buckled shape. We find a 2D master profile with which various elliptical 3D shapes can be formed. More complex natural and artificial hollow shapes, such as strawberry, hourglass and wheel, can also be achieved via strategic design and pattern engraving on the ribbons. The nonlinear response of the post-buckling regime is rationalized through finite-element analysis, which shows good quantitative agreement with experiments. This robust fabrication should complement conventional techniques and provide a rich arena for future studies on the mechanics and new applications of elastic hollow structures.

Mixed-mode fracture mechanics parameters of elliptical interface cracks in anisotropic bimaterials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xue, Y.; Qu, J.

1999-07-01

Two-dimensional interface cracks in anisotropic bimaterials have been studied extensively in the literature. However, solutions to three-dimensional interface cracks in anisotropic bimaterials are not available, except for circular (penny-shaped) cracks. In this paper, an elliptical crack on the interface between two anisotropic elastic half-spaces is considered. A formal solution is obtained by using the Stroh method in two dimensional elasticity in conjunction with the Fourier transform method. To illustrate the solution procedure, an elliptical delamination in a cross-ply composite is solved. Numerical results of the stress intensity factors and energy release rate along the crack front are obtained terms ofmore » the interfacial matrix M. It is found that the fields near the crack front are often in mixed mode, due to material anisotropy and the three dimensional nature of the crack front.« less

Guided solitary waves.

PubMed

Miles, J

1980-04-01

Transversely periodic solitary-wave solutions of the Boussinesq equations (which govern wave propagation in a weakly dispersive, weakly nonlinear physical system) are determined. The solutions for negative dispersion (e.g., gravity waves) are singular and therefore physically unacceptable. The solutions for positive dispersion (e.g., capillary waves or magnetosonic waves in a plasma) are physically acceptable except in a limited parametric interval, in which they are complex. The two end points of this interval are associated with (two different) resonant interactions among three basic solitary waves, two of which are two-dimensional complex conjugates and the third of which is one-dimensional and real.

A one dimensional numerical approach for computing the eigenmodes of elastic waves in buried pipelines

NASA Astrophysics Data System (ADS)

Duan, Wenbo; Kirby, Ray; Mudge, Peter; Gan, Tat-Hean

2016-12-01

Ultrasonic guided waves are often used in the detection of defects in oil and gas pipelines. It is common for these pipelines to be buried underground and this may restrict the length of the pipe that can be successfully tested. This is because acoustic energy travelling along the pipe walls may radiate out into the surrounding medium. Accordingly, it is important to develop a better understanding of the way in which elastic waves propagate along the walls of buried pipes, and so in this article a numerical model is developed that is suitable for computing the eigenmodes for uncoated and coated buried pipes. This is achieved by combining a one dimensional eigensolution based on the semi-analytic finite element (SAFE) method, with a perfectly matched layer (PML) for the infinite medium surrounding the pipe. This article also explores an alternative exponential complex coordinate stretching function for the PML in order to improve solution convergence. It is shown for buried pipelines that accurate solutions may be obtained over the entire frequency range typically used in long range ultrasonic testing (LRUT) using a PML layer with a thickness equal to the pipe wall thickness. This delivers a fast and computationally efficient method and it is shown for pipes buried in sand or soil that relevant eigenmodes can be computed and sorted in less than one second using relatively modest computer hardware. The method is also used to find eigenmodes for a buried pipe coated with the viscoelastic material bitumen. It was recently observed in the literature that a viscoelastic coating may effectively isolate particular eigenmodes so that energy does not radiate from these modes into the surrounding [elastic] medium. A similar effect is also observed in this article and it is shown that this occurs even for a relatively thin layer of bitumen, and when the shear impedance of the coating material is larger than that of the surrounding medium.

Influence of nematic range on birefringence, heat capacity and elastic modulus near a nematic-smectic-A phase transition

NASA Astrophysics Data System (ADS)

Beaubois, F.; Claverie, T.; Marcerou, J. P.; Rouillon, J. C.; Nguyen, H. T.; Garland, C. W.; Haga, H.

1997-11-01

The birefringence Δn, the specific heat Cp, and the layer compressional elastic modulus B are reported for two liquid crystals near the nematic (N) to smectic-A (SmA) phase transition. As predicted long ago by MacMillan and de Gennes [P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon, Oxford, 1993)] the coupling of the nematic orientational order parameter to the smectic-A layering order parameter can substantially alter the critical behavior near the N-SmA transition if the nematic range is small and the nematic order parameter susceptibility is large. In this paper, we present a direct experimental comparison of two compounds: 4-octyloxy-4'-cyanobiphenyl (8OCB) with a short nematic range and 4-octyloxybenzoyloxy-4'-cyanotolane (C8tolane) with a very large N range. The temperature variations of the apparent birefringence Δn and the specific heat Cp across the N-SmA phase transition show the definite influence of the proximity of the isotropic phase in the case of 8OCB while the C8tolane behaves as expected for the three-dimensional XY universality class. The elastic modulus B in the SmA phase, measured at several wave vectors by the second-sound resonance technique, was studied with high resolution as a function of temperature on approaching Tc(N-SmA). These elastic data confirm the B leveling off in both cases with an apparent breakdown of hydrodynamics in the case of the C8tolane compound.

Elastic anisotropy of layered rocks: Ultrasonic measurements of plagioclase-biotite-muscovite (sillimanite) gneiss versus texture-based theoretical predictions (effective media modeling)

NASA Astrophysics Data System (ADS)

Ivankina, T. I.; Zel, I. Yu.; Lokajicek, T.; Kern, H.; Lobanov, K. V.; Zharikov, A. V.

2017-08-01

In this paper we present experimental and theoretical studies on a highly anisotropic layered rock sample characterized by alternating layers of biotite and muscovite (retrogressed from sillimanite) and plagioclase and quartz, respectively. We applied two different experimental methods to determine seismic anisotropy at pressures up to 400 MPa: (1) measurement of P- and S-wave phase velocities on a cube in three foliation-related orthogonal directions and (2) measurement of P-wave group velocities on a sphere in 132 directions The combination of the spatial distribution of P-wave velocities on the sphere (converted to phase velocities) with S-wave velocities of three orthogonal structural directions on the cube made it possible to calculate the bulk elastic moduli of the anisotropic rock sample. On the basis of the crystallographic preferred orientations (CPOs) of major minerals obtained by time-of-flight neutron diffraction, effective media modeling was performed using different inclusion methods and averaging procedures. The implementation of a nonlinear approximation of the P-wave velocity-pressure relation was applied to estimate the mineral matrix properties and the orientation distribution of microcracks. Comparison of theoretical calculations of elastic properties of the mineral matrix with those derived from the nonlinear approximation showed discrepancies in elastic moduli and P-wave velocities of about 10%. The observed discrepancies between the effective media modeling and ultrasonic velocity data are a consequence of the inhomogeneous structure of the sample and inability to perform long-wave approximation. Furthermore, small differences between elastic moduli predicted by the different theoretical models, including specific fabric characteristics such as crystallographic texture, grain shape and layering were observed. It is shown that the bulk elastic anisotropy of the sample is basically controlled by the CPO of biotite and muscovite and their volume proportions in the layers dominated by phyllosilicate minerals.

Controlling of the electromagnetic solitary waves generation in the wake of a two-color laser

NASA Astrophysics Data System (ADS)

Pan, K. Q.; Li, S. W.; Guo, L.; Yang, D.; Li, Z. C.; Zheng, C. Y.; Jiang, S. E.; Zhang, B. H.; He, X. T.

2018-05-01

Electromagnetic solitary waves generated by a two-color laser interaction with an underdense plasma are investigated. It is shown that, when the former wave packet of the two-color laser is intense enough, it will excite nonlinear wakefields and generate electron density cavities. The latter wave packets will beat with the nonlinear wakefield and generate both high-frequency and low-frequency components. When the peak density of the cavities exceeds the critical density of the low-frequency component, this part of the electromagnetic field will be trapped to generate electromagnetic solitary waves. By changing the laser and plasma parameters, we can control the wakefield generation, which will also control the generation of the solitary waves. One-dimensional particle-in-cell simulations are performed to prove the controlling of the solitary waves. The simulation results also show that solitary waves generated by higher laser intensities will become moving solitary waves. The two-dimensional particle-in-cell also shows the generation of the solitary waves. In the two-dimensional case, solitary waves are distributed in the transverse directions because of the filamentation instability.

Tunable modulation of refracted lamb wave front facilitated by adaptive elastic metasurfaces

NASA Astrophysics Data System (ADS)

Li, Shilong; Xu, Jiawen; Tang, J.

2018-01-01

This letter reports designs of adaptive metasurfaces capable of modulating incoming wave fronts of elastic waves through electromechanical-tuning of their cells. The proposed elastic metasurfaces are composed of arrayed piezoelectric units with individually connected negative capacitance elements that are online tunable. By adjusting the negative capacitances properly, accurately formed, discontinuous phase profiles along the elastic metasurfaces can be achieved. Subsequently, anomalous refraction with various angles can be realized on the transmitted lowest asymmetric mode Lamb wave. Moreover, designs to facilitate planar focal lenses and source illusion devices can also be accomplished. The proposed flexible and versatile strategy to manipulate elastic waves has potential applications ranging from structural fault detection to vibration/noise control.

Acoustic and elastic waves in metamaterials for underwater applications

NASA Astrophysics Data System (ADS)

Titovich, Alexey S.

Elastic effects in acoustic metamaterials are investigated. Water-based periodic arrays of elastic scatterers, sonic crystals, suffer from low transmission due to the impedance and index mismatch of typical engineering materials with water. A new type of acoustic metamaterial element is proposed that can be tuned to match the acoustic properties of water in the quasi-static regime. The element comprises a hollow elastic cylindrical shell fitted with an optimized internal substructure consisting of a central mass supported by an axisymmetric distribution of elastic stiffeners, which dictate the shell's effective bulk modulus and density. The derived closed form scattering solution for this system shows that the subsonic flexural waves excited in the shell by the attachment of stiffeners are suppressed by including a sufficiently large number of such stiffeners. As an example of refraction-based wave steering, a cylindrical-to-plane wave lens is designed by varying the bulk modulus in the array according to the conformal mapping of a unit circle to a square. Elastic shells provide rich scattering properties, mainly due to their ability to support highly dispersive flexural waves. Analysis of flexural-borne waves on a pair of shells yields an analytical expression for the width of a flexural resonance, which is then used with the theory of multiple scattering to accurately predict the splitting of the resonance frequency. This analysis leads to the discovery of the acoustic Poisson-like effect in a periodic wave medium. This effect redirects an incident acoustic wave by 90° in an otherwise acoustically transparent sonic crystal. An unresponsive "deaf" antisymmetric mode locked to band gap boundaries is unlocked by matching Bragg scattering with a quadrupole flexural resonance of the shell. The dynamic effect causes normal unidirectional wave motion to strongly couple to perpendicular motion, analogous to the quasi-static Poisson effect in solids. The Poisson-like effect is demonstrated using the first flexural resonance of an acrylic shell. This represent a new type of material which cannot be accurately described as an effective acoustic medium. The study concludes with an analysis of a non-zero shear modulus in a pentamode cloak via the two-scale method with the shear modulus as the perturbation parameter.

Pressure induced elastic softening in framework aluminosilicate- albite (NaAlSi 3O 8)

DOE PAGES

Mookherjee, Mainak; Mainprice, David; Maheshwari, Ketan; ...

2016-10-13

Albite (NaAlSi 3O 8) is an aluminosilicate mineral. Its crystal structure consists of 3-D framework of Al and Si tetrahedral units. We have used Density Functional Theory to investigate the high-pressure behavior of the crystal structure and how it affects the elasticity of albite. Our results indicate elastic softening between 6–8 GPa. This is observed in all the individual elastic stiffness components. Our analysis indicates that the softening is due to the response of the three-dimensional tetrahedral framework, in particular by the pressure dependent changes in the tetrahedral tilts. At pressure <6 GPa, the PAW-GGA can be described by amore » Birch-Murnaghan equation of state with V GGA 0 = 687.4Å 3, K GGA 0 = 51.7 GPa, and G GGA 0 = 4.7. The shear modulus and its pressure derivative are K ⊕GGA 0 = 33.7 GPa, and G ⊕GGA 0 = 2.9. At 1 bar, the azimuthal compressional and shear wave anisotropy AV GGA P = 42.8%, and AV GGA S = 50.1%. We also investigate the densification of albite to a mixture of jadeite and quartz. The transformation is likely to cause a discontinuity in density, compressional, and shear wave velocity across the crust and mantle. Furthermore, this could partially account for the Mohorovicic discontinuity in thickened continental crustal regions.« less

Diagnostic performance of quantitative shear wave elastography in the evaluation of solid breast masses: determination of the most discriminatory parameter.

PubMed

Au, Frederick Wing-Fai; Ghai, Sandeep; Moshonov, Hadas; Kahn, Harriette; Brennan, Cressida; Dua, Hemi; Crystal, Pavel

2014-09-01

The purpose of this article is to assess the diagnostic performance of quantitative shear wave elastography in the evaluation of solid breast masses and to determine the most discriminatory parameter. B-mode ultrasound and shear wave elastography were performed before core biopsy of 123 masses in 112 women. The diagnostic performance of ultrasound and quantitative shear wave elastography parameters (mean elasticity, maximum elasticity, and elasticity ratio) were compared. The added effect of shear wave elastography on the performance of ultrasound was determined. The mean elasticity, maximum elasticity, and elasticity ratio were 24.8 kPa, 30.3 kPa, and 1.90, respectively, for 79 benign masses and 130.7 kPa, 154.9 kPa, and 11.52, respectively, for 44 malignant masses (p < 0.001). The optimal cutoff value for each parameter was determined to be 42.5 kPa, 46.7 kPa, and 3.56, respectively. The AUC of each shear wave elastography parameter was higher than that of ultrasound (p < 0.001); the AUC value for the elasticity ratio (0.943) was the highest. By adding shear wave elastography parameters to the evaluation of BI-RADS category 4a masses, about 90% of masses could be downgraded to BI-RADS category 3. The numbers of downgraded masses were 40 of 44 (91%) for mean elasticity, 39 of 44 (89%) for maximum elasticity, and 42 of 44 (95%) for elasticity ratio. The numbers of correctly downgraded masses were 39 of 40 (98%) for mean elasticity, 38 of 39 (97%) for maximum elasticity, and 41 of 42 (98%) for elasticity ratio. There was improvement in the diagnostic performance of ultrasound of mass assessment with shear wave elastography parameters added to BI-RADS category 4a masses compared with ultrasound alone. Combined ultrasound and elasticity ratio had the highest improvement, from 35.44% to 87.34% for specificity, from 45.74% to 80.77% for positive predictive value, and from 57.72% to 90.24% for accuracy (p < 0.0001). The AUC of combined ultrasound and elasticity ratio (0.914) was the highest compared with the other combined parameters. There was a statistically significant difference in the values of the quantitative shear wave elastography parameters of benign and malignant solid breast masses. By adding shear wave elastography parameters to BI-RADS category 4a masses, we found that about 90% of them could be correctly downgraded to BI-RADS category 3, thereby avoiding biopsy. Elasticity ratio (cutoff, 3.56) appeared to be the most discriminatory parameter.

Elastic medium equivalent to Fresnel's double-refraction crystal.

PubMed

Carcione, José M; Helbig, Klaus

2008-10-01

In 1821, Fresnel obtained the wave surface of an optically biaxial crystal, assuming that light waves are vibrations of the ether in which longitudinal vibrations (P waves) do not propagate. An anisotropic elastic medium mathematically analogous to Fresnel's crystal exists. The medium has four elastic constants: a P-wave modulus, associated with a spherical P wave surface, and three elastic constants, c(44), c(55), and c(66), associated with the shear waves, which are mathematically equivalent to the three dielectric permittivity constants epsilon(11), epsilon(22), and epsilon(33) as follows: mu(0)epsilon(11)<==>rho/c(44), mu(0)epsilon(22)<==>rho/c(55), mu(0)epsilon(33)<==>rho/c(66), where mu(0) is the magnetic permeability of vacuum and rho is the mass density. These relations also represent the equivalence between the elastic and electromagnetic wave velocities along the principal axes of the medium. A complete mathematical equivalence can be obtained by setting the P-wave modulus equal to zero, but this yields an unstable elastic medium (the hypothetical ether). To obtain stability the P-wave velocity has to be assumed infinite (incompressibility). Another equivalent Fresnel's wave surface corresponds to a medium with anomalous polarization. This medium is physically unstable even for a nonzero P-wave modulus.

Grain size effect on Lcr elastic wave for surface stress measurement of carbon steel

NASA Astrophysics Data System (ADS)

Liu, Bin; Miao, Wenbing; Dong, Shiyun; He, Peng

2018-04-01

Based on critical refraction longitudinal wave (Lcr wave) acoustoelastic theory, correction method for grain size effect on surface stress measurement was discussed in this paper. Two fixed distance Lcr wave transducers were used to collect Lcr wave, and difference in time of flight between Lcr waves was calculated with cross-correlation coefficient function, at last relationship of Lcr wave acoustoelastic coefficient and grain size was obtained. Results show that as grain size increases, propagation velocity of Lcr wave decreases, one cycle is optimal step length for calculating difference in time of flight between Lcr wave. When stress value is within stress turning point, relationship of difference in time of flight between Lcr wave and stress is basically consistent with Lcr wave acoustoelastic theory, while there is a deviation and it is higher gradually as stress increasing. Inhomogeneous elastic plastic deformation because of inhomogeneous microstructure and average value of surface stress in a fixed distance measured with Lcr wave were considered as the two main reasons for above results. As grain size increasing, Lcr wave acoustoelastic coefficient decreases in the form of power function, then correction method for grain size effect on surface stress measurement was proposed. Finally, theoretical discussion was verified by fracture morphology observation.

A model for seasonal changes in GPS positions and seismic wave speeds due to thermoelastic and hydrologic variations

USGS Publications Warehouse

Tsai, V.C.

2011-01-01

It is known that GPS time series contain a seasonal variation that is not due to tectonic motions, and it has recently been shown that crustal seismic velocities may also vary seasonally. In order to explain these changes, a number of hypotheses have been given, among which thermoelastic and hydrology-induced stresses and strains are leading candidates. Unfortunately, though, since a general framework does not exist for understanding such seasonal variations, it is currently not possible to quickly evaluate the plausibility of these hypotheses. To fill this gap in the literature, I generalize a two-dimensional thermoelastic strain model to provide an analytic solution for the displacements and wave speed changes due to either thermoelastic stresses or hydrologic loading, which consists of poroelastic stresses and purely elastic stresses. The thermoelastic model assumes a periodic surface temperature, and the hydrologic models similarly assume a periodic near-surface water load. Since all three models are two-dimensional and periodic, they are expected to only approximate any realistic scenario; but the models nonetheless provide a quantitative framework for estimating the effects of thermoelastic and hydrologic variations. Quantitative comparison between the models and observations is further complicated by the large uncertainty in some of the relevant parameters. Despite this uncertainty, though, I find that maximum realistic thermoelastic effects are unlikely to explain a large fraction of the observed annual variation in a typical GPS displacement time series or of the observed annual variations in seismic wave speeds in southern California. Hydrologic loading, on the other hand, may be able to explain a larger fraction of both the annual variations in displacements and seismic wave speeds. Neither model is likely to explain all of the seismic wave speed variations inferred from observations. However, more definitive conclusions cannot be made until the model parameters are better constrained. Copyright ?? 2011 by the American Geophysical Union.

Faraday wave lattice as an elastic metamaterial.

PubMed

Domino, L; Tarpin, M; Patinet, S; Eddi, A

2016-05-01

Metamaterials enable the emergence of novel physical properties due to the existence of an underlying subwavelength structure. Here, we use the Faraday instability to shape the fluid-air interface with a regular pattern. This pattern undergoes an oscillating secondary instability and exhibits spontaneous vibrations that are analogous to transverse elastic waves. By locally forcing these waves, we fully characterize their dispersion relation and show that a Faraday pattern presents an effective shear elasticity. We propose a physical mechanism combining surface tension with the Faraday structured interface that quantitatively predicts the elastic wave phase speed, revealing that the liquid interface behaves as an elastic metamaterial.

Elastic wave manipulation by using a phase-controlling meta-layer

NASA Astrophysics Data System (ADS)

Shen, Xiaohui; Sun, Chin-Teh; Barnhart, Miles V.; Huang, Guoliang

2018-03-01

In this work, a high pass meta-layer for elastic waves is proposed. An elastic phase-controlling meta-layer is theoretically realized using parallel and periodically arranged metamaterial sections based on the generalized Snell's law. The elastic meta-layer is composed of periodically repeated supercells, in which the frequency dependent elastic properties of the metamaterial are used to control a phase gradient at the interface between the meta-layer and conventional medium. It is analytically and numerically demonstrated that with a normal incident longitudinal wave, the wave propagation characteristics can be directly manipulated by the periodic length of the meta-layer element at the sub-wavelength scale. It is found that propagation of the incident wave through the interface is dependent on whether the working wavelength is longer or shorter than the periodic length of the meta-layer element. Specifically, a mode conversion of the P-wave to an SV-wave is investigated as the incident wave passes through the meta-layer region. Since the most common and damaging elastic waves in civil and mechanical industries are in the low frequency region, the work in this paper has great potential in the seismic shielding, engine vibration isolation, and other highly dynamic fields.

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

PubMed

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Application of the nudged elastic band method to the point-to-point radio wave ray tracing in IRI modeled ionosphere

NASA Astrophysics Data System (ADS)

Nosikov, I. A.; Klimenko, M. V.; Bessarab, P. F.; Zhbankov, G. A.

2017-07-01

Point-to-point ray tracing is an important problem in many fields of science. While direct variational methods where some trajectory is transformed to an optimal one are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., this approach is not widely known in ionospheric point-to-point ray tracing. We apply the Nudged Elastic Band (NEB) method to a radio wave propagation problem. In the NEB method, a chain of points which gives a discrete representation of the radio wave ray is adjusted iteratively to an optimal configuration satisfying the Fermat's principle, while the endpoints of the trajectory are kept fixed according to the boundary conditions. Transverse displacements define the radio ray trajectory, while springs between the points control their distribution along the ray. The method is applied to a study of point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model taking into account traveling ionospheric disturbances. A 2-dimensional representation of the optical path functional is developed and used to gain insight into the fundamental difference between high and low rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively.

Wave propagation of carbon nanotubes embedded in an elastic medium

NASA Astrophysics Data System (ADS)

Natsuki, Toshiaki; Hayashi, Takuya; Endo, Morinobu

2005-02-01

This paper presents analytical models of wave propagation in single- and double-walled carbon nanotubes, as well as nanotubes embedded in an elastic matrix. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The double-walled nanotubes are coupled together through the van der Waals force between the inner and outer nanotubes. For carbon nanotubes embedded in an elastic matrix, the surrounding elastic medium can be described by a Winkler model. Tube wave propagation of both symmetrical and asymmetrical modes can be analyzed based on the present elastic continuum model. It is found that the asymmetrical wave behavior of single- and double-walled nanotubes is significantly different. The behavior is also different from that in the surrounding elastic medium.

A finite difference analysis of the field present behind an acoustically impenetrable two-layer barrier.

PubMed

Hurrell, Andrew M

2008-06-01

The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface.

Ultrasonic Characterization of the Linear Elastic Properties of Myocardium and Other Anisotropic Soft Tissues

NASA Astrophysics Data System (ADS)

Hoffmeister, Brentley Keith

1995-01-01

This thesis seeks to contribute to a better understanding of the physics of interaction of ultrasonic waves with inhomogeneous and anisotropic media, one example of which is the human heart. The clinical success of echocardiography has generated a considerable interest in the development of ultrasonic techniques to measure the elastic properties of heart tissue. It is hypothesized that the elastic properties of myocardium are influenced by the interstitial content and organization of collagen. Collagen, which is the main component of tendon, interconnects the muscle cells of the heart to form locally unidirectional myofibers. This thesis therefore employs ultrasonic techniques to characterize the linear elastic properties of both heart and tendon. The linear elastic properties of tissues possessing a unidirectional arrangement of fibers may be described in terms of five independent elastic stiffness coefficients. Three of these coefficients were determined for formalin fixed specimens of bovine Achilles tendon and human myocardium by measuring the velocity of longitudinal mode ultrasonic pulses as a function of angle of propagation relative to the fiber axis of the tissue. The remaining two coefficients were determined by measuring the velocity of transverse mode ultrasonic waves through these tissues. To overcome technical difficulties associated with the extremely high attenuation of transverse mode waves at low megahertz frequencies, a novel measurement system was developed based on the sampled continuous wave technique. Results of these measurements were used to assess the influence of interstitial collagen, and to model the mechanical properties of heart wall.

Waveform Tomography of Two-Dimensional Three-Component Seismic Data for HTI Anisotropic Media

NASA Astrophysics Data System (ADS)

Gao, Fengxia; Wang, Yanghua; Wang, Yun

2018-06-01

Reservoirs with vertically aligned fractures can be represented equivalently by horizontal transverse isotropy (HTI) media. But inverting for the anisotropic parameters of HTI media is a challenging inverse problem, because of difficulties inherent in a multiple parameter inversion. In this paper, when we invert for the anisotropic parameters, we consider for the first time the azimuthal rotation of a two-dimensional seismic survey line from the symmetry of HTI. The established wave equations for the HTI media with azimuthal rotation consist of nine elastic coefficients, expressed in terms of five modified Thomsen parameters. The latter are parallel to the Thomsen parameters for describing velocity characteristics of weak vertical transverse isotropy media. We analyze the sensitivity differences of the five modified Thomsen parameters from their radiation patterns, and attempt to balance the magnitude and sensitivity differences between the parameters through normalization and tuning factors which help to update the model parameters properly. We demonstrate an effective inversion strategy by inverting velocity parameters in the first stage and updates the five modified Thomsen parameters simultaneously in the second stage, for generating reliably reconstructed models.

Characterization of Viscoelastic Materials Using Group Shear Wave Speeds.

PubMed

Rouze, Ned C; Deng, Yufeng; Trutna, Courtney A; Palmeri, Mark L; Nightingale, Kathryn R

2018-05-01

Recent investigations of viscoelastic properties of materials have been performed by observing shear wave propagation following localized, impulsive excitations, and Fourier decomposing the shear wave signal to parameterize the frequency-dependent phase velocity using a material model. This paper describes a new method to characterize viscoelastic materials using group shear wave speeds , , and determined from the shear wave displacement, velocity, and acceleration signals, respectively. Materials are modeled using a two-parameter linear attenuation model with phase velocity and dispersion slope at a reference frequency of 200 Hz. Analytically calculated lookup tables are used to determine the two material parameters from pairs of measured group shear wave speeds. Green's function calculations are used to validate the analytic model. Results are reported for measurements in viscoelastic and approximately elastic phantoms and demonstrate good agreement with phase velocities measured using Fourier analysis of the measured shear wave signals. The calculated lookup tables are relatively insensitive to the excitation configuration. While many commercial shear wave elasticity imaging systems report group shear wave speeds as the measures of material stiffness, this paper demonstrates that differences , , and of group speeds are first-order measures of the viscous properties of materials.

Numerical and experimental study on the wave attenuation in bone--FDTD simulation of ultrasound propagation in cancellous bone.

PubMed

Nagatani, Yoshiki; Mizuno, Katsunori; Saeki, Takashi; Matsukawa, Mami; Sakaguchi, Takefumi; Hosoi, Hiroshi

2008-11-01

In cancellous bone, longitudinal waves often separate into fast and slow waves depending on the alignment of bone trabeculae in the propagation path. This interesting phenomenon becomes an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. Since the fast wave mainly propagates in trabeculae, this wave is considered to reflect the structure of trabeculae. For a new diagnosis method using the information of this fast wave, therefore, it is necessary to understand the generation mechanism and propagation behavior precisely. In this study, the generation process of fast wave was examined by numerical simulations using elastic finite-difference time-domain (FDTD) method and experimental measurements. As simulation models, three-dimensional X-ray computer tomography (CT) data of actual bone samples were used. Simulation and experimental results showed that the attenuation of fast wave was always higher in the early state of propagation, and they gradually decreased as the wave propagated in bone. This phenomenon is supposed to come from the complicated propagating paths of fast waves in cancellous bone.

3D Modeling of Ultrasonic Wave Interaction with Disbonds and Weak Bonds

NASA Technical Reports Server (NTRS)

Leckey, C.; Hinders, M.

2011-01-01

Ultrasonic techniques, such as the use of guided waves, can be ideal for finding damage in the plate and pipe-like structures used in aerospace applications. However, the interaction of waves with real flaw types and geometries can lead to experimental signals that are difficult to interpret. 3-dimensional (3D) elastic wave simulations can be a powerful tool in understanding the complicated wave scattering involved in flaw detection and for optimizing experimental techniques. We have developed and implemented parallel 3D elastodynamic finite integration technique (3D EFIT) code to investigate Lamb wave scattering from realistic flaws. This paper discusses simulation results for an aluminum-aluminum diffusion disbond and an aluminum-epoxy disbond and compares results from the disbond case to the common artificial flaw type of a flat-bottom hole. The paper also discusses the potential for extending the 3D EFIT equations to incorporate physics-based weak bond models for simulating wave scattering from weak adhesive bonds.

Evolutions of elastic-plastic shock compression waves in different materials

NASA Astrophysics Data System (ADS)

Kanel, G. I.; Zaretsky, E. B.; Razorenov, S. V.; Savinykh, A. S.; Garkushin, G. V.

2017-01-01

In the paper, we discuss such unexpected features in the wave evolution in solids as a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface, effects of internal friction at shock compression of glasses and some other effects.

The role of gap edge instabilities in setting the depth of planet gaps in protoplanetary discs

NASA Astrophysics Data System (ADS)

Hallam, P. D.; Paardekooper, S.-J.

2017-08-01

It is known that an embedded massive planet will open a gap in a protoplanetary disc via angular momentum exchange with the disc material. The resulting surface density profile of the disc is investigated for one-dimensional and two-dimensional disc models and, in agreement with previous work, it is found that one-dimensional gaps are significantly deeper than their two-dimensional counterparts for the same initial conditions. We find, by applying one-dimensional torque density distributions to two-dimensional discs containing no planet, that the excitement of the Rossby wave instability and the formation of Rossby vortices play a critical role in setting the equilibrium depth of the gap. Being a two-dimensional instability, this is absent from one-dimensional simulations and does not limit the equilibrium gap depth there. We find similar gap depths between two-dimensional gaps formed by torque density distributions, in which the Rossby wave instability is present, and two-dimensional planet gaps, in which no Rossby wave instability is present. This can be understood if the planet gap is maintained at marginal stability, even when there is no obvious Rossby wave instability present. Further investigation shows the final equilibrium gap depth is very sensitive to the form of the applied torque density distribution, and using improved one-dimensional approximations from three-dimensional simulations can go even further towards reducing the discrepancy between one- and two-dimensional models, especially for lower mass planets. This behaviour is found to be consistent across discs with varying parameters.

Stability of a flow down an incline with respect to two-dimensional and three-dimensional disturbances for Newtonian and non-Newtonian fluids.

PubMed

Allouche, M H; Millet, S; Botton, V; Henry, D; Ben Hadid, H; Rousset, F

2015-12-01

Squire's theorem, which states that the two-dimensional instabilities are more dangerous than the three-dimensional instabilities, is revisited here for a flow down an incline, making use of numerical stability analysis and Squire relationships when available. For flows down inclined planes, one of these Squire relationships involves the slopes of the inclines. This means that the Reynolds number associated with a two-dimensional wave can be shown to be smaller than that for an oblique wave, but this oblique wave being obtained for a larger slope. Physically speaking, this prevents the possibility to directly compare the thresholds at a given slope. The goal of the paper is then to reach a conclusion about the predominance or not of two-dimensional instabilities at a given slope, which is of practical interest for industrial or environmental applications. For a Newtonian fluid, it is shown that, for a given slope, oblique wave instabilities are never the dominant instabilities. Both the Squire relationships and the particular variations of the two-dimensional wave critical curve with regard to the inclination angle are involved in the proof of this result. For a generalized Newtonian fluid, a similar result can only be obtained for a reduced stability problem where some term connected to the perturbation of viscosity is neglected. For the general stability problem, however, no Squire relationships can be derived and the numerical stability results show that the thresholds for oblique waves can be smaller than the thresholds for two-dimensional waves at a given slope, particularly for large obliquity angles and strong shear-thinning behaviors. The conclusion is then completely different in that case: the dominant instability for a generalized Newtonian fluid flowing down an inclined plane with a given slope can be three dimensional.

Three-Dimensional Numerical Analyses of Earth Penetration Dynamics

DTIC Science & Technology

1979-01-31

Lagrangian formulation based on the HEMP method and has been adapted and validated for treatment of normal-incidence (axisymmetric) impact and...code, is a detailed analysis of the structural response of the EPW. This analysis is generated using a nonlinear dynamic, elastic- plastic finite element...based on the HEMP scheme. Thus, the code has the same material modeling capabilities and abilities to track large scale motion found in the WAVE-L code

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Non-overlapped P- and S-wave Poynting vectors and their solution by the grid method

NASA Astrophysics Data System (ADS)

Lu, Yongming; Liu, Qiancheng

2018-06-01

The Poynting vector represents the local directional energy flux density of seismic waves in geophysics. It is widely used in elastic reverse time migration to analyze source illumination, suppress low-wavenumber noise, correct for image polarity and extract angle-domain common-image gathers. However, the P- and S-waves are mixed together during wavefield propagation so that the P and S energy fluxes are not clean everywhere, especially at the overlapped points. In this paper, we use a modified elastic-wave equation in which the P and S vector wavefields are naturally separated. Then, we develop an efficient method to evaluate the separable P and S Poynting vectors, respectively, based on the view that the group velocity and phase velocity have the same direction in isotropic elastic media. We furthermore formulate our method using an unstructured mesh-based modeling method named the grid method. Finally, we verify our method using two numerical examples.

Two-Dimensional Computational Model for Wave Rotor Flow Dynamics

NASA Technical Reports Server (NTRS)

Welch, Gerard E.

1996-01-01

A two-dimensional (theta,z) Navier-Stokes solver for multi-port wave rotor flow simulation is described. The finite-volume form of the unsteady thin-layer Navier-Stokes equations are integrated in time on multi-block grids that represent the stationary inlet and outlet ports and the moving rotor passages of the wave rotor. Computed results are compared with three-port wave rotor experimental data. The model is applied to predict the performance of a planned four-port wave rotor experiment. Two-dimensional flow features that reduce machine performance and influence rotor blade and duct wall thermal loads are identified. The performance impact of rounding the inlet port wall, to inhibit separation during passage gradual opening, is assessed.

Temperature maxima in stable two-dimensional shock waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kum, O.; Hoover, W.G.; Hoover, C.G.

1997-07-01

We use molecular dynamics to study the structure of moderately strong shock waves in dense two-dimensional fluids, using Lucy{close_quote}s pair potential. The stationary profiles show relatively broad temperature maxima, for both the longitudinal and the average kinetic temperatures, just as does Mott-Smith{close_quote}s model for strong shock waves in dilute three-dimensional gases. {copyright} {ital 1997} {ital The American Physical Society}

Studies of Sound Absorption by and Transmission Through Layers of Elastic Noise Control Foams: Finite Element Modeling and Effects of Anisotropy

NASA Astrophysics Data System (ADS)

Kang, Yeon June

In this thesis an elastic-absorption finite element model of isotropic elastic porous noise control materials is first presented as a means of investigating the effects of finite dimension and edge constraints on the sound absorption by, and transmission through, layers of acoustical foams. Methods for coupling foam finite elements with conventional acoustic and structural finite elements are also described. The foam finite element model based on the Biot theory allows for the simultaneous propagation of the three types of waves known to exist in an elastic porous material. Various sets of boundary conditions appropriate for modeling open, membrane-sealed and panel-bonded foam surfaces are formulated and described. Good agreement was achieved when finite element predictions were compared with previously established analytical results for the plane wave absorption coefficient and transmission loss in the case of wave propagation both in foam-filled waveguides and through foam-lined double panel structures of infinite lateral extent. The primary effect of the edge constraints of a foam layer was found to be an acoustical stiffening of the foam. Constraining the ends of the facing panels in foam-lined double panel systems was also found to increase the sound transmission loss significantly in the low frequency range. In addition, a theoretical multi-dimensional model for wave propagation in anisotropic elastic porous materials was developed to study the effect of anisotropy on the sound transmission of foam-lined noise control treatments. The predictions of the theoretical anisotropic model have been compared with experimental measurements for the random incidence sound transmission through double panel structure lined with polyimide foam. The predictions were made by using the measured and estimated macroscopic physical parameters of polyimide foam samples which were known to be anisotropic. It has been found that the macroscopic physical parameters in the direction normal to the face of foam layer play the principal role in determining the acoustical behavior of polyimide foam layers, although more satisfactory agreement between experimental measurements and theoretical predictions of transmission loss is obtained when the anisotropic properties are allowed in the model.

Simulating wave-turbulence on thin elastic plates with arbitrary boundary conditions

NASA Astrophysics Data System (ADS)

van Rees, Wim M.; Mahadevan, L.

2016-11-01

The statistical characteristics of interacting waves are described by the theory of wave turbulence, with the study of deep water gravity wave turbulence serving as a paradigmatic physical example. Here we consider the elastic analog of this problem in the context of flexural waves arising from vibrations of a thin elastic plate. Such flexural waves generate the unique sounds of so-called thunder machines used in orchestras - thin metal plates that make a thunder-like sound when forcefully shaken. Wave turbulence in elastic plates is typically investigated numerically using spectral simulations with periodic boundary conditions, which are not very realistic. We will present the results of numerical simulations of the dynamics of thin elastic plates in physical space, with arbitrary shapes, boundary conditions, anisotropy and inhomogeneity, and show first results on wave turbulence beyond the conventionally studied rectangular plates. Finally, motivated by a possible method to measure ice-sheet thicknesses in the open ocean, we will further discuss the behavior of a vibrating plate when floating on an inviscid fluid.

Point force and point electric charge applied to the boundary of three-dimensional anisotropic piezoelectric solid

DOE PAGES

Borovikov, V. A.; Kalinin, S. V.; Khavin, Yu.; ...

2015-08-19

We derive the Green's functions for a three-dimensional semi-infinite fully anisotropic piezoelectric material using the plane wave theory method. The solution gives the complete set of electromechanical fields due to an arbitrarily oriented point force and a point electric charge applied to the boundary of the half-space. Moreover, the solution constitutes generalization of Boussinesq's and Cerruti's problems of elastic isotropy for the anisotropic piezoelectric materials. On the example of piezoceramics PZT-6B, the present results are compared with the previously obtained solution for the special case of transversely isotropic piezoelectric solid subjected to the same boundary condition.

A first-order statistical smoothing approximation for the coherent wave field in random porous random media

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-04-01

An important dissipation mechanism for waves in randomly inhomogeneous poroelastic media is the effect of wave-induced fluid flow. In the framework of Biot's theory of poroelasticity, this mechanism can be understood as scattering from fast into slow compressional waves. To describe this conversion scattering effect in poroelastic random media, the dynamic characteristics of the coherent wavefield using the theory of statistical wave propagation are analyzed. In particular, the method of statistical smoothing is applied to Biot's equations of poroelasticity. Within the accuracy of the first-order statistical smoothing an effective wave number of the coherent field, which accounts for the effect of wave-induced flow, is derived. This wave number is complex and involves an integral over the correlation function of the medium's fluctuations. It is shown that the known one-dimensional (1-D) result can be obtained as a special case of the present 3-D theory. The expression for the effective wave number allows to derive a model for elastic attenuation and dispersion due to wave-induced fluid flow. These wavefield attributes are analyzed in a companion paper. .

Controlling spiral waves and turbulent states in cardiac tissue by traveling wave perturbations

NASA Astrophysics Data System (ADS)

Wang, Peng-Ye; Xie, Ping

2000-03-01

We propose a traveling wave perturbation method to control the spatiotemporal dynamics in cardiac tissue. With a two-variable model we demonstrate that the method can successfully suppress the wave instability (alternans in action potential duration) in the one-dimensional case and convert spiral waves and turbulent states to the normal traveling wave state in the two-dimensional case. An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.

Diffraction of Harmonic Flexural Waves in a Cracked Elastic Plate Carrying Electrical Current

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.; Hasanyan, Davresh; Librescu, iviu; Qin, Zhanming

2005-01-01

The scattering effect of harmonic flexural waves at a through crack in an elastic plate carrying electrical current is investigated. In this context, the Kirchhoffean bending plate theory is extended as to include magnetoelastic interactions. An incident wave giving rise to bending moments symmetric about the longitudinal z-axis of the crack is applied. Fourier transform technique reduces the problem to dual integral equations, which are then cast to a system of two singular integral equations. Efficient numerical computation is implemented to get the bending moment intensity factor for arbitrary frequency of the incident wave and of arbitrary electrical current intensity. The asymptotic behaviour of the bending moment intensity factor is analysed and parametric studies are conducted.

Hydroelastic behaviour of a structure exposed to an underwater explosion

PubMed Central

Colicchio, G.; Greco, M.; Brocchini, M.; Faltinsen, O. M.

2015-01-01

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid–structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151–168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid–structure interaction is examined, highlighting the need of the fluid–structure coupling to capture correctly the possible inception of cavitation. PMID:25512585

Two dimensional kinetic analysis of electrostatic harmonic plasma waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fonseca-Pongutá, E. C.; Ziebell, L. F.; Gaelzer, R.

2016-06-15

Electrostatic harmonic Langmuir waves are virtual modes excited in weakly turbulent plasmas, first observed in early laboratory beam-plasma experiments as well as in rocket-borne active experiments in space. However, their unequivocal presence was confirmed through computer simulated experiments and subsequently theoretically explained. The peculiarity of harmonic Langmuir waves is that while their existence requires nonlinear response, their excitation mechanism and subsequent early time evolution are governed by essentially linear process. One of the unresolved theoretical issues regards the role of nonlinear wave-particle interaction process over longer evolution time period. Another outstanding issue is that existing theories for these modes aremore » limited to one-dimensional space. The present paper carries out two dimensional theoretical analysis of fundamental and (first) harmonic Langmuir waves for the first time. The result shows that harmonic Langmuir wave is essentially governed by (quasi)linear process and that nonlinear wave-particle interaction plays no significant role in the time evolution of the wave spectrum. The numerical solutions of the two-dimensional wave spectra for fundamental and harmonic Langmuir waves are also found to be consistent with those obtained by direct particle-in-cell simulation method reported in the literature.« less

Finite element simulation of ultrasonic waves in corroded reinforced concrete for early-stage corrosion detection

NASA Astrophysics Data System (ADS)

Tang, Qixiang; Yu, Tzuyang

2017-04-01

In reinforced concrete (RC) structures, corrosion of steel rebar introduces internal stress at the interface between rebar and concrete, ultimately leading to debonding and separation between rebar and concrete. Effective early-stage detection of steel rebar corrosion can significantly reduce maintenance costs and enable early-stage repair. In this paper, ultrasonic detection of early-stage steel rebar corrosion inside concrete is numerically investigated using the finite element method (FEM). Commercial FEM software (ABAQUS) was used in all simulation cases. Steel rebar was simplified and modeled by a cylindrical structure. 1MHz ultrasonic elastic waves were generated at the interface between rebar and concrete. Two-dimensional plain strain element was adopted in all FE models. Formation of surface rust in rebar was modeled by changing material properties and expanding element size in order to simulate the rust interface between rebar and concrete and the presence of interfacial stress. Two types of surface rust (corroded regions) were considered. Time domain and frequency domain responses of displacement were studied. From our simulation result, two corrosion indicators, baseline (b) and center frequency (fc) were proposed for detecting and quantifying corrosion.

Two- and Three-Dimensional Probes of Parity in Primordial Gravity Waves.

PubMed

Masui, Kiyoshi Wesley; Pen, Ue-Li; Turok, Neil

2017-06-02

We show that three-dimensional information is critical to discerning the effects of parity violation in the primordial gravity-wave background. If present, helical gravity waves induce parity-violating correlations in the cosmic microwave background (CMB) between parity-odd polarization B modes and parity-even temperature anisotropies (T) or polarization E modes. Unfortunately, EB correlations are much weaker than would be naively expected, which we show is due to an approximate symmetry resulting from the two-dimensional nature of the CMB. The detectability of parity-violating correlations is exacerbated by the fact that the handedness of individual modes cannot be discerned in the two-dimensional CMB, leading to a noise contribution from scalar matter perturbations. In contrast, the tidal imprints of primordial gravity waves fossilized into the large-scale structure of the Universe are a three-dimensional probe of parity violation. Using such fossils the handedness of gravity waves may be determined on a mode-by-mode basis, permitting future surveys to probe helicity at the percent level if the amplitude of primordial gravity waves is near current observational upper limits.

Design of Visco-Elastic Dampers for RC Frame for Site-Specific Earthquake

NASA Astrophysics Data System (ADS)

Kamatchi, P.; Rama Raju, K.; Ravisankar, K.; Iyer, Nagesh R.

2016-12-01

Number of Reinforced Concrete (RC) framed buildings have got damaged at Ahmedabad city, India located at about 240 km away from epicenter during January 2001, 7.6 moment magnitude (Mw) Bhuj earthquake. In the present study, two dimensional nonlinear time history dynamic analyses of a typical 13 storey frame assumed to be located at Ahmedabad is carried out with the rock level and surface level site-specific ground motion for scenario earthquake of Mw 7.6 from Bhuj. Artificial ground motions are generated using extended finite source stochastic model with seismological parameters reported in literature for 2001 Bhuj earthquake. Surface level ground motions are obtained for a typical soil profile of 100 m depth reported in literature through one dimensional equivalent linear wave propagation analyses. From the analyses, failure of frame is observed for surface level ground motions which indicates that, in addition to the in-adequacy of the cross sections and reinforcement of the RC members of the frame chosen, the rich energy content of the surface level ground motion near the fundamental time period of the frame has also contributed for the failure of frame. As a part of retrofitting measure, five Visco-elastic Dampers (VED) in chevron bracing are added to frame. For the frame considered in the present study, provision of VED is found to be effective to mitigate damage for the soil site considered.

A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, Gerald W.; Mahadevan, L.

1987-01-01

A hybrid stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes were implemented in a finite element program for static and dynamic analysis of linear anisotropic two dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid stress approach gives much better results than the displacement method. Preliminary work on extensions of this method to three dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included.

A two-dimensional hybrid method for modeling seismic waves propagation in laterally-varying anisotropic media and its application to central Tibet

NASA Astrophysics Data System (ADS)

Zhao, L.; Wen, L.

2009-12-01

The shear wave splitting measurements provide important information on mantle flow, deformation and mineralogy. They are now routinely made using the method developed by Silver and Chan (1994). More and more dense regional observations also begin to reveal sharp spatial variations of seismic anisotropy which could not be explained by simplified horizontal homogeneous anisotropic structures. To better constrain the mantle anisotropy beneath those regions, we developed a two-dimensional hybrid method for simulating seismic wave propagation in laterally-varying anisotropic media [Zhao et al., 2008]. In this presentation, we apply the method to study anisotropic structures beneath central Tibet by waveform modeling the teleseismic SKS phases recorded in the International Deep Profiling of Tibet and the Himalayas project (INDEPTH) III. Using data from two events that were selected such that the stations and sources can be approximated as a two-dimensional profile, we derived an optimal model for the anisotropic structures of the upper mantle beneath the study region: a 50-70 km thick anisotropic layer with a fast direction trending N95°E beneath the Qiangtang block, a 150 km thick and 60 km wide anisotropic segment with an axis trending N95°E beneath the northernmost Lhasa block, and a ~30 km wide transition zone in between within which the fast direction trends N45°E and the depth extent of anisotropy decreases northward sharply. Synthetic waveform modeling further suggests that an anisotropic model with a horizontal symmetry axis can explain the observations better than that with a dipping symmetry, and a low velocity zone possibly underlies or mixes with the anisotropic structures in the northern portion of the region. The optimal model yields synthetic seismograms that are in good agreement with the observations in both amplitudes and relative arrival times of SKS phases. Synthetic tests also indicate that different elastic constants, source parameters and depth extents of anisotropy adopted in the calculations do not affect the general conclusions, although trade-offs exist between the model parameters. Our modeling results suggest that, if the complex seismic structures in central Tibet are associated with the underthrusting of the Indian lithosphere beneath the Asian lithosphere, the inferred horizontal symmetry of anisotropy was likely generated during the collision because an inherited anisotropy would have a dipping angle of symmetry axis that is parallel to the underthrusting direction. References Silver, P. G., and M. K. Savage (1994), The interpretation of shear-wave splitting parameters in the presence of two anisotropic layers, Geophys. J. Int., 119, 949-963. Zhao L., L.X. Wen, L. Chen, T.Y. Zheng (2008). A two-dimensional hybrid method for modeling seismic wave propagation in anisotropic media, J. Geophys. Res., 113, B12307, doi:10.1029/2008JB005733.

Wave propagation through elastic porous media containing two immiscible fluids

NASA Astrophysics Data System (ADS)

Lo, Wei-Cheng; Sposito, Garrison; Majer, Ernest

2005-02-01

Acoustic wave phenomena in porous media containing multiphase fluids have received considerable attention in recent years because of an increasing scientific awareness of poroelastic behavior in groundwater aquifers. To improve quantitative understanding of these phenomena, a general set of coupled partial differential equations was derived to describe dilatational wave propagation through an elastic porous medium permeated by two immiscible fluids. These equations, from which previous models of dilatational wave propagation can be recovered as special cases, incorporate both inertial coupling and viscous drag in an Eulerian frame of reference. Two important poroelasticity concepts, the linearized increment of fluid content and the closure relation for porosity change, originally defined for an elastic porous medium containing a single fluid, also are generalized for a two-fluid system. To examine the impact of relative fluid saturation and wave excitation frequency (50, 100, 150, and 200 Hz) on free dilatational wave behavior in unconsolidated porous media, numerical simulations of the three possible modes of wave motion were conducted for Columbia fine sandy loam containing either an air-water or oil-water mixture. The results showed that the propagating (P1) mode, which results from in-phase motions of the solid framework and the two pore fluids, moves with a speed equal to the square root of the ratio of an effective bulk modulus to an effective density of the fluid-containing porous medium, regardless of fluid saturation and for both fluid mixtures. The nature of the pore fluids exerts a significant influence on the attenuation of the P1 wave. In the air-water system, attenuation was controlled by material density differences and the relative mobilities of the pore fluids, whereas in the oil-water system an effective kinematic shear viscosity of the pore fluids was the controlling parameter. On the other hand, the speed and attenuation of the two diffusive modes (P2, resulting from out-of-phase motions of the solid framework and the fluids, and P3, the result of capillary pressure fluctuations) were closely associated with an effective dynamic shear viscosity of the pore fluids. The P2 and P3 waves also had the same constant value of the quality factor, and by comparison of our results with previous research on these two dilatational wave modes in sandstones, both were found to be sensitive to the state of consolidation of the porous medium.

Numerical investigation of implementation of air-earth boundary by acoustic-elastic boundary approach

USGS Publications Warehouse

Xu, Y.; Xia, J.; Miller, R.D.

2007-01-01

The need for incorporating the traction-free condition at the air-earth boundary for finite-difference modeling of seismic wave propagation has been discussed widely. A new implementation has been developed for simulating elastic wave propagation in which the free-surface condition is replaced by an explicit acoustic-elastic boundary. Detailed comparisons of seismograms with different implementations for the air-earth boundary were undertaken using the (2,2) (the finite-difference operators are second order in time and space) and the (2,6) (second order in time and sixth order in space) standard staggered-grid (SSG) schemes. Methods used in these comparisons to define the air-earth boundary included the stress image method (SIM), the heterogeneous approach, the scheme of modifying material properties based on transversely isotropic medium approach, the acoustic-elastic boundary approach, and an analytical approach. The method proposed achieves the same or higher accuracy of modeled body waves relative to the SIM. Rayleigh waves calculated using the explicit acoustic-elastic boundary approach differ slightly from those calculated using the SIM. Numerical results indicate that when using the (2,2) SSG scheme for SIM and our new method, a spatial step of 16 points per minimum wavelength is sufficient to achieve 90% accuracy; 32 points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. When using the (2,6) SSG scheme for the two methods, a spatial step of eight points per minimum wavelength achieves 95% accuracy in modeled Rayleigh waves. Our proposed method is physically reasonable and, based on dispersive analysis of simulated seismographs from a layered half-space model, is highly accurate. As a bonus, our proposed method is easy to program and slightly faster than the SIM. ?? 2007 Society of Exploration Geophysicists.

Uncertainty relations for angular momentum eigenstates in two and three spatial dimensions

NASA Astrophysics Data System (ADS)

Bracher, Christian

2011-03-01

I reexamine Heisenberg's uncertainty relation for two- and three-dimensional wave packets with fixed angular momentum quantum numbers m or ℓ. A simple proof shows that the product of the average extent Δr and Δp of a two-dimensional wave packet in position and momentum space is bounded from below by ΔrΔp ≥ℏ(|m|+1). The minimum uncertainty is attained by modified Gaussian wave packets that are special eigenstates of the two-dimensional isotropic harmonic oscillator, which include the ground states of electrons in a uniform magnetic field. Similarly, the inequality ΔrΔp ≥ℏ(ℓ +3/2) holds for three-dimensional wave packets with fixed total angular momentum ℓ and the equality holds for a Gaussian radial profile. I also discuss some applications of these uncertainty relations.

Scattering of antiplane shear waves by a circular cylinder in a traction-free plate

PubMed

Wang; Ying; Li

2000-09-01

Following a well-established formula used by many researchers, the scattering of an anti-plane shear wave by an infinite elastic cylinder of arbitrary relative radius centered in a traction-free two-dimensional isotropic plate has been examined. The plate is divided into three regions by introducing two imaginary planes located symmetrically away from the surface of the cylinder and perpendicular to surfaces of the plate. The wave field is expanded into cylinder wave modes in the central bounded region containing the cylinder, while the fields in the other two outer regions are expanded into plate wave modes. A system of equations determining the expansion coefficients is obtained according to the traction-free boundary conditions on the plate walls and the stress and displacement continuity conditions across the imaginary planes. By taking an appropriate finite number of terms of the infinite expansion series and a few selected points on the two properly chosen virtual planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. The method of how to choose the locations of the imaginary planes and the terms of the expansion series as well as the points on each respective boundary is given in Sec. III in detail. Curves of the reflection and transmission coefficients against the relative radius of the cylinder in welded and slip or cracked interfacial conditions are shown. Analysis on the contrast variations of the reflection and transmission coefficients for a cylinder in bonded and debonded interfacial situations is made. The relative errors estimated by the deviation of the numerical results from the principle of the conservation of energy are found to be less than 2%.

A memory-efficient staining algorithm in 3D seismic modelling and imaging

NASA Astrophysics Data System (ADS)

Jia, Xiaofeng; Yang, Lu

2017-08-01

The staining algorithm has been proven to generate high signal-to-noise ratio (S/N) images in poorly illuminated areas in two-dimensional cases. In the staining algorithm, the stained wavefield relevant to the target area and the regular source wavefield forward propagate synchronously. Cross-correlating these two wavefields with the backward propagated receiver wavefield separately, we obtain two images: the local image of the target area and the conventional reverse time migration (RTM) image. This imaging process costs massive computer memory for wavefield storage, especially in large scale three-dimensional cases. To make the staining algorithm applicable to three-dimensional RTM, we develop a method to implement the staining algorithm in three-dimensional acoustic modelling in a standard staggered grid finite difference (FD) scheme. The implementation is adaptive to the order of spatial accuracy of the FD operator. The method can be applied to elastic, electromagnetic, and other wave equations. Taking the memory requirement into account, we adopt a random boundary condition (RBC) to backward extrapolate the receiver wavefield and reconstruct it by reverse propagation using the final wavefield snapshot only. Meanwhile, we forward simulate the stained wavefield and source wavefield simultaneously using the nearly perfectly matched layer (NPML) boundary condition. Experiments on a complex geologic model indicate that the RBC-NPML collaborative strategy not only minimizes the memory consumption but also guarantees high quality imaging results. We apply the staining algorithm to three-dimensional RTM via the proposed strategy. Numerical results show that our staining algorithm can produce high S/N images in the target areas with other structures effectively muted.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Lax pair, conservation laws and solitons for a (2 + 1)-dimensional fourth-order nonlinear Schrödinger equation governing an α-helical protein

NASA Astrophysics Data System (ADS)

Chai, Jun; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong

2015-11-01

Energy transfer through a (2+1)-dimensional α-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and N-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γ, while the soliton' direction and amplitude do not depend on γ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.

Rayleigh-type waves in nonlocal micropolar solid half-space.

PubMed

Khurana, Aarti; Tomar, S K

2017-01-01

Propagation of Rayleigh type surface waves in nonlocal micropolar elastic solid half-space has been investigated. Two modes of Rayleigh-type waves are found to propagate under certain approximations. Frequency equations of these Rayleigh type modes and their conditions of existence have been derived. These frequency equations are found to be dispersive in character due to the presence of micropolarity and nonlocality parameters in the medium. One of the frequency equations is a counterpart of the classical Rayleigh waves and the other is new and has appeared due to micropolarity of the medium. Phase speeds of these waves are computed numerically for Magnesium crystal and their variation against wavenumber are presented graphically. Comparisons have been made between the phase speeds of Rayleigh type waves through nonlocal micropolar, local micropolar and elastic solid half-spaces. Copyright © 2016 Elsevier B.V. All rights reserved.

Prediction study of structural, elastic and electronic properties of FeMP (M = Ti, Zr, Hf) compounds

NASA Astrophysics Data System (ADS)

Tanto, A.; Chihi, T.; Ghebouli, M. A.; Reffas, M.; Fatmi, M.; Ghebouli, B.

2018-06-01

First principles calculations are applied in the study of FeMP (M = Ti, Zr, Hf) compounds. We investigate the structural, elastic, mechanical and electronic properties by combining first-principles calculations with the CASTEP approach. For ideal polycrystalline FeMP (M = Ti, Zr, Hf) the shear modulus, Young's modulus, Poisson's ratio, elastic anisotropy indexes, Pugh's criterion, elastic wave velocities and Debye temperature are also calculated from the single crystal elastic constants. The shear anisotropic factors and anisotropy are obtained from the single crystal elastic constants. The Debye temperature is calculated from the average elastic wave velocity obtained from shear and bulk modulus as well as the integration of elastic wave velocities in different directions of the single crystal.

Effects of elastic bed on hydrodynamic forces for a submerged sphere in an ocean of finite depth

NASA Astrophysics Data System (ADS)

Mohapatra, Smrutiranjan

2017-08-01

In this paper, we consider a hydroelastic model to examine the radiation of waves by a submerged sphere for both heave and sway motions in a single-layer fluid flowing over an infinitely extended elastic bottom surface in an ocean of finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The effect of the presence of surface tension at the free-surface is neglected. In such situation, there exist two modes of time-harmonic waves: the one with a lower wavenumber (surface mode) propagates along the free-surface and the other with higher wavenumber (flexural mode) propagates along the elastic bottom surface. Based on the small amplitude wave theory and by using the multipole expansion method, we find the particular solution for the problem of wave radiation by a submerged sphere of finite depth. Furthermore, this method eliminates the need to use large and cumbersome numerical packages for the solution of such problem and leads to an infinite system of linear algebraic equations which are easily solved numerically by any standard technique. The added-mass and damping coefficients for both heave and sway motions are derived and plotted for different submersion depths of the sphere and flexural rigidity of the elastic bottom surface. It is observed that, whenever the sphere nearer to the elastic bed, the added-mass move toward to a constant value of 1, which is approximately twice of the value of added-mass of a moving sphere in a single-layer fluid flowing over a rigid and flat bottom surface.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swinteck, N., E-mail: swinteck@email.arizona.edu; Matsuo, S.; Runge, K.

Recent progress in electronic and electromagnetic topological insulators has led to the demonstration of one way propagation of electron and photon edge states and the possibility of immunity to backscattering by edge defects. Unfortunately, such topologically protected propagation of waves in the bulk of a material has not been observed. We show, in the case of sound/elastic waves, that bulk waves with unidirectional backscattering-immune topological states can be observed in a time-dependent elastic superlattice. The superlattice is realized via spatial and temporal modulation of the stiffness of an elastic material. Bulk elastic waves in this superlattice are supported by amore » manifold in momentum space with the topology of a single twist Möbius strip. Our results demonstrate the possibility of attaining one way transport and immunity to scattering of bulk elastic waves.« less

Two-dimensional auto-correlation analysis and Fourier-transform analysis of second-harmonic-generation image for quantitative analysis of collagen fiber in human facial skin

NASA Astrophysics Data System (ADS)

Ogura, Yuki; Tanaka, Yuji; Hase, Eiji; Yamashita, Toyonobu; Yasui, Takeshi

2018-02-01

We compare two-dimensional auto-correlation (2D-AC) analysis and two-dimensional Fourier transform (2D-FT) for evaluation of age-dependent structural change of facial dermal collagen fibers caused by intrinsic aging and extrinsic photo-aging. The age-dependent structural change of collagen fibers for female subjects' cheek skin in their 20s, 40s, and 60s were more noticeably reflected in 2D-AC analysis than in 2D-FT analysis. Furthermore, 2D-AC analysis indicated significantly higher correlation with the skin elasticity measured by Cutometer® than 2D-AC analysis. 2D-AC analysis of SHG image has a high potential for quantitative evaluation of not only age-dependent structural change of collagen fibers but also skin elasticity.

Shallow near-fault material self organizes so it is just nonlinear in typical strong shaking

NASA Astrophysics Data System (ADS)

Sleep, N. H.

2011-12-01

Cracking within shallow compliant fault zones self-organizes so that strong dynamic stresses marginally exceed the elastic limit. To the first order, the compliant material experiences strain boundary conditions imposed by underlying stiffer rock. A major strike-slip fault yields simple dimensional relations. The near-field velocity pulse is essentially a Love wave. The dynamic strain is the ratio of the measured particle velocity over the deep S-wave velocity. The shallow dynamic stress is this quantity times the local shear modulus. I obtain the equilibrium shear modulus by starting a sequence of earthquakes with intact stiff rock surrounding the shallow fault zone. The imposed dynamic strain in stiff rock causes Coulomb failure and leaves cracks in it wake. Cracked rock is more compliant than the original intact rock. Each subsequent event causes more cracking until the rock becomes compliant enough that it just reaches its elastic limit. Further events maintain the material at the shear modulus where it just fails. Analogously, shallow damaged regolith forms with its shear modulus and S-wave velocity increasing with depth so it just reaches failure during typical strong shaking. The general conclusion is that shallow rocks in seismically active areas just become nonlinear during typical shaking. This process causes transient changes in S-wave velocity, but not strong nonlinear attenuation of seismic waves. Wave amplitudes significantly larger than typical ones would strongly attenuate and strongly damage the rock. The equilibrium shear modulus and S-wave velocity depend only modestly on the effective coefficient of internal friction.

Fracture and damage localization in volcanic edifice rocks from El Hierro, Stromboli and Tenerife.

PubMed

Harnett, Claire E; Benson, Philip M; Rowley, Pete; Fazio, Marco

2018-01-31

We present elastic wave velocity and strength data from a suite of three volcanic rocks taken from the volcanic edifices of El Hierro and Tenerife (Canary Islands, Spain), and Stromboli (Aeolian Islands, Italy). These rocks span a range of porosity and are taken from volcanoes that suffer from edifice instability. We measure elastic wave velocities at known incident angles to the generated through-going fault as a function of imposed strain, and examine the effect of the damage zone on P-wave velocity. Such data are important as field measurements of elastic wave tomography are key tools for understanding volcanic regions, yet hidden fractures are likely to have a significant effect on elastic wave velocity. We then use elastic wave velocity evolution to calculate concomitant crack density evolution which ranges from 0 to 0.17: highest values were correlated to the damage zone in rocks with the highest initial porosity.

Energy in elastic fiber embedded in elastic matrix containing incident SH wave

NASA Technical Reports Server (NTRS)

Williams, James H., Jr.; Nagem, Raymond J.

1989-01-01

A single elastic fiber embedded in an infinite elastic matrix is considered. An incident plane SH wave is assumed in the infinite matrix, and an expression is derived for the total energy in the fiber due to the incident SH wave. A nondimensional form of the fiber energy is plotted as a function of the nondimensional wavenumber of the SH wave. It is shown that the fiber energy attains maximum values at specific values of the wavenumber of the incident wave. The results obtained here are interpreted in the context of phenomena observed in acousto-ultrasonic experiments on fiber reinforced composite materials.

Unifying model for random matrix theory in arbitrary space dimensions

NASA Astrophysics Data System (ADS)

Cicuta, Giovanni M.; Krausser, Johannes; Milkus, Rico; Zaccone, Alessio

2018-03-01

A sparse random block matrix model suggested by the Hessian matrix used in the study of elastic vibrational modes of amorphous solids is presented and analyzed. By evaluating some moments, benchmarked against numerics, differences in the eigenvalue spectrum of this model in different limits of space dimension d , and for arbitrary values of the lattice coordination number Z , are shown and discussed. As a function of these two parameters (and their ratio Z /d ), the most studied models in random matrix theory (Erdos-Renyi graphs, effective medium, and replicas) can be reproduced in the various limits of block dimensionality d . Remarkably, the Marchenko-Pastur spectral density (which is recovered by replica calculations for the Laplacian matrix) is reproduced exactly in the limit of infinite size of the blocks, or d →∞ , which clarifies the physical meaning of space dimension in these models. We feel that the approximate results for d =3 provided by our method may have many potential applications in the future, from the vibrational spectrum of glasses and elastic networks to wave localization, disordered conductors, random resistor networks, and random walks.

On Flexible Tubes Conveying Fluid: Geometric Nonlinear Theory, Stability and Dynamics

NASA Astrophysics Data System (ADS)

Gay-Balmaz, François; Putkaradze, Vakhtang

2015-08-01

We derive a fully three-dimensional, geometrically exact theory for flexible tubes conveying fluid. The theory also incorporates the change of the cross section available to the fluid motion during the dynamics. Our approach is based on the symmetry-reduced, exact geometric description for elastic rods, coupled with the fluid transport and subject to the volume conservation constraint for the fluid. We first derive the equations of motion directly, by using an Euler-Poincaré variational principle. We then justify this derivation with a more general theory elucidating the interesting mathematical concepts appearing in this problem, such as partial left (elastic) and right (fluid) invariance of the system, with the added holonomic constraint (volume). We analyze the fully nonlinear behavior of the model when the axis of the tube remains straight. We then proceed to the linear stability analysis and show that our theory introduces important corrections to previously derived results, both in the consistency at all wavelength and in the effects arising from the dynamical change of the cross section. Finally, we derive and analyze several analytical, fully nonlinear solutions of traveling wave type in two dimensions.

Changes in Ultrasonic Velocity from Fluid Substitution, Calculated with Laboratory Methods, Digital Rock Physics, and Biot Theory

NASA Astrophysics Data System (ADS)

Goldfarb, E. J.; Ikeda, K.; Tisato, N.

2017-12-01

Seismic and ultrasonic velocities of rocks are function of several variables including fluid saturation and type. Understanding the effect of each variable on elastic waves can be valuable when using seismic methods for subsurface modeling. Fluid type and saturation are of specific interest to volcanology, water, and hydrocarbon exploration. Laboratory testing is often employed to understand the effects of fluids on elastic waves. However, laboratory testing is expensive and time consuming. It normally requires cutting rare samples into regular shapes. Fluid injection can also destroy specimens as removing the fluid after testing can prove difficult. Another option is theoretical modeling, which can be used to predict the effect of fluids on elastic properties, but it is often inaccurate. Alternatively, digital rock physics (DRP) can be used to investigate the effect of fluid substitution. DRP has the benefit of being non invasive, as it does not require regular sample shapes or fluid injection. Here, we compare the three methods for dry and saturated Berea sandstone to test the reliability of DRP. First, ultrasonic velocities were obtained from laboratory testing. Second, for comparison, we used a purely theoretical approach - i.e., Hashin-Shtrikman and Biot theory - to estimate the wave speeds at dry and wet conditions. Third, we used DRP. The dry sample was scanned with micro Computed Tomography (µCT), and a three dimensional (3D) array was recorded. We employed a segmentation-less method to convert each 3D array value to density, porosity, elastic moduli, and wave speeds. Wave propagation was simulated numerically at similar frequency as the laboratory. To simulate fluid substitution, we numerically substituted air values for water and repeated the simulation. The results from DRP yielded similar velocities to the laboratory, and accurately predicted the velocity change from fluid substitution. Theoretical modeling could not accurately predict velocity, and under-predicted the velocity change from fluid substitution. The mathematical approach proved to be a poor comparison for the laboratory measurement. DRP proved to be effective, and could be used in future with drill cuttings, perhaps to limit the use of expensive cores. DRP could also limit the requirement for physically testing fluid substitution.

Effective modeling and reverse-time migration for novel pure acoustic wave in arbitrary orthorhombic anisotropic media

NASA Astrophysics Data System (ADS)

Xu, Shigang; Liu, Yang

2018-03-01

The conventional pseudo-acoustic wave equations (PWEs) in arbitrary orthorhombic anisotropic (OA) media usually have coupled P- and SV-wave modes. These coupled equations may introduce strong SV-wave artifacts and numerical instabilities in P-wave simulation results and reverse-time migration (RTM) profiles. However, pure acoustic wave equations (PAWEs) completely decouple the P-wave component from the full elastic wavefield and naturally solve all the aforementioned problems. In this article, we present a novel PAWE in arbitrary OA media and compare it with the conventional coupled PWEs. Through decomposing the solution of the corresponding eigenvalue equation for the original PWE into an ellipsoidal differential operator (EDO) and an ellipsoidal scalar operator (ESO), the new PAWE in time-space domain is constructed by applying the combination of these two solvable operators and can effectively describe P-wave features in arbitrary OA media. Furthermore, we adopt the optimal finite-difference method (FDM) to solve the newly derived PAWE. In addition, the three-dimensional (3D) hybrid absorbing boundary condition (HABC) with some reasonable modifications is developed for reducing artificial edge reflections in anisotropic media. To improve computational efficiency in 3D case, we adopt graphic processing unit (GPU) with Compute Unified Device Architecture (CUDA) instead of traditional central processing unit (CPU) architecture. Several numerical experiments for arbitrary OA models confirm that the proposed schemes can produce pure, stable and accurate P-wave modeling results and RTM images with higher computational efficiency. Moreover, the 3D numerical simulations can provide us with a comprehensive and real description of wave propagation.

Free vibration analysis of a cracked shear deformable beam on a two-parameter elastic foundation using a lattice spring model

NASA Astrophysics Data System (ADS)

Attar, M.; Karrech, A.; Regenauer-Lieb, K.

2014-05-01

The free vibration of a shear deformable beam with multiple open edge cracks is studied using a lattice spring model (LSM). The beam is supported by a so-called two-parameter elastic foundation, where normal and shear foundation stiffnesses are considered. Through application of Timoshenko beam theory, the effects of transverse shear deformation and rotary inertia are taken into account. In the LSM, the beam is discretised into a one-dimensional assembly of segments interacting via rotational and shear springs. These springs represent the flexural and shear stiffnesses of the beam. The supporting action of the elastic foundation is described also by means of normal and shear springs acting on the centres of the segments. The relationship between stiffnesses of the springs and the elastic properties of the one-dimensional structure are identified by comparing the homogenised equations of motion of the discrete system and Timoshenko beam theory.

Two-dimensional dissipative rogue waves due to time-delayed feedback in cavity nonlinear optics.

PubMed

Tlidi, Mustapha; Panajotov, Krassimir

2017-01-01

We demonstrate a way to generate two-dimensional rogue waves in two types of broad area nonlinear optical systems subject to time-delayed feedback: in the generic Lugiato-Lefever model and in the model of a broad-area surface-emitting laser with saturable absorber. The delayed feedback is found to induce a spontaneous formation of rogue waves. In the absence of delayed feedback, spatial pulses are stationary. The rogue waves are exited and controlled by the delay feedback. We characterize their formation by computing the probability distribution of the pulse height. The long-tailed statistical contribution, which is often considered as a signature of the presence of rogue waves, appears for sufficiently strong feedback. The generality of our analysis suggests that the feedback induced instability leading to the spontaneous formation of two-dimensional rogue waves is a universal phenomenon.

Finite difference elastic wave modeling with an irregular free surface using ADER scheme

NASA Astrophysics Data System (ADS)

Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.

2015-06-01

In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.

Speed of fast and slow rupture fronts along frictional interfaces

NASA Astrophysics Data System (ADS)

Trømborg, Jørgen Kjoshagen; Sveinsson, Henrik Andersen; Thøgersen, Kjetil; Scheibert, Julien; Malthe-Sørenssen, Anders

2015-07-01

The transition from stick to slip at a dry frictional interface occurs through the breaking of microjunctions between the two contacting surfaces. Typically, interactions between junctions through the bulk lead to rupture fronts propagating from weak and/or highly stressed regions, whose junctions break first. Experiments find rupture fronts ranging from quasistatic fronts, via fronts much slower than elastic wave speeds, to fronts faster than the shear wave speed. The mechanisms behind and selection between these fronts are still imperfectly understood. Here we perform simulations in an elastic two-dimensional spring-block model where the frictional interaction between each interfacial block and the substrate arises from a set of junctions modeled explicitly. We find that material slip speed and rupture front speed are proportional across the full range of front speeds we observe. We revisit a mechanism for slow slip in the model and demonstrate that fast slip and fast fronts have a different, inertial origin. We highlight the long transients in front speed even along homogeneous interfaces, and we study how both the local shear to normal stress ratio and the local strength are involved in the selection of front type and front speed. Last, we introduce an experimentally accessible integrated measure of block slip history, the Gini coefficient, and demonstrate that in the model it is a good predictor of the history-dependent local static friction coefficient of the interface. These results will contribute both to building a physically based classification of the various types of fronts and to identifying the important mechanisms involved in the selection of their propagation speed.

Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

NASA Astrophysics Data System (ADS)

Wang, Heng; Zheng, Shuhua

2017-06-01

By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

One- and Two-dimensional Solitary Wave States in the Nonlinear Kramers Equation with Movement Direction as a Variable

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Ishibashi, Kazuya

2018-06-01

We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.

Elastic-plastic deformation of molybdenum single crystals shocked along [100

DOE PAGES

Mandal, A.; Gupta, Y. M.

2017-01-24

To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) – a body-centered cubic (BCC) metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ~0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ~3.6 GPa. Numerical simulations ofmore » the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}<111> and/or {112}<111> slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single crystals could not be explained in terms of dislocation multiplication alone. A dislocation generation mechanism, operative for shear stresses larger than that at the elastic limit, was required to model the rapid elastic wave attenuation and to provide a good overall match to the measured wave profiles. However, the physical basis for this mechanism was not established for the high-purity single crystal samples used in this study. As a result, the numerical simulations also suggested that Mo single crystals do not work harden significantly under shock loading in contrast to the behavior observed under quasi-static loading.« less

Elasticity of fractal materials using the continuum model with non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Numerical modeling of surface wave development under the action of wind

NASA Astrophysics Data System (ADS)

Chalikov, Dmitry

2018-06-01

The numerical modeling of two-dimensional surface wave development under the action of wind is performed. The model is based on three-dimensional equations of potential motion with a free surface written in a surface-following nonorthogonal curvilinear coordinate system in which depth is counted from a moving surface. A three-dimensional Poisson equation for the velocity potential is solved iteratively. A Fourier transform method, a second-order accuracy approximation of vertical derivatives on a stretched vertical grid and fourth-order Runge-Kutta time stepping are used. Both the input energy to waves and dissipation of wave energy are calculated on the basis of earlier developed and validated algorithms. A one-processor version of the model for PC allows us to simulate an evolution of the wave field with thousands of degrees of freedom over thousands of wave periods. A long-time evolution of a two-dimensional wave structure is illustrated by the spectra of wave surface and the input and output of energy.

Fluid mechanics of Windkessel effect.

PubMed

Mei, C C; Zhang, J; Jing, H X

2018-01-08

We describe a mechanistic model of Windkessel phenomenon based on the linear dynamics of fluid-structure interactions. The phenomenon has its origin in an old-fashioned fire-fighting equipment where an air chamber serves to transform the intermittent influx from a pump to a more steady stream out of the hose. A similar mechanism exists in the cardiovascular system where blood injected intermittantly from the heart becomes rather smooth after passing through an elastic aorta. In existing haeodynamics literature, this mechanism is explained on the basis of electric circuit analogy with empirical impedances. We present a mechanistic theory based on the principles of fluid/structure interactions. Using a simple one-dimensional model, wave motion in the elastic aorta is coupled to the viscous flow in the rigid peripheral artery. Explicit formulas are derived that exhibit the role of material properties such as the blood density, viscosity, wall elasticity, and radii and lengths of the vessels. The current two-element model in haemodynamics is shown to be the limit of short aorta and low injection frequency and the impedance coefficients are derived theoretically. Numerical results for different aorta lengths and radii are discussed to demonstrate their effects on the time variations of blood pressure, wall shear stress, and discharge. Graphical Abstract A mechanistic analysis of Windkessel Effect is described which confirms theoretically the well-known feature that intermittent influx becomes continuous outflow. The theory depends only on the density and viscosity of the blood, the elasticity and dimensions of the vessel. Empirical impedence parameters are avoided.

Three-dimensional elastic stress and displacement analysis of finite circular geometry solids containing cracks

NASA Technical Reports Server (NTRS)

Gyekenyesi, J. P.; Mendelson, A.; Kring, J.

1973-01-01

A seminumerical method is presented for solving a set of coupled partial differential equations subject to mixed and coupled boundary conditions. The use of this method is illustrated by obtaining solutions for two circular geometry and mixed boundary value problems in three-dimensional elasticity. Stress and displacement distributions are calculated in an axisymmetric, circular bar of finite dimensions containing a penny-shaped crack. Approximate results for an annular plate containing internal surface cracks are also presented.

Rayleigh wave effects in an elastic half-space.

NASA Technical Reports Server (NTRS)

Aggarwal, H. R.

1972-01-01

Consideration of Rayleigh wave effects in a homogeneous isotropic linearly elastic half-space subject to an impulsive uniform disk pressure loading. An approximate formula is obtained for the Rayleigh wave effects. It is shown that the Rayleigh waves near the center of loading arise from the portion of the dilatational and shear waves moving toward the axis, after they originate at the edge of the load disk. A study is made of the vertical displacement due to Rayleigh waves at points on the axis near the surface of the elastic half-space.

Pressure wave propagation in fluid-filled co-axial elastic tubes. Part 1: Basic theory.

PubMed

Berkouk, K; Carpenter, P W; Lucey, A D

2003-12-01

Our work is motivated by ideas about the pathogenesis of syringomyelia. This is a serious disease characterized by the appearance of longitudinal cavities within the spinal cord. Its causes are unknown, but pressure propagation is probably implicated. We have developed an inviscid theory for the propagation of pressure waves in co-axial, fluid-filled, elastic tubes. This is intended as a simple model of the intraspinal cerebrospinal-fluid system. Our approach is based on the classic theory for the propagation of longitudinal waves in single, fluid-filled, elastic tubes. We show that for small-amplitude waves the governing equations reduce to the classic wave equation. The wave speed is found to be a strong function of the ratio of the tubes' cross-sectional areas. It is found that the leading edge of a transmural pressure pulse tends to generate compressive waves with converging wave fronts. Consequently, the leading edge of the pressure pulse steepens to form a shock-like elastic jump. A weakly nonlinear theory is developed for such an elastic jump.

Elastic interactions between two-dimensional geometric defects

NASA Astrophysics Data System (ADS)

Moshe, Michael; Sharon, Eran; Kupferman, Raz

2015-12-01

In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects—point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mandal, A.; Gupta, Y. M.

To understand the elastic-plastic deformation response of shock-compressed molybdenum (Mo) – a body-centered cubic (BCC) metal, single crystal samples were shocked along the [100] crystallographic orientation to an elastic impact stress of 12.5 GPa. Elastic-plastic wave profiles, measured at different propagation distances ranging between ~0.23 to 2.31 mm using laser interferometry, showed a time-dependent material response. Within experimental scatter, the measured elastic wave amplitudes were nearly constant over the propagation distances examined. These data point to a large and rapid elastic wave attenuation near the impact surface, before reaching a threshold value (elastic limit) of ~3.6 GPa. Numerical simulations ofmore » the measured wave profiles, performed using a dislocation-based continuum model, suggested that {110}<111> and/or {112}<111> slip systems are operative under shock loading. In contrast to shocked metal single crystals with close-packed structures, the measured wave profiles in Mo single crystals could not be explained in terms of dislocation multiplication alone. A dislocation generation mechanism, operative for shear stresses larger than that at the elastic limit, was required to model the rapid elastic wave attenuation and to provide a good overall match to the measured wave profiles. However, the physical basis for this mechanism was not established for the high-purity single crystal samples used in this study. As a result, the numerical simulations also suggested that Mo single crystals do not work harden significantly under shock loading in contrast to the behavior observed under quasi-static loading.« less

Shear wave anisotropy from aligned inclusions: ultrasonic frequency dependence of velocity and attenuation

NASA Astrophysics Data System (ADS)

de Figueiredo, J. J. S.; Schleicher, J.; Stewart, R. R.; Dayur, N.; Omoboya, B.; Wiley, R.; William, A.

2013-04-01

To understand their influence on elastic wave propagation, anisotropic cracked media have been widely investigated in many theoretical and experimental studies. In this work, we report on laboratory ultrasound measurements carried out to investigate the effect of source frequency on the elastic parameters (wave velocities and the Thomsen parameter γ) and shear wave attenuation) of fractured anisotropic media. Under controlled conditions, we prepared anisotropic model samples containing penny-shaped rubber inclusions in a solid epoxy resin matrix with crack densities ranging from 0 to 6.2 per cent. Two of the three cracked samples have 10 layers and one has 17 layers. The number of uniform rubber inclusions per layer ranges from 0 to 100. S-wave splitting measurements have shown that scattering effects are more prominent in samples where the seismic wavelength to crack aperture ratio ranges from 1.6 to 1.64 than in others where the ratio varied from 2.72 to 2.85. The sample with the largest cracks showed a magnitude of scattering attenuation three times higher compared with another sample that had small inclusions. Our S-wave ultrasound results demonstrate that elastic scattering, scattering and anelastic attenuation, velocity dispersion and crack size interfere directly in shear wave splitting in a source-frequency dependent manner, resulting in an increase of scattering attenuation and a reduction of shear wave anisotropy with increasing frequency.

Permeability and elastic properties of cracked glass under pressure

NASA Astrophysics Data System (ADS)

Ougier-Simonin, A.; GuéGuen, Y.; Fortin, J.; Schubnel, A.; Bouyer, F.

2011-07-01

Fluid flow in rocks is allowed through networks of cracks and fractures at all scales. In fact, cracks are of high importance in various applications ranging from rock elastic and transport properties to nuclear waste disposal. The present work aims at investigating thermomechanical cracking effects on elastic wave velocities, mechanical strength, and permeability of cracked glass under pressure. We performed the experiments on a triaxial cell at room temperature which allows for independent controls of the confining pressure, the axial stress, and pore pressure. We produced cracks in original borosilicate glass samples with a reproducible method (thermal treatment with a thermal shock of 300°C). The evolution of the elastic and transport properties have been monitored using elastic wave velocity sensors, strain gage, and flow measurements. The results obtained evidence for (1) a crack family with identified average aspect ratio and crack aperture, (2) a very small permeability which decreases as a power (exponential) function of pressure, and depends on (3) the crack aperture cube. We also show that permeability behavior of a cracked elastic brittle solid is reversible and independent of the fluid nature. Two independent methods (permeability and elastic wave velocity measurements) give these consistent results. This study provides data on the mechanical and transport properties of an almost ideal elastic brittle solid in which a crack population has been introduced. Comparisons with similar data on rocks allow for drawing interesting conclusions. Over the timescale of our experiments, our results do not provide any data on stress corrosion, which should be considered in further study.

The impact of intraocular pressure on elastic wave velocity estimates in the crystalline lens.

PubMed

Park, Suhyun; Yoon, Heechul; Larin, Kirill V; Emelianov, Stanislav Y; Aglyamov, Salavat R

2016-12-20

Intraocular pressure (IOP) is believed to influence the mechanical properties of ocular tissues including cornea and sclera. The elastic properties of the crystalline lens have been mainly investigated with regard to presbyopia, the age-related loss of accommodation power of the eye. However, the relationship between the elastic properties of the lens and IOP remains to be established. The objective of this study is to measure the elastic wave velocity, which represents the mechanical properties of tissue, in the crystalline lens ex vivo in response to changes in IOP. The elastic wave velocities in the cornea and lens from seven enucleated bovine globe samples were estimated using ultrasound shear wave elasticity imaging. To generate and then image the elastic wave propagation, an ultrasound imaging system was used to transmit a 600 µs pushing pulse at 4.5 MHz center frequency and to acquire ultrasound tracking frames at 6 kHz frame rate. The pushing beams were separately applied to the cornea and lens. IOP in the eyeballs was varied from 5 to 50 mmHg. The results indicate that while the elastic wave velocity in the cornea increased from 0.96  ±  0.30 m s -1 to 6.27  ±  0.75 m s -1 as IOP was elevated from 5 to 50 mmHg, there were insignificant changes in the elastic wave velocity in the crystalline lens with the minimum and the maximum speeds of 1.44  ±  0.27 m s -1 and 2.03  ±  0.46 m s -1 , respectively. This study shows that ultrasound shear wave elasticity imaging can be used to assess the biomechanical properties of the crystalline lens noninvasively. Also, it was observed that the dependency of the crystalline lens stiffness on the IOP was significantly lower in comparison with that of cornea.

Wave propagation problem for a micropolar elastic waveguide

NASA Astrophysics Data System (ADS)

Kovalev, V. A.; Murashkin, E. V.; Radayev, Y. N.

2018-04-01

A propagation problem for coupled harmonic waves of translational displacements and microrotations along the axis of a long cylindrical waveguide is discussed at present study. Microrotations modeling is carried out within the linear micropolar elasticity frameworks. The mathematical model of the linear (or even nonlinear) micropolar elasticity is also expanded to a field theory model by variational least action integral and the least action principle. The governing coupled vector differential equations of the linear micropolar elasticity are given. The translational displacements and microrotations in the harmonic coupled wave are decomposed into potential and vortex parts. Calibrating equations providing simplification of the equations for the wave potentials are proposed. The coupled differential equations are then reduced to uncoupled ones and finally to the Helmholtz wave equations. The wave equations solutions for the translational and microrotational waves potentials are obtained for a high-frequency range.

Shock-induced Plasticity and Brittle Cracks in Aluminum Nitride

NASA Astrophysics Data System (ADS)

Branicio, Paulo; Kalia, Rajiv

2005-03-01

Two hundred and nine million atom molecular-dynamics simulation of hypervelocity projectile impact in aluminum nitride reveals strong interplay between shock-induced structural phase transformation, plastic deformation and brittle cracks. The shock wave splits into an elastic precursor and a wurtzite-to-rocksalt structural transformation wave. When the elastic wave reflected from the boundary of the sample interacts with the transformation wave front, nanocavities are generated along the penetration path of the projectile and dislocations in adjacent regions. The nanocavities coalesce to form mode I brittle cracks while dislocations generate kink bands that give rise to mode II cracks. These simulations provide a microscopic view of defects associated with simultaneous tensile and shear cracking at the structural phase transformation boundary due to shock impact in high-strength ceramics.

Experimental investigation of stress wave propagation in standing trees

Treesearch

Houjiang Zhang; Xiping Wang; Juan Su

2011-01-01

The objective of this study was to investigate how a stress wave travels in a standing tree as it is introduced into the tree trunk through a mechanical impact. A series of stress wave time-of-flight (TOF) data were obtained from three freshly-cut red pine (Pinus resinosa Ait.) logs by means of a two-probe stress wave timer. Two-dimensional (2D) and three-dimensional (...

A fourth order accurate finite difference scheme for the computation of elastic waves

NASA Technical Reports Server (NTRS)

Bayliss, A.; Jordan, K. E.; Lemesurier, B. J.; Turkel, E.

1986-01-01

A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.

On the strain energy of laminated composite plates

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

The present effort to obtain the asymptotically correct form of the strain energy in inhomogeneous laminated composite plates proceeds from the geometrically nonlinear elastic theory-based three-dimensional strain energy by decomposing the nonlinear three-dimensional problem into a linear, through-the-thickness analysis and a nonlinear, two-dimensional analysis analyzing plate formation. Attention is given to the case in which each lamina exhibits material symmetry about its middle surface, deriving closed-form analytical expressions for the plate elastic constants and the displacement and strain distributions through the plate's thickness. Despite the simplicity of the plate strain energy's form, there are no restrictions on the magnitudes of displacement and rotation measures.

Two new ways of mapping sea ice thickness using ocean waves

NASA Astrophysics Data System (ADS)

Wadhams, P.

2010-12-01

TWO NEW METHODS OF MAPPING SEA ICE THICKNESS USING OCEAN WAVES. P. Wadhams (1,2), Martin Doble (1,2) and F. Parmiggiani (3) (1) Dept. of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, UK. (2) Laboratoire d’Océanographie de Villefranche, Université Pierre et Marie Curie, 06234 Villefranche-sur-Mer, France (2) ISAC-CNR, Bologna, Italy Two new methods of mapping ice thickness have been recently developed and tested, both making use of the dispersion relation of ocean waves in ice of radically different types. In frazil-pancake ice, a young ice type in which cakes less than 5 m across float in a suspension of individual ice crystals, the propagation of waves has been successfully modelled by treating the ice layer as a highly viscous fluid. The model predicts a shortening of wavelengths within the ice. Two-dimensional Fourier analysis of successive SAR subscenes to track the directional spectrum of a wave field as it enters an ice edge shows that waves do indeed shorten within the ice, and the change has been successfully used to predict the thickness of the frazil-pancake layer. Concurrent shipborne sampling in the Antarctic has shown that the method is accurate, and we now propose its use throughout the important frazil-pancake regimes in the world ocean (Antarctic circumpolar ice edge zone, Greenland Sea, Bering Sea and others). A radically different type of dispersion occurs when ocean waves enter the continuous icefields of the central Arctic, when they couple with the elastic ice cover to propagate as a flexural-gravity wave. A two-axis tiltmeter array has been used to measure the resulting change in the dispersion relation for long ocean swell (15-30 s) originating from storms in the Greenland Sea. The dispersion relation is slightly different from swell in the open ocean, so if two such arrays are placed a substantial distance (100s of km) apart and used to observe the changing wave period of arrivals from a given storm, the time delay between the arrival of the same frequency at two sites gives the dispersion, and hence the modal ice thickness along the great circle route connecting the arrays. The two quite different methods thus share the use of ocean wave dispersion to infer sea ice thickness.

Numerical simulation and experimental validation of Lamb wave propagation behavior in composite plates

NASA Astrophysics Data System (ADS)

Kim, Sungwon; Uprety, Bibhisha; Mathews, V. John; Adams, Daniel O.

2015-03-01

Structural Health Monitoring (SHM) based on Acoustic Emission (AE) is dependent on both the sensors to detect an impact event as well as an algorithm to determine the impact location. The propagation of Lamb waves produced by an impact event in thin composite structures is affected by several unique aspects including material anisotropy, ply orientations, and geometric discontinuities within the structure. The development of accurate numerical models of Lamb wave propagation has important benefits towards the development of AE-based SHM systems for impact location estimation. Currently, many impact location algorithms utilize the time of arrival or velocities of Lamb waves. Therefore the numerical prediction of characteristic wave velocities is of great interest. Additionally, the propagation of the initial symmetric (S0) and asymmetric (A0) wave modes is important, as these wave modes are used for time of arrival estimation. In this investigation, finite element analyses were performed to investigate aspects of Lamb wave propagation in composite plates with active signal excitation. A comparative evaluation of two three-dimensional modeling approaches was performed, with emphasis placed on the propagation and velocity of both the S0 and A0 wave modes. Results from numerical simulations are compared to experimental results obtained from active AE testing. Of particular interest is the directional dependence of Lamb waves in quasi-isotropic carbon/epoxy composite plates. Numerical and experimental results suggest that although a quasi-isotropic composite plate may have the same effective elastic modulus in all in-plane directions, the Lamb wave velocity may have some directional dependence. Further numerical analyses were performed to investigate Lamb wave propagation associated with circular cutouts in composite plates.

Numerical Investigation of Three-dimensional Instability of Standing Waves

NASA Astrophysics Data System (ADS)

Zhu, Qiang; Liu, Yuming; Yue, Dick K. P.

2002-11-01

We study the three-dimensional instability of finite-amplitude standing waves under the influence of gravity using the transition matrix method. For accurate calculation of the transition matrices, we apply an efficient high-order spectral element method for nonlinear wave dynamics in complex domain. We consider two types of standing waves: (a) plane standing waves; and (b) standing waves in a circular tank. For the former, in addition to the confirmation of the side-band-like instability, we find a new three-dimensional instability for arbitrary base standing waves. The dominant component of the unstable disturbance is an oblique standing wave, with an arbitrary angle relative to the base flow, whose frequency is approximately equal to that of the base standing wave. Based on direct simulations, we confirm such a three-dimensional instability and show the occurrence of the Fermi-Pasta-Ulam recurrence phenomenon during nonlinear evolution. For the latter, we find that beyond a threshold wave steepness, the standing wave with frequency Ω becomes unstable to a small three-dimensional disturbance, which contains two dominant standing-wave components with frequencies ω1 and ω_2, provided that 2Ω ω1 + ω_2. The threshold wave steepness is found to decrease/increase as the radial/azimuthal wavenumber of the base standing wave increases. We show that the instability of standing waves in rectangular and circular tanks is caused by third-order quartet resonances between base flow and disturbance.

Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

NASA Astrophysics Data System (ADS)

Sander, Oliver; Schiela, Anton

2014-12-01

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both, we show existence of solutions of the coupled problems, using the direct method of the calculus of variations. From the first-order optimality conditions, we also derive the corresponding conditions for the dual variables. These are then interpreted in mechanical terms.

Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure

NASA Astrophysics Data System (ADS)

Vorotnikov, K.; Starosvetsky, Y.

2018-01-01

The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.

Metastability at the Yield-Stress Transition in Soft Glasses

NASA Astrophysics Data System (ADS)

Lulli, Matteo; Benzi, Roberto; Sbragaglia, Mauro

2018-04-01

We study the solid-to-liquid transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable "fluidized" state, which relaxes back to a metastable "solid" state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheological branches, as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible experimental tests.

The simulation of shock- and impact-driven flows with Mie-Gruneisen equations of state

NASA Astrophysics Data System (ADS)

Ward, Geoffrey M.

An investigation of shock- and impact-driven flows with Mie-Gruneisen equation of state derived from a linear shock-particle speed Hugoniot relationship is presented. Cartesian mesh methods using structured adaptive refinement are applied to simulate several flows of interest in an Eulerian frame of reference. The flows central to the investigation include planar Richtmyer-Meshkov instability, the impact of a sphere with a plate, and an impact-driven Mach stem. First, for multicomponent shock-driven flows, a dimensionally unsplit, spatially high-order, hybrid, center-difference, limiter methodology is developed. Effective switching between center-difference and upwinding schemes is achieved by a set of robust tolerance and Lax-entropy-based criteria [49]. Oscillations that result from such a mixed stencil scheme are minimized by requiring that the upwinding method approaches the center-difference method in smooth regions. The solver is then applied to investigate planar Richtmyer-Meshkov instability in the context of an equation of state comparison. Comparisons of simulations with materials modeled by isotropic stress Mie-Gruneisen equations of state derived from a linear shock-particle speed Hugoniot relationship [36,52] to those of perfect gases are made with the intention of exposing the role of the equation of state. First, results for single- and triple-mode planar Richtmyer-Meshkov instability between mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Gruneisen equations of state are presented for the case of a reflected shock. The single-mode case is explored for incident shock Mach numbers of 1.5 and 2.5. Additionally, examined is single-mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. Vorticity distribution and corrugation centerline shortly after shock interaction is also examined. The formation of incipient weak shock waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected. Next, the ghost fluid method [83] is explored for application to impact-driven flows with Mie-Gruneisen equations of state in a vacuum. Free surfaces are defined utilizing a level-set approach. The level-set is reinitialized to the signed distance function periodically by solution to a Hamilton-Jacobi differential equation in artificial time. Flux reconstruction along each Cartesian direction of the domain is performed by subdividing in a way that allows for robust treatment of grid-scale sized voids. Ghost cells in voided regions near the material-vacuum interface are determined from surface-normal Riemann problem solution. The method is then applied to several impact problems of interest. First, a one-dimensional impact problem is examined in Mie-Gruneisen aluminum with simple point erosion used to model separation by spallation under high tension. A similar three-dimensional axisymmetric simulation of two rods impacting is then performed without a model for spallation. Further results for three-dimensional axisymmetric simulation of a sphere hitting a plate are then presented. Finally, a brief investigation of the assumptions utilized in modeling solids as isotropic fluids is undertaken. An Eulerian solver approach to handling elastic and elastic-plastic solids is utilized for comparison to the simple fluid model assumption. First, in one dimension an impact problem is examined for elastic, elastic-plastic, and fluid equations of state for aluminum. The results demonstrate that in one dimension the fluid models the plastic shock structure of the flow well. Further investigation is made using a three-dimensional axisymmetric simulation of an impact problem involving a copper cylinder surrounded by aluminum. An aluminum slab impact drives a faster shock in the outer aluminum region yielding a Mach reflection in the copper. The results demonstrate similar plastic shock structures. Several differences are also notable that include a lack of roll-up instability at the material interface and slip-line emanating from the Mach stem's triple point. (Abstract shortened by UMI.)

Stimulated Brillouin scattering in the field of a two-dimensionally localized pumping wave

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solikhov, D. K., E-mail: davlat56@mail.ru; Dvinin, S. A., E-mail: dvinin@phys.msu.ru

2016-06-15

Stimulated Brillouin scattering of electromagnetic waves in the field of a two-dimensionally localized pump wave at arbitrary scattering angles in the regime of forward scattering is analyzed. Spatial variations in the amplitudes of interacting waves are studied for different values of the pump field and different dimensions of the pump wave localization region. The intensity of scattered radiation is determined as a function of the scattering angle and the dimensions of the pump wave localization region. It is shown that the intensity increases with increasing scattering angle.

External vibration multi-directional ultrasound shearwave elastography (EVMUSE): application in liver fibrosis staging.

PubMed

Zhao, Heng; Song, Pengfei; Meixner, Duane D; Kinnick, Randall R; Callstrom, Matthew R; Sanchez, William; Urban, Matthew W; Manduca, Armando; Greenleaf, James F; Chen, Shigao

2014-11-01

Shear wave speed can be used to assess tissue elasticity, which is associated with tissue health. Ultrasound shear wave elastography techniques based on measuring the propagation speed of the shear waves induced by acoustic radiation force are becoming promising alternatives to biopsy in liver fibrosis staging. However, shear waves generated by such methods are typically very weak. Therefore, the penetration may become problematic, especially for overweight or obese patients. In this study, we developed a new method called external vibration multi-directional ultrasound shearwave elastography (EVMUSE), in which external vibration from a loudspeaker was used to generate a multi-directional shear wave field. A directional filter was then applied to separate the complex shear wave field into several shear wave fields propagating in different directions. A 2-D shear wave speed map was reconstructed from each individual shear wave field, and a final 2-D shear wave speed map was constructed by compounding these individual wave speed maps. The method was validated using two homogeneous phantoms and one multi-purpose tissue-mimicking phantom. Ten patients undergoing liver magnetic resonance elastography (MRE) were also studied with EVMUSE to compare results between the two methods. Phantom results showed EVMUSE was able to quantify tissue elasticity accurately with good penetration. In vivo EVMUSE results were well correlated with MRE results, indicating the promise of using EVMUSE for liver fibrosis staging.

From supersonic shear wave imaging to full-field optical coherence shear wave elastography

NASA Astrophysics Data System (ADS)

Nahas, Amir; Tanter, Mickaël; Nguyen, Thu-Mai; Chassot, Jean-Marie; Fink, Mathias; Claude Boccara, A.

2013-12-01

Elasticity maps of tissue have proved to be particularly useful in providing complementary contrast to ultrasonic imaging, e.g., for cancer diagnosis at the millimeter scale. Optical coherence tomography (OCT) offers an endogenous contrast based on singly backscattered optical waves. Adding complementary contrast to OCT images by recording elasticity maps could also be valuable in improving OCT-based diagnosis at the microscopic scale. Static elastography has been successfully coupled with full-field OCT (FF-OCT) in order to realize both micrometer-scale sectioning and elasticity maps. Nevertheless, static elastography presents a number of drawbacks, mainly when stiffness quantification is required. Here, we describe the combination of two methods: transient elastography, based on speed measurements of shear waves induced by ultrasonic radiation forces, and FF-OCT, an en face OCT approach using an incoherent light source. The use of an ultrafast ultrasonic scanner and an ultrafast camera working at 10,000 to 30,000 images/s made it possible to follow shear wave propagation with both modalities. As expected, FF-OCT is found to be much more sensitive than ultrafast ultrasound to tiny shear vibrations (a few nanometers and micrometers, respectively). Stiffness assessed in gel phantoms and an ex vivo rat brain by FF-OCT is found to be in good agreement with ultrasound shear wave elastography.

Elastic scattering losses from colliding Bose-Einstein condensates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zin Pawel; Chwedenczuk, Jan; Trippenbach, Marek

2006-03-15

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zin et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insightmore » into correlation properties of scattered atoms.« less

An Experiment on Two-Dimensional Interaction of Solitary Waves in Shallow Water System

NASA Astrophysics Data System (ADS)

Tsuji, Hidekazu; Yufu, Kei; Marubayashi, Kenji

2012-11-01

The dynamics of solitary waves in horizontally two-dimensional region is not yet well understood. Recently two-dimensional soliton interaction of Kadmotsetv-Petviashvili (KP) equation which describes the weakly nonlinear long wave in shallow water system has been theoretically studied (e.g. Kodama (2010)). It is clarified that the ``resonant'' interaction which forms Y-shaped triad can be described by exact solution. Li et al. (2011) experimentally studied the reflection of solitary wave at the wall and verified the theory of KP equation. To investigate more general interaction process, an experiment in wave tank using two wave makers which are controlled independently is carried out. The wave tank is 4 m in length and 3.6 m in width. The depth of the water is about 8cm. The wavemakers, which are piston-type and have board about 1.5 m in length, can produce orderly solitary wave which amplitude is 1.0-3.5 cm. We observe newly generated solitary wave due to interaction of original solitary waves which have different amplitude and/or propagation direction. The results are compared with the aforementioned theory of KP equation.

Shocks in oscillated granular layers

NASA Astrophysics Data System (ADS)

Bougie, J.; Moon, Sung Joon; Swift, J. B.; Swinney, Harry L.

2001-11-01

We study shock formation in vertically oscillated granular layers, where shock waves form with each collision between the layer and the bottom plate of the container. We use both three-dimensional numerical solutions of continuum equations developed by Jenkins and Richman (J.T. Jenkins and M.W. Richman, Arch. Rat. Mech. Anal. 87), 355 (1985) for smooth and nearly elastic hard spheres, and previously validated molecular dynamics (MD) simulations (C. Bizon, M.D. Shattuck, J.B. Swift, W.D. McCormick, and H.L. Swinney, Phys. Rev. Lett. 80), 57 (1998). Both methods capture the shock formation, and the two methods agree quantitatively for small dissipation. We also investigate the effect of inelasticity on shock formation, and use both smooth and rough hard-sphere MD simulations to investigate the effect of friction in this system.

DYNAMIC PLANE-STRAIN SHEAR RUPTURE WITH A SLIP-WEAKENING FRICTION LAW CALCULATED BY A BOUNDARY INTEGRAL METHOD.

USGS Publications Warehouse

Andrews, D.J.

1985-01-01

A numerical boundary integral method, relating slip and traction on a plane in an elastic medium by convolution with a discretized Green function, can be linked to a slip-dependent friction law on the fault plane. Such a method is developed here in two-dimensional plane-strain geometry. Spontaneous plane-strain shear ruptures can make a transition from sub-Rayleigh to near-P propagation velocity. Results from the boundary integral method agree with earlier results from a finite difference method on the location of this transition in parameter space. The methods differ in their prediction of rupture velocity following the transition. The trailing edge of the cohesive zone propagates at the P-wave velocity after the transition in the boundary integral calculations. Refs.

Quasi-optical theory of relativistic surface-wave oscillators with one-dimensional and two-dimensional periodic planar structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ginzburg, N. S.; Zaslavsky, V. Yu.; Institute of Applied Physics of Russian Academy of Sciences, 46 Ulyanov St., Nizhny Novgorod 603950

2013-11-15

Within the framework of a quasi-optical approach, we develop 2D and 3D self-consistent theory of relativistic surface-wave oscillators. Presenting the radiation field as a sum of two counter-propagating wavebeams coupled on a shallow corrugated surface, we describe formation of an evanescent slow wave. Dispersion characteristics of the evanescent wave following from this method are in good compliance with those found from the direct cst simulations. Considering excitation of the slow wave by a sheet electron beam, we simulate linear and nonlinear stages of interaction, which allows us to determine oscillation threshold conditions, electron efficiency, and output coupling. The transition frommore » the model of surface-wave oscillator operating in the π-mode regime to the canonical model of relativistic backward wave oscillator is considered. We also described a modified scheme of planar relativistic surface-wave oscillators exploiting two-dimensional periodic gratings. Additional transverse propagating waves emerging on these gratings synchronize the emission from a wide sheet rectilinear electron beam allowing realization of a Cherenkov millimeter-wave oscillators with subgigawatt output power level.« less

Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1994-01-01

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

D-Wave Electron-H, -He+, and -Li2+ Elastic Scattering and Photoabsorption in P States of Two-Electron Systems

NASA Technical Reports Server (NTRS)

Bhatia, A. K.

2014-01-01

In previous papers [A. K. Bhatia, Phys. Rev. A 85, 052708 (2012); 86, 032709 (2012); 87, 042705 (2013)] electron-H, -He+, and -Li2+ P-wave scattering phase shifts were calculated using the variational polarized orbital theory. This method is now extended to the singlet and triplet D-wave scattering in the elastic region. The long-range correlations are included in the Schrodinger equation by using the method of polarized orbitals variationally. Phase shifts are compared to those obtained by other methods. The present calculation provides results which are rigorous lower bonds to the exact phase shifts. Using the presently calculated D-wave and previously calculated S-wave continuum functions, photoionization of singlet and triplet P states of He and Li+ are also calculated, along with the radiative recombination rate coefficients at various electron temperatures.

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Pseudospectral modeling and dispersion analysis of Rayleigh waves in viscoelastic media

USGS Publications Warehouse

Zhang, K.; Luo, Y.; Xia, J.; Chen, C.

2011-01-01

Multichannel Analysis of Surface Waves (MASW) is one of the most widely used techniques in environmental and engineering geophysics to determine shear-wave velocities and dynamic properties, which is based on the elastic layered system theory. Wave propagation in the Earth, however, has been recognized as viscoelastic and the propagation of Rayleigh waves presents substantial differences in viscoelastic media as compared with elastic media. Therefore, it is necessary to carry out numerical simulation and dispersion analysis of Rayleigh waves in viscoelastic media to better understand Rayleigh-wave behaviors in the real world. We apply a pseudospectral method to the calculation of the spatial derivatives using a Chebyshev difference operator in the vertical direction and a Fourier difference operator in the horizontal direction based on the velocity-stress elastodynamic equations and relations of linear viscoelastic solids. This approach stretches the spatial discrete grid to have a minimum grid size near the free surface so that high accuracy and resolution are achieved at the free surface, which allows an effective incorporation of the free surface boundary conditions since the Chebyshev method is nonperiodic. We first use an elastic homogeneous half-space model to demonstrate the accuracy of the pseudospectral method comparing with the analytical solution, and verify the correctness of the numerical modeling results for a viscoelastic half-space comparing the phase velocities of Rayleigh wave between the theoretical values and the dispersive image generated by high-resolution linear Radon transform. We then simulate three types of two-layer models to analyze dispersive-energy characteristics for near-surface applications. Results demonstrate that the phase velocity of Rayleigh waves in viscoelastic media is relatively higher than in elastic media and the fundamental mode increases by 10-16% when the frequency is above 10. Hz due to the velocity dispersion of P and S waves. ?? 2011 Elsevier Ltd.

Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces.

PubMed

Colombi, Andrea; Ageeva, Victoria; Smith, Richard J; Clare, Adam; Patel, Rikesh; Clark, Matt; Colquitt, Daniel; Roux, Philippe; Guenneau, Sebastien; Craster, Richard V

2017-07-28

Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400-600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.

A coupled-mode model for the hydroelastic analysis of large floating bodies over variable bathymetry regions

NASA Astrophysics Data System (ADS)

Belibassakis, K. A.; Athanassoulis, G. A.

2005-05-01

The consistent coupled-mode theory (Athanassoulis & Belibassakis, J. Fluid Mech. vol. 389, 1999, p. 275) is extended and applied to the hydroelastic analysis of large floating bodies of shallow draught or ice sheets of small and uniform thickness, lying over variable bathymetry regions. A parallel-contour bathymetry is assumed, characterized by a continuous depth function of the form h( {x,y}) {=} h( x ), attaining constant, but possibly different, values in the semi-infinite regions x {<} a and x {>} b. We consider the scattering problem of harmonic, obliquely incident, surface waves, under the combined effects of variable bathymetry and a floating elastic plate, extending from x {=} a to x {=} b and {-} infty {<} y{<}infty . Under the assumption of small-amplitude incident waves and small plate deflections, the hydroelastic problem is formulated within the context of linearized water-wave and thin-elastic-plate theory. The problem is reformulated as a transition problem in a bounded domain, for which an equivalent, Luke-type (unconstrained), variational principle is given. In order to consistently treat the wave field beneath the elastic floating plate, down to the sloping bottom boundary, a complete, local, hydroelastic-mode series expansion of the wave field is used, enhanced by an appropriate sloping-bottom mode. The latter enables the consistent satisfaction of the Neumann bottom-boundary condition on a general topography. By introducing this expansion into the variational principle, an equivalent coupled-mode system of horizontal equations in the plate region (a {≤} x {≤} b) is derived. Boundary conditions are also provided by the variational principle, ensuring the complete matching of the wave field at the vertical interfaces (x{=}a and x{=}b), and the requirements that the edges of the plate are free of moment and shear force. Numerical results concerning floating structures lying over flat, shoaling and corrugated seabeds are presented and compared, and the effects of wave direction, bottom slope and bottom corrugations on the hydroelastic response are presented and discussed. The present method can be easily extended to the fully three-dimensional hydroelastic problem, including bodies or structures characterized by variable thickness (draught), flexural rigidity and mass distributions.

The load separation technique in the elastic-plastic fracture analysis of two- and three-dimensional geometries

NASA Technical Reports Server (NTRS)

Sharobeam, Monir H.

1994-01-01

Load separation is the representation of the load in the test records of geometries containing cracks as a multiplication of two separate functions: a crack geometry function and a material deformation function. Load separation is demonstrated in the test records of several two-dimensional geometries such as compact tension geometry, single edge notched bend geometry, and center cracked tension geometry and three-dimensional geometries such as semi-elliptical surface crack. The role of load separation in the evaluation of the fracture parameter J-integral and the associated factor eta for two-dimensional geometries is discussed. The paper also discusses the theoretical basis and the procedure for using load separation as a simplified yet accurate approach for plastic J evaluation in semi-elliptical surface crack which is a three-dimensional geometry. The experimental evaluation of J, and particularly J(sub pl), for three-dimensional geometries is very challenging. A few approaches have been developed in this regard and they are either complex or very approximate. The paper also presents the load separation as a mean to identify the blunting and crack growth regions in the experimental test records of precracked specimens. Finally, load separation as a methodology in elastic-plastic fracture mechanics is presented.

Time Reversal Methods for Structural Health Monitoring of Metallic Structures Using Guided Waves

DTIC Science & Technology

2011-09-01

measure elastic properties of thin isotropic materials and laminated composite plates. Two types of waves propagate a symmetric wave and antisymmetric...compare it to the original signal. In this time reversal procedure wave propagation from point-A to point-B and can be modeled as a convolution ...where * is the convolution operator and transducer transmit and receive transfer function are neglected for simplification. In the frequency

Verification of elastic-wave static displacement in solids. [using ultrasonic techniques on Ge single crystals

NASA Technical Reports Server (NTRS)

Cantrell, J. H., Jr.; Winfree, W. P.

1980-01-01

The solution of the nonlinear differential equation which describes an initially sinusoidal finite-amplitude elastic wave propagating in a solid contains a static-displacement term in addition to the harmonic terms. The static-displacement amplitude is theoretically predicted to be proportional to the product of the squares of the driving-wave amplitude and the driving-wave frequency. The first experimental verification of the elastic-wave static displacement in a solid (the 111 direction of single-crystal germanium) is reported, and agreement is found with the theoretical predictions.

Evolution of a primary pulse in the granular dimers mounted on a linear elastic foundation: An analytical and numerical study.

PubMed

Ahsan, Zaid; Jayaprakash, K R

2016-10-01

In this exposition we consider the wave dynamics of a one-dimensional periodic granular dimer (diatomic) chain mounted on a damped and an undamped linear elastic foundation (otherwise called the on-site potential). It is very well known that periodic granular dimers support solitary wave propagation (similar to that in the homogeneous granular chains) for a specific discrete set of mass ratios. In this work we present the analytical investigation of the evolution of solitary waves and primary pulses in granular dimers when they are mounted on on-site potential with and without velocity proportional foundation damping. We invoke a methodology based on the multiple time-scale asymptotic analysis and partition the dynamics of the perturbed dimer chain into slow and fast components. The dynamics of the dimer chain in the limit of large mass mismatch (auxiliary chain) mounted on on-site potential and foundation damping is used as the basis for the analysis. A systematic analytical procedure is then developed for the slowly varying response of the beads and in estimating primary pulse amplitude evolution resulting in a nonlinear map relating the relative displacement amplitudes of two adjacent beads. The methodology is applicable for arbitrary mass ratios between the beads. We present several examples to demonstrate the efficacy of the proposed method. It is observed that the amplitude evolution predicted by the described methodology is in good agreement with the numerical simulation of the original system. This work forms a basis for further application of the considered methodology to weakly coupled granular dimers which finds practical relevance in designing shock mitigating granular layers.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation.

PubMed

Liu, Wei; Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota's bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides.

Rogue waves in the two dimensional nonlocal nonlinear Schrödinger equation and nonlocal Klein-Gordon equation

PubMed Central

Zhang, Jing; Li, Xiliang

2018-01-01

In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. Solitons and periodic line waves as exact solutions of these two nonlocal equations are derived by employing the Hirota’s bilinear method. Like the nonlocal NLS equation, these solutions may have singularities. However, by suitable constraints of parameters, nonsingular breather solutions are generated. Besides, by taking a long wave limit of these obtained soliton solutions, rogue wave solutions and semi-rational solutions are derived. For the two dimensional NLS equation, rogue wave solutions are line rogue waves, which arise from a constant background with a line profile and then disappear into the same background. The semi-rational solutions shows intriguing dynamical behaviours: line rogue wave and line breather arise from a constant background together and then disappear into the constant background again uniformly. For the coupled nonlocal Klein-Gordon equation, rogue waves are localized in both space and time, semi-rational solutions are composed of rogue waves, breathers and periodic line waves. These solutions are demonstrated analytically to exist for special classes of nonlocal equations relevant to optical waveguides. PMID:29432495

Deformation of compound shells under action of internal shock wave loading

NASA Astrophysics Data System (ADS)

Chernobryvko, Marina; Kruszka, Leopold; Avramov, Konstantin

2015-09-01

The compound shells under the action of internal shock wave loading are considered. The compound shell consists of a thin cylindrical shell and two thin parabolic shells at the edges. The boundary conditions in the shells joints satisfy the equality of displacements. The internal shock wave loading is modelled as the surplus pressure surface. This pressure is a function of the shell coordinates and time. The strain rate deformation of compound shell takes place in both the elastic and in plastic stages. In the elastic stage the equations of the structure motions are obtained by the assumed-modes method, which uses the kinetic and potential energies of the cylindrical and two parabolic shells. The dynamic behaviour of compound shells is treated. In local plastic zones the 3-D thermo-elastic-plastic model is used. The deformations are described by nonlinear model. The stress tensor elements are determined using dynamic deformation theory. The deformation properties of materials are influenced by the strain rate behaviour, the influence of temperature parameters, and the elastic-plastic properties of materials. The dynamic yield point of materials and Pisarenko-Lebedev's criterion of destruction are used. The modified adaptive finite differences method of numerical analysis is suggested for those simulations. The accuracy of the numerical simulation is verified on each temporal step of calculation and in the case of large deformation gradients.

Characteristics of wind waves in shallow tidal basins and how they affect bed shear stress, bottom erosion, and the morphodynamic evolution of coupled marsh and mudflat landforms

NASA Astrophysics Data System (ADS)

Tommasini, Laura; Carniello, Luca; Goodwin, Guillaume; Mudd, Simon M.; Matticchio, Bruno; D'Alpaos, Andrea

2017-04-01

Wind-wave induced erosion is one of the main processes controlling the morphodynamic evolution of shallow tidal basins, because wind waves promote the erosion of subtidal platforms, tidal flats and salt marshes. Our study considered zero-, one-and two-dimensional wave models. First, we analyzed the relations between wave parameters, depth and bed shear stress with constant and variable wave period considering two zero-dimensional models based on the Young and Verhagen (1996), and Carniello et al. (2005, 2011) approaches. The first one is an empirical method that computes wave height and the variable wave period from wind velocity, fetch and water depth. The second one is based on the solution of wave action conservation equation, we use this second approach for computing the bottom shear stress and wave height, considering variable and constant (t=2s) wave period. Second, we compared the wave spectral model SWAN with a fully coupled Wind-Wave Tidal Model applied to a 1D rectangular domain. These models describe both the growth and propagation of wind waves. Finally, we applied the two-dimensional Wind Wave Tidal Model (WWTM) to six different configurations of the Venice lagoon considering the same boundary conditions and we evaluated the spatial variation of mean wave power density. The analysis with zero-dimensional models show that the effects of the different model assumptions on the wave period and on the wave height computation cannot be neglected. In particular, the relationships between bottom shear stress and water depth have different shapes. Two results emerge: first, the differences are higher for small depths, and then the maximum values reached with the Young and Verhagen (1996) approach are greater than the maximum values obtained with WWTM approach. The results obtained with two-dimensional models suggest that the wave height is different in particular for small fetch, this could be due to the different formulation of the wave period. Finally, the application of WWTM for the entire Lagoon basin underlines an increase of the mean power density in the last four centuries, in particular in the central-southern part of the lagoon between Chioggia and Malamocco inlets.

Heterogeneous mechanics of the mouse pulmonary arterial network.

PubMed

Lee, Pilhwa; Carlson, Brian E; Chesler, Naomi; Olufsen, Mette S; Qureshi, M Umar; Smith, Nicolas P; Sochi, Taha; Beard, Daniel A

2016-10-01

Individualized modeling and simulation of blood flow mechanics find applications in both animal research and patient care. Individual animal or patient models for blood vessel mechanics are based on combining measured vascular geometry with a fluid structure model coupling formulations describing dynamics of the fluid and mechanics of the wall. For example, one-dimensional fluid flow modeling requires a constitutive law relating vessel cross-sectional deformation to pressure in the lumen. To investigate means of identifying appropriate constitutive relationships, an automated segmentation algorithm was applied to micro-computerized tomography images from a mouse lung obtained at four different static pressures to identify the static pressure-radius relationship for four generations of vessels in the pulmonary arterial network. A shape-fitting function was parameterized for each vessel in the network to characterize the nonlinear and heterogeneous nature of vessel distensibility in the pulmonary arteries. These data on morphometric and mechanical properties were used to simulate pressure and flow velocity propagation in the network using one-dimensional representations of fluid and vessel wall mechanics. Moreover, wave intensity analysis was used to study effects of wall mechanics on generation and propagation of pressure wave reflections. Simulations were conducted to investigate the role of linear versus nonlinear formulations of wall elasticity and homogeneous versus heterogeneous treatments of vessel wall properties. Accounting for heterogeneity, by parameterizing the pressure/distention equation of state individually for each vessel segment, was found to have little effect on the predicted pressure profiles and wave propagation compared to a homogeneous parameterization based on average behavior. However, substantially different results were obtained using a linear elastic thin-shell model than were obtained using a nonlinear model that has a more physiologically realistic pressure versus radius relationship.

Hydroelastic behaviour of a structure exposed to an underwater explosion.

PubMed

Colicchio, G; Greco, M; Brocchini, M; Faltinsen, O M

2015-01-28

The hydroelastic interaction between an underwater explosion and an elastic plate is investigated num- erically through a domain-decomposition strategy. The three-dimensional features of the problem require a large computational effort, which is reduced through a weak coupling between a one-dimensional radial blast solver, which resolves the blast evolution far from the boundaries, and a three-dimensional compressible flow solver used where the interactions between the compression wave and the boundaries take place and the flow becomes three-dimensional. The three-dimensional flow solver at the boundaries is directly coupled with a modal structural solver that models the response of the solid boundaries like elastic plates. This enables one to simulate the fluid-structure interaction as a strong coupling, in order to capture hydroelastic effects. The method has been applied to the experimental case of Hung et al. (2005 Int. J. Impact Eng. 31, 151-168 (doi:10.1016/j.ijimpeng.2003.10.039)) with explosion and structure sufficiently far from other boundaries and successfully validated in terms of the evolution of the acceleration induced on the plate. It was also used to investigate the interaction of an underwater explosion with the bottom of a close-by ship modelled as an orthotropic plate. In the application, the acoustic phase of the fluid-structure interaction is examined, highlighting the need of the fluid-structure coupling to capture correctly the possible inception of cavitation. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

The complex variable reproducing kernel particle method for bending problems of thin plates on elastic foundations

NASA Astrophysics Data System (ADS)

Chen, L.; Cheng, Y. M.

2018-07-01

In this paper, the complex variable reproducing kernel particle method (CVRKPM) for solving the bending problems of isotropic thin plates on elastic foundations is presented. In CVRKPM, one-dimensional basis function is used to obtain the shape function of a two-dimensional problem. CVRKPM is used to form the approximation function of the deflection of the thin plates resting on elastic foundation, the Galerkin weak form of thin plates on elastic foundation is employed to obtain the discretized system equations, the penalty method is used to apply the essential boundary conditions, and Winkler and Pasternak foundation models are used to consider the interface pressure between the plate and the foundation. Then the corresponding formulae of CVRKPM for thin plates on elastic foundations are presented in detail. Several numerical examples are given to discuss the efficiency and accuracy of CVRKPM in this paper, and the corresponding advantages of the present method are shown.

An analytical model of a curved beam with a T shaped cross section

NASA Astrophysics Data System (ADS)

Hull, Andrew J.; Perez, Daniel; Cox, Donald L.

2018-03-01

This paper derives a comprehensive analytical dynamic model of a closed circular beam that has a T shaped cross section. The new model includes in-plane and out-of-plane vibrations derived using continuous media expressions which produces results that have a valid frequency range above those available from traditional lumped parameter models. The web is modeled using two-dimensional elasticity equations for in-plane motion and the classical flexural plate equation for out-of-plane motion. The flange is modeled using two sets of Donnell shell equations: one for the left side of the flange and one for the right side of the flange. The governing differential equations are solved with unknown wave propagation coefficients multiplied by spatial domain and time domain functions which are inserted into equilibrium and continuity equations at the intersection of the web and flange and into boundary conditions at the edges of the system resulting in 24 algebraic equations. These equations are solved to yield the wave propagation coefficients and this produces a solution to the displacement field in all three dimensions. An example problem is formulated and compared to results from finite element analysis.

A novel model of photothermal diffusion (PTD) for polymer nano-composite semiconducting of thin circular plate

NASA Astrophysics Data System (ADS)

Lotfy, Kh.

2018-05-01

In this article, theoretical discussions for a novel mathematical-physical Photothermal diffusion (PTD) model in the generalized thermoelasticity theory with photothermal processes and chemical action are introduced. The mean idea of this model depends on the interaction between quasi-particles (plasma waves) that depends on the kind of the used materials, the mechanical forces acting on the surface, the generalized thermo and mass diffusion (due to coupling of temperature fields with thermal waves and chemical potential) and the elastic waves. The one dimensional Laplace transforms is used to obtain the exact solution for some physical and chemical quantities for a thin circular plate of a semiconducting polymer nanocomposite such as silicon (Si). New variables are deduced and discussed. The obtained results of the physical quantities are presented analytically and illustrated graphically with some important applications.

Approximate non-linear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-03-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-waves scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform (GRT). After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic non-linear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P-wave and S-wave information.

Nonlinear Elastic Effects on the Energy Flux Deviation of Ultrasonic Waves in GR/EP Composites

NASA Technical Reports Server (NTRS)

Prosser, William H.; Kriz, R. D.; Fitting, Dale W.

1992-01-01

In isotropic materials, the direction of the energy flux (energy per unit time per unit area) of an ultrasonic plane wave is always along the same direction as the normal to the wave front. In anisotropic materials, however, this is true only along symmetry directions. Along other directions, the energy flux of the wave deviates from the intended direction of propagation. This phenomenon is known as energy flux deviation and is illustrated. The direction of the energy flux is dependent on the elastic coefficients of the material. This effect has been demonstrated in many anisotropic crystalline materials. In transparent quartz crystals, Schlieren photographs have been obtained which allow visualization of the ultrasonic waves and the energy flux deviation. The energy flux deviation in graphite/epoxy (gr/ep) composite materials can be quite large because of their high anisotropy. The flux deviation angle has been calculated for unidirectional gr/ep composites as a function of both fiber orientation and fiber volume content. Experimental measurements have also been made in unidirectional composites. It has been further demonstrated that changes in composite materials which alter the elastic properties such as moisture absorption by the matrix or fiber degradation, can be detected nondestructively by measurements of the energy flux shift. In this research, the effects of nonlinear elasticity on energy flux deviation in unidirectional gr/ep composites were studied. Because of elastic nonlinearity, the angle of the energy flux deviation was shown to be a function of applied stress. This shift in flux deviation was modeled using acoustoelastic theory and the previously measured second and third order elastic stiffness coefficients for T300/5208 gr/ep. Two conditions of applied uniaxial stress were considered. In the first case, the direction of applied uniaxial stress was along the fiber axis (x3) while in the second case it was perpendicular to the fiber axis along the laminate stacking direction (x1).

Analytical Solution for the Aeroelastic Response of a Two-Dimensional Elastic Plate in Axial Flow

NASA Astrophysics Data System (ADS)

Medina, Cory; Kang, Chang-Kwon

2017-11-01

The aeroelastic response of an elastic plate in an unsteady flow describes many engineering problems from bio-locomotion, deforming airfoils, to energy harvesting. However, the analysis is challenging because the shape of the plate is a priori unknown. This study presents an analytical model that can predict the two-way tightly coupled aeroelastic response of a two-dimensional elastic plate including the effects of plate curvature along the flow direction. The plate deforms due to the dynamic balance of wing inertia, elastic restoring force, and aerodynamic force. The coupled model utilizes the linearized Euler-Bernoulli beam theory for the structural model and thin airfoil theory as presented by Theodorsen, which assumes incompressible potential flow, for the aerodynamic model. The coupled equations of motion are solved via Galerkin's method, where closed form solutions for the plate deformation are obtained by deriving the unsteady aerodynamic pressure with respect to the plate normal functions, expressed in a Chebyshev polynomial expansion. Stability analysis is performed for a range of mass ratios obtaining the flutter velocities and corresponding frequencies and the results agree well with the results reported in the literature.

Uniform high order spectral methods for one and two dimensional Euler equations

NASA Technical Reports Server (NTRS)

Cai, Wei; Shu, Chi-Wang

1991-01-01

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

Acoustic Radiation Force-Induced Creep-Recovery (ARFICR): A Noninvasive Method to Characterize Tissue Viscoelasticity.

PubMed

Amador Carrascal, Carolina; Chen, Shigao; Urban, Matthew W; Greenleaf, James F

2018-01-01

Ultrasound shear wave elastography is a promising noninvasive, low cost, and clinically viable tool for liver fibrosis staging. Current shear wave imaging technologies on clinical ultrasound scanners ignore shear wave dispersion and use a single group velocity measured over the shear wave bandwidth to estimate tissue elasticity. The center frequency and bandwidth of shear waves induced by acoustic radiation force depend on the ultrasound push beam (push duration, -number, etc.) and the viscoelasticity of the medium, and therefore are different across scanners from different vendors. As a result, scanners from different vendors may give different tissue elasticity measurements within the same patient. Various methods have been proposed to evaluate shear wave dispersion to better estimate tissue viscoelasticity. A rheological model such as the Kelvin-Voigt model is typically fitted to the shear wave dispersion to solve for the elasticity and viscosity of tissue. However, these rheological models impose strong assumptions about frequency dependence of elasticity and viscosity. Here, we propose a new method called Acoustic Radiation Force Induced Creep-Recovery (ARFICR) capable of quantifying rheological model-independent measurements of elasticity and viscosity for more robust tissue health assessment. In ARFICR, the creep-recovery time signal at the focus of the push beam is used to calculate the relative elasticity and viscosity (scaled by an unknown constant) over a wide frequency range. Shear waves generated during the ARFICR measurement are also detected and used to calculate the shear wave velocity at its center frequency, which is then used to calibrate the relative elasticity and viscosity to absolute elasticity and viscosity. In this paper, finite-element method simulations and experiments in tissue mimicking phantoms are used to validate and characterize the extent of viscoelastic quantification of ARFICR. The results suggest that ARFICR can measure tissue viscoelasticity reliably. Moreover, the results showed the strong frequency dependence of viscoelastic parameters in tissue mimicking phantoms and healthy liver.

Parallel Program Systems for the Analysis of Wave Processes in Elastic-Plastic, Granular, Porous and Multi-Blocky Media

NASA Astrophysics Data System (ADS)

Sadovskaya, Oxana; Sadovskii, Vladimir

2017-04-01

Under modeling the wave propagation processes in geomaterials (granular and porous media, soils and rocks) it is necessary to take into account the structural inhomogeneity of these materials. Parallel program systems for numerical solution of 2D and 3D problems of the dynamics of deformable media with constitutive relationships of rather general form on the basis of universal mathematical model describing small strains of elastic, elastic-plastic, granular and porous materials are worked out. In the case of an elastic material, the model is reduced to the system of equations, hyperbolic by Friedrichs, written in terms of velocities and stresses in a symmetric form. In the case of an elastic-plastic material, the model is a special formulation of the Prandtl-Reuss theory in the form of variational inequality with one-sided constraints on the stress tensor. Generalization of the model to describe granularity and the collapse of pores is obtained by means of the rheological approach, taking into account different resistance of materials to tension and compression. Rotational motion of particles in the material microstructure is considered within the framework of a mathematical model of the Cosserat continuum. Computational domain may have a blocky structure, composed of an arbitrary number of layers, strips in a layer and blocks in a strip from different materials with self-consistent curvilinear interfaces. At the external boundaries of computational domain the main types of dissipative boundary conditions in terms of velocities, stresses or mixed boundary conditions can be given. Shock-capturing algorithm is proposed for implementation of the model on supercomputers with cluster architecture. It is based on the two-cyclic splitting method with respect to spatial variables and the special procedures of the stresses correction to take into account plasticity, granularity or porosity of a material. An explicit monotone ENO-scheme is applied for solving one-dimensional systems of equations at the stages of splitting method. The parallelizing of computations is carried out using the MPI library and the SPMD technology. The data exchange between processors occurs at step "predictor" of the finite-difference scheme. Program systems allow simulate the propagation of waves produced by external mechanical effects in a medium, aggregated of arbitrary number of heterogeneous blocks. Some computations of dynamic problems with and without taking into account the moment properties of a material were performed on clusters of ICM SB RAS (Krasnoyarsk) and JSCC RAS (Moscow). Parallel program systems 2Dyn_Granular, 3Dyn_Granular, 2Dyn_Cosserat, 3Dyn_Cosserat and 2Dyn_Blocks_MPI for numerical solution of 2D and 3D elastic-plastic problems of the dynamics of granular media and problems of the Cosserat elasticity theory, as well as for modeling of the dynamic processes in multi-blocky media with pliant viscoelastic, porous and fluid-saturated interlayers on cluster systems were registered by Rospatent.

Experimental determination of third-order elastic constants of diamond.

PubMed

Lang, J M; Gupta, Y M

2011-03-25

To determine the nonlinear elastic response of diamond, single crystals were shock compressed along the [100], [110], and [111] orientations to 120 GPa peak elastic stresses. Particle velocity histories and elastic wave velocities were measured by using laser interferometry. The measured elastic wave profiles were used, in combination with published acoustic measurements, to determine the complete set of third-order elastic constants. These constants represent the first experimental determination, and several differ significantly from those calculated by using theoretical models.

Evaluation of microcrack thermal shock damage in ceramics: Modeling and experiment

NASA Technical Reports Server (NTRS)

Chu, Y. C.; Hefetz, M.; Rokhlin, S. I.

1992-01-01

In this paper we present an experimental and theoretical study of the effect of microcrack damage on ceramic properties. For the experimental investigation, ceramic samples of aluminum oxide and reaction bonded silicon nitride (RBSN) are used. Thermal shock treatment from different temperatures up to 1000 C is applied to produce the microcracks. Both surface and bulk ultrasonic wave methods are used to correlate the change of elastic constants to microstructural degradation and to determine the change in elastic anisotropy induced by microcrack damage. For the theoretical investigation, damage mechanics, which relates microstructural damage to material service life and mechanical failure, is used. The change in elastic properties due to microcrack damage calculated from the theoretical model is compared with the experimental results for determination of the applicability of damage theory. It is shown that two independent experimental methods (bulk wave and surface wave) give the same results for shear moduli of damaged ceramics. The experimental results aagree reasonably well with the moduli predicted from the cracked solid model.

Non-invasive evaluation of stable renal allograft function using point shear-wave elastography.

PubMed

Kim, Bom Jun; Kim, Chan Kyo; Park, Jung Jae

2018-01-01

To investigate the feasibility of point shear-wave elastography (SWE) in evaluating patients with stable renal allograft function who underwent protocol biopsies. 95 patients with stable renal allograft function that underwent ultrasound-guided biopsies at predefined time points (10 days or 1 year after transplantation) were enrolled. Ultrasound and point SWE examinations were performed immediately before protocol biopsies. Patients were categorized into two groups: subclinical rejection (SCR) and non-SCR. Tissue elasticity (kPa) on SWE was measured in the cortex of all renal allografts. SCR was pathologically confirmed in 34 patients. Tissue elasticity of the SCR group (31.0 kPa) was significantly greater than that of the non-SCR group (24.5 kPa) (=0.016), while resistive index value did not show a significant difference between the two groups (p = 0.112). Tissue elasticity in renal allografts demonstrated significantly moderate negative correlation with estimated glomerular filtration rate (correlation coefficient = -0.604, p < 0.001). Tissue elasticity was not independent factor for SCR prediction on multivariate analysis. As a non-invasive tool, point SWE appears feasible in distinguishing between patients with SCR and without SCR in stable functioning renal allografts. Moreover, it may demonstrate the functional state of renal allografts. Advances in knowledge: On point SWE, SCR has greater tissue elasticity than non-SCR.

Numerical and experimental study of Lamb wave propagation in a two-dimensional acoustic black hole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yan, Shiling; Shen, Zhonghua, E-mail: shenzh@njust.edu.cn; Lomonosov, Alexey M.

2016-06-07

The propagation of laser-generated Lamb waves in a two-dimensional acoustic black-hole structure was studied numerically and experimentally. The geometrical acoustic theory has been applied to calculate the beam trajectories in the region of the acoustic black hole. The finite element method was also used to study the time evolution of propagating waves. An optical system based on the laser-Doppler vibration method was assembled. The effect of the focusing wave and the reduction in wave speed of the acoustic black hole has been validated.

Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies

NASA Astrophysics Data System (ADS)

Zhao, Nian; Yang, Jin; Yu, Qiangmo; Zhao, Jiangxin; Liu, Jun; Wen, Yumei; Li, Ping

2016-01-01

This work has demonstrated a novel piezoelectric energy harvester without a complex structure and appended component that is capable of scavenging vibration energy from arbitrary directions with multiple resonant frequencies. In this harvester, a spiral-shaped elastic thin beam instead of a traditional thin cantilever beam was adopted to absorb external vibration with arbitrary direction in three-dimensional (3D) spaces owing to its ability to bend flexibly and stretch along arbitrary direction. Furthermore, multiple modes in the elastic thin beam contribute to a possibility to widen the working bandwidth with multiple resonant frequencies. The experimental results show that the harvester was capable of scavenging the vibration energy in 3D arbitrary directions; they also exhibited triple power peaks at about 16 Hz, 21 Hz, and 28 Hz with the powers of 330 μW, 313 μW, and 6 μW, respectively. In addition, human walking and water wave energies were successfully converted into electricity, proving that our harvester was practical to scavenge the time-variant or multi-directional vibration energies in our daily life.

Three-dimensional piezoelectric vibration energy harvester using spiral-shaped beam with triple operating frequencies.

PubMed

Zhao, Nian; Yang, Jin; Yu, Qiangmo; Zhao, Jiangxin; Liu, Jun; Wen, Yumei; Li, Ping

2016-01-01

This work has demonstrated a novel piezoelectric energy harvester without a complex structure and appended component that is capable of scavenging vibration energy from arbitrary directions with multiple resonant frequencies. In this harvester, a spiral-shaped elastic thin beam instead of a traditional thin cantilever beam was adopted to absorb external vibration with arbitrary direction in three-dimensional (3D) spaces owing to its ability to bend flexibly and stretch along arbitrary direction. Furthermore, multiple modes in the elastic thin beam contribute to a possibility to widen the working bandwidth with multiple resonant frequencies. The experimental results show that the harvester was capable of scavenging the vibration energy in 3D arbitrary directions; they also exhibited triple power peaks at about 16 Hz, 21 Hz, and 28 Hz with the powers of 330 μW, 313 μW, and 6 μW, respectively. In addition, human walking and water wave energies were successfully converted into electricity, proving that our harvester was practical to scavenge the time-variant or multi-directional vibration energies in our daily life.

Three-dimensional NDE of VHTR core components via simulation-based testing. Final report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guzina, Bojan; Kunerth, Dennis

2014-09-30

A next generation, simulation-driven-and-enabled testing platform is developed for the 3D detection and characterization of defects and damage in nuclear graphite and composite structures in Very High Temperature Reactors (VHTRs). The proposed work addresses the critical need for the development of high-fidelity Non-Destructive Examination (NDE) technologies for as-manufactured and replaceable in-service VHTR components. Centered around the novel use of elastic (sonic and ultrasonic) waves, this project deploys a robust, non-iterative inverse solution for the 3D defect reconstruction together with a non-contact, laser-based approach to the measurement of experimental waveforms in VHTR core components. In particular, this research (1) deploys three-dimensionalmore » Scanning Laser Doppler Vibrometry (3D SLDV) as a means to accurately and remotely measure 3D displacement waveforms over the accessible surface of a VHTR core component excited by mechanical vibratory source; (2) implements a powerful new inverse technique, based on the concept of Topological Sensitivity (TS), for non-iterative elastic waveform tomography of internal defects - that permits robust 3D detection, reconstruction and characterization of discrete damage (e.g. holes and fractures) in nuclear graphite from limited-aperture NDE measurements; (3) implements state-of-the art computational (finite element) model that caters for accurately simulating elastic wave propagation in 3D blocks of nuclear graphite; (4) integrates the SLDV testing methodology with the TS imaging algorithm into a non-contact, high-fidelity NDE platform for the 3D reconstruction and characterization of defects and damage in VHTR core components; and (5) applies the proposed methodology to VHTR core component samples (both two- and three-dimensional) with a priori induced, discrete damage in the form of holes and fractures. Overall, the newly established SLDV-TS testing platform represents a next-generation NDE tool that surpasses all existing techniques for the 3D ultrasonic imaging of material damage from non-contact, limited-aperture waveform measurements. Outlook. The next stage in the development of this technology includes items such as (a) non-contact generation of mechanical vibrations in VHTR components via thermal expansion created by high-intensity laser; (b) development and incorporation of Synthetic Aperture Focusing Technique (SAFT) for elevating the accuracy of 3D imaging in highly noisy environments with minimal accessible surface; (c) further analytical and computational developments to facilitate the reconstruction of diffuse damage (e.g. microcracks) in nuclear graphite as they lead to the dispersion of elastic waves, (d) concept of model updating for accurate tracking of the evolution of material damage via periodic inspections; (d) adoption of the Bayesian framework to obtain information on the certainty of obtained images; and (e) optimization of the computational scheme toward real-time, model-based imaging of damage in VHTR core components.« less

Phase-resolved acoustic radiation force optical coherence elastography

NASA Astrophysics Data System (ADS)

Qi, Wenjuan; Chen, Ruimin; Chou, Lidek; Liu, Gangjun; Zhang, Jun; Zhou, Qifa; Chen, Zhongping

2012-11-01

Many diseases involve changes in the biomechanical properties of tissue, and there is a close correlation between tissue elasticity and pathology. We report on the development of a phase-resolved acoustic radiation force optical coherence elastography method (ARF-OCE) to evaluate the elastic properties of tissue. This method utilizes chirped acoustic radiation force to produce excitation along the sample's axial direction, and it uses phase-resolved optical coherence tomography (OCT) to measure the vibration of the sample. Under 500-Hz square wave modulated ARF signal excitation, phase change maps of tissue mimicking phantoms are generated by the ARF-OCE method, and the resulting Young's modulus ratio is correlated with a standard compression test. The results verify that this technique could efficiently measure sample elastic properties accurately and quantitatively. Furthermore, a three-dimensional ARF-OCE image of the human atherosclerotic coronary artery is obtained. The result indicates that our dynamic phase-resolved ARF-OCE method can delineate tissues with different mechanical properties.

Findings in Ps-H scattering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ray, Hasi

2006-06-15

The best three-channel projectile-inelastic close-coupling approximation (CCA) is used to study the resonances in positronium (Ps) and hydrogen (H) scattering at the energy region below the inelastic threshold. The s-wave elastic phase shifts and s-wave elastic cross sections are studied using the static-exchange, two- and three-channel projectile-inelastic CCA for both the singlet (+) and triplet (-) channels. The singlet resonances detected using different CCA schemes confirm previous predictions [Drachman and Houston, Phys. Rev. A 12, 885 (1975); Page, J. Phys. B. 9, 1111 (1976)]. We report a resonance in the triplet channel too using the present three-channel CCA scheme.

Emergence of charge density waves and a pseudogap in single-layer TiTe2.

PubMed

Chen, P; Pai, Woei Wu; Chan, Y-H; Takayama, A; Xu, C-Z; Karn, A; Hasegawa, S; Chou, M Y; Mo, S-K; Fedorov, A-V; Chiang, T-C

2017-09-11

Two-dimensional materials constitute a promising platform for developing nanoscale devices and systems. Their physical properties can be very different from those of the corresponding three-dimensional materials because of extreme quantum confinement and dimensional reduction. Here we report a study of TiTe 2 from the single-layer to the bulk limit. Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy and spectroscopy, we observed the emergence of a (2 × 2) charge density wave order in single-layer TiTe 2 with a transition temperature of 92 ± 3 K. Also observed was a pseudogap of about 28 meV at the Fermi level at 4.2 K. Surprisingly, no charge density wave transitions were observed in two-layer and multi-layer TiTe 2 , despite the quasi-two-dimensional nature of the material in the bulk. The unique charge density wave phenomenon in the single layer raises intriguing questions that challenge the prevailing thinking about the mechanisms of charge density wave formation.Due to reduced dimensionality, the properties of 2D materials are often different from their 3D counterparts. Here, the authors identify the emergence of a unique charge density wave (CDW) order in monolayer TiTe 2 that challenges the current understanding of CDW formation.

Ultrasonic Tomography of Fractured Rocks to Characterize Elastic Weakening Induced by Finite-Amplitude Waves

NASA Astrophysics Data System (ADS)

Riviere, J.; Roux, P.

2017-12-01

The use of seismic noise in seismology enables one to detect small velocity changes induced by earthquakes, earth tides or volcanic activity. In particular, co-seismic drops in velocity followed by a slow relaxation back (or partially back) to the original velocity have been observed across various tectonic regions. The co-seismic drop is typically attributed to the creation of damage within the fault zone, while the slow recovery is attributed to post-seismic healing processes. At the laboratory scale, a dynamic perturbation of strain amplitude as low as 10-6 in rocks also results in a transient elastic softening, followed by a log(t)-type relaxation back to the initial state once the perturbation is turned off. This suggests that radiated waves produced during unstable slip are partially responsible for the co-seismic velocity drops. The main objective of this work is to help interpret the elastic changes observed in the field and in particular to disentangle velocity drops that originate from damage creation along the slip surface from the ones produced during radiation of finite-amplitude waves. To do so, we use a technique called Dynamic Acousto-Elastic Testing that provides comprehensive details on the nonlinear elastic response of consolidated granular media (e.g. rocks), including tension/compression asymmetry, hysteretic behaviors as well as conditioning and relaxation effects. Such technique uses a pump-probe scheme where a high frequency, low amplitude wave probes the state of a sample that is dynamically disturbed by a low frequency, large amplitude pump wave. While previous work typically involved a single pair of probing transducers, here we use two dense arrays of ultrasonic transducers to image a sample of Westerly granite with a complex fracture. We apply double beamforming to disentangle complex arrivals and conduct ray-based and finite-frequency tomography using both travel time and amplitude information. By comparing images obtained before, during and after the pump wave disturbance, we are able to locate and characterize elastic changes within the sample. We discuss their locations with regard to low velocity/high attenuation zones and relate our observations to large-scale data.

Stress fields around two pores in an elastic body: exact quadrature domain solutions.

PubMed

Crowdy, Darren

2015-08-08

Analytical solutions are given for the stress fields, in both compression and far-field shear, in a two-dimensional elastic body containing two interacting non-circular pores. The two complex potentials governing the solutions are found by using a conformal mapping from a pre-image annulus with those potentials expressed in terms of the Schottky-Klein prime function for the annulus. Solutions for a three-parameter family of elastic bodies with two equal symmetric pores are presented and the compressibility of a special family of pore pairs is studied in detail. The methodology extends to two unequal pores. The importance for boundary value problems of plane elasticity of a special class of planar domains known as quadrature domains is also elucidated. This observation provides the route to generalization of the mathematical approach here to finding analytical solutions for the stress fields in bodies containing any finite number of pores.

Measurement of Shear Elastic Moduli in Quasi-Incompressible Soft Solids

NASA Astrophysics Data System (ADS)

Rénier, Mathieu; Gennisson, Jean-Luc; Barrière, Christophe; Catheline, Stefan; Tanter, Mickaël; Royer, Daniel; Fink, Mathias

2008-06-01

Recently a nonlinear equation describing the plane shear wave propagation in isotropic quasi-incompressible media has been developed using a new expression of the strain energy density, as a function of the second, third and fourth order shear elastic constants (respectively μ, A, D) [1]. In such a case, the shear nonlinearity parameter βs depends only from these last coefficients. To date, no measurement of the parameter D have been carried out in soft solids. Using a set of two experiments, acoustoelasticity and finite amplitude shear waves, the shear elastic moduli up to the fourth order of soft solids are measured. Firstly, this theoretical background is applied to the acoustoelasticity theory, giving the variations of the shear wave speed as a function of the stress applied to the medium. From such variations, both linear (μ) and third order shear modulus (A) are deduced in agar-gelatin phantoms. Experimentally the radiation force induced by a focused ultrasound beam is used to generate quasi-plane linear shear waves within the medium. Then the shear wave propagation is imaged with an ultrafast ultrasound scanner. Secondly, in order to give rise to finite amplitude plane shear waves, the radiation force generation technique is replaced by a vibrating plate applied at the surface of the phantoms. The propagation is also imaged using the same ultrafast scanner. From the assessment of the third harmonic amplitude, the nonlinearity parameter βS is deduced. Finally, combining these results with the acoustoelasticity experiment, the fourth order modulus (D) is deduced. This set of experiments provides the characterization, up to the fourth order, of the nonlinear shear elastic moduli in quasi-incompressible soft media. Measurements of the A moduli reveal that while the behaviors of both soft solids are close from a linear point of view, the corresponding nonlinear moduli A are quite different. In a 5% agar-gelatin phantom, the fourth order elastic constant D is found to be 30±10 kPa.

Feasibility of Using Elastic Wave Velocity Monitoring for Early Warning of Rainfall-Induced Slope Failure.

PubMed

Chen, Yulong; Irfan, Muhammad; Uchimura, Taro; Zhang, Ke

2018-03-27

Rainfall-induced landslides are one of the most widespread slope instability phenomena posing a serious risk to public safety worldwide so that their temporal prediction is of great interest to establish effective warning systems. The objective of this study is to determine the effectiveness of elastic wave velocities in the surface layer of the slope in monitoring, prediction and early warning of landslide. The small-scale fixed and varied, and large-scale slope model tests were conducted. Analysis of the results has established that the elastic wave velocity continuously decreases in response of moisture content and deformation and there was a distinct surge in the decrease rate of wave velocity when failure was initiated. Based on the preliminary results of this analysis, the method using the change in elastic wave velocity proves superior for landslide early warning and suggests that a warning be issued at switch of wave velocity decrease rate.

Approximate nonlinear multiparameter inversion for multicomponent single and double P-wave scattering in isotropic elastic media

NASA Astrophysics Data System (ADS)

Ouyang, Wei; Mao, Weijian

2018-07-01

An asymptotic quadratic true-amplitude inversion method for isotropic elastic P waves is proposed to invert medium parameters. The multicomponent P-wave scattered wavefield is computed based on a forward relationship using second-order Born approximation and corresponding high-frequency ray theoretical methods. Within the local double scattering mechanism, the P-wave transmission factors are elaborately calculated, which results in the radiation pattern for P-wave scattering being a quadratic combination of the density and Lamé's moduli perturbation parameters. We further express the elastic P-wave scattered wavefield in a form of generalized Radon transform. After introducing classical backprojection operators, we obtain an approximate solution of the inverse problem by solving a quadratic nonlinear system. Numerical tests with synthetic data computed by finite-differences scheme demonstrate that our quadratic inversion can accurately invert perturbation parameters for strong perturbations, compared with the P-wave single-scattering linear inversion method. Although our inversion strategy here is only syncretized with P-wave scattering, it can be extended to invert multicomponent elastic data containing both P- and S-wave information.

The two Faces of Equipartition

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Perton, M.; Rodriguez-Castellanos, A.; Campillo, M.; Weaver, R. L.; Rodriguez, M.; Prieto, G.; Luzon, F.; McGarr, A.

2008-12-01

Equipartition is good. Beyond its philosophical implications, in many instances of statistical physics it implies that the available kinetic and potential elastic energy, in phase space, is distributed in the same fixed proportions among the possible "states". There are at least two distinct and complementary descriptions of such states in a diffuse elastic wave field u(r,t). One asserts that u may be represented as an incoherent isotropic superposition of incident plane waves of different polarizations. Each type of wave has an appropriate share of the available energy. This definition introduced by Weaver is similar to the room acoustics notion of a diffuse field, and it suffices to permit prediction of field correlations. The other description assumes that the degrees of freedom of the system, in this case, the kinetic energy densities, are all incoherently excited with equal expected amplitude. This definition, introduced by Maxwell, is also familiar from room acoustics using the normal modes of vibration within an arbitrarily large body. Usually, to establish if an elastic field is diffuse and equipartitioned only the first description has been applied, which requires the separation of dilatational and shear waves using carefully designed experiments. When the medium is bounded by an interface, waves of other modes, for example Rayleigh waves, complicate the measurement of these energies. As a consequence, it can be advantageous to use the second description. Moreover, each spatial component of the energy densities is linked, when an elastic field is diffuse and equipartitioned, to the component of the imaginary part of the Green function at the source. Accordingly, one can use the second description to retrieve the Green function and obtain more information about the medium. The equivalence between the two descriptions of equipartition are given for an infinite space and extended to the case of a half-space. These two descriptiosn are equivalent thanks to the relationship of average autocorrelations with the imaginary part of Green function at the source. Preliminary results are displayed in data sets from Chilpancingo, Mexico, and the Tautona Gold Mine, South Africa, that strongly suggest that equipartition, that guarantees the diffuse nature of seismic fields, has more than one face. Acknowledgements. Partial supports from DGAPA-UNAM, Project IN114706, Mexico; from Proyect MCyT CGL2005-05500-C02/BTE, Spain; from project DyETI of INSU-CNRS, France, and from the Instituto Mexicano del Petróleo are greatly appreciated.

Superficial ultrasound shear wave speed measurements in soft and hard elasticity phantoms: repeatability and reproducibility using two ultrasound systems.

PubMed

Dillman, Jonathan R; Chen, Shigao; Davenport, Matthew S; Zhao, Heng; Urban, Matthew W; Song, Pengfei; Watcharotone, Kuanwong; Carson, Paul L

2015-03-01

There is a paucity of data available regarding the repeatability and reproducibility of superficial shear wave speed (SWS) measurements at imaging depths relevant to the pediatric population. To assess the repeatability and reproducibility of superficial shear wave speed measurements acquired from elasticity phantoms at varying imaging depths using three imaging methods, two US systems and multiple operators. Soft and hard elasticity phantoms manufactured by Computerized Imaging Reference Systems Inc. (Norfolk, VA) were utilized for our investigation. Institution No. 1 used an Acuson S3000 US system (Siemens Medical Solutions USA, Malvern, PA) and three shear wave imaging method/transducer combinations, while institution No. 2 used an Aixplorer US system (SuperSonic Imagine, Bothell, WA) and two different transducers. Ten stiffness measurements were acquired from each phantom at three depths (1.0 cm, 2.5 cm and 4.0 cm) by four operators at each institution. Student's t-test was used to compare SWS measurements between imaging techniques, while SWS measurement agreement was assessed with two-way random effects single-measure intra-class correlation coefficients (ICCs) and coefficients of variation. Mixed model regression analysis determined the effect of predictor variables on SWS measurements. For the soft phantom, the average of mean SWS measurements across the various imaging methods and depths was 0.84 ± 0.04 m/s (mean ± standard deviation) for the Acuson S3000 system and 0.90 ± 0.02 m/s for the Aixplorer system (P = 0.003). For the hard phantom, the average of mean SWS measurements across the various imaging methods and depths was 2.14 ± 0.08 m/s for the Acuson S3000 system and 2.07 ± 0.03 m/s Aixplorer system (P > 0.05). The coefficients of variation were low (0.5-6.8%), and interoperator agreement was near-perfect (ICCs ≥ 0.99). Shear wave imaging method and imaging depth significantly affected measured SWS (P < 0.0001). Superficial shear wave speed measurements in elasticity phantoms demonstrate minimal variability across imaging method/transducer combinations, imaging depths and operators. The exact clinical significance of this variation is uncertain and may change according to organ and specific disease state.

Diffusely scattered and transmitted elastic waves by random rough solid-solid interfaces using an elastodynamic Kirchhoff approximation

NASA Astrophysics Data System (ADS)

Shi, Fan; Lowe, Mike; Craster, Richard

2017-06-01

Elastic waves scattered by random rough interfaces separating two distinct media play an important role in modeling phonon scattering and impact upon thermal transport models, and are also integral to ultrasonic inspection. We introduce theoretical formulas for the diffuse field of elastic waves scattered by, and transmitted across, random rough solid-solid interfaces using the elastodynamic Kirchhoff approximation. The new formulas are validated by comparison with numerical Monte Carlo simulations, for a wide range of roughness (rms σ ≤λ /3 , correlation length λ0≥ wavelength λ ), demonstrating a significant improvement over the widely used small-perturbation approach, which is valid only for surfaces with small rms values. Physical analysis using the theoretical formulas derived here demonstrates that increasing the rms value leads to a considerable change of the scattering patterns for each mode. The roughness has different effects on the reflection and the transmission, with a strong dependence on the material properties. In the special case of a perfect match of the wave speed of the two solid media, the transmission is the same as the case for a flat interface. We pay particular attention to scattering in the specular direction, often used as an observable quantity, in terms of the roughness parameters, showing a peak at an intermediate value of rms; this rms value coincides with that predicted by the Rayleigh parameter.

Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

NASA Technical Reports Server (NTRS)

Newman, J. C., Jr.; Bigelow, C. A.; Shivakumar, K. N.

1993-01-01

Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastic-perfectly plastic material under monotonic and cyclic loading. Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor alpha(sub g) was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region. Values of alpha(sub g) were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.

Computing the Dynamic Response of a Stratified Elastic Half Space Using Diffuse Field Theory

NASA Astrophysics Data System (ADS)

Sanchez-Sesma, F. J.; Perton, M.; Molina Villegas, J. C.

2015-12-01

The analytical solution for the dynamic response of an elastic half-space for a normal point load at the free surface is due to Lamb (1904). For a tangential force, we have Chaós (1960) formulae. For an arbitrary load at any depth within a stratified elastic half space, the resulting elastic field can be given in the same fashion, by using an integral representation in the radial wavenumber domain. Typically, computations use discrete wave number (DWN) formalism and Fourier analysis allows for solution in space and time domain. Experimentally, these elastic Greeńs functions might be retrieved from ambient vibrations correlations when assuming a diffuse field. In fact, the field could not be totally diffuse and only parts of the Green's functions, associated to surface or body waves, are retrieved. In this communication, we explore the computation of Green functions for a layered media on top of a half-space using a set of equipartitioned elastic plane waves. Our formalism includes body and surface waves (Rayleigh and Love waves). These latter waves correspond to the classical representations in terms of normal modes in the asymptotic case of large separation distance between source and receiver. This approach allows computing Green's functions faster than DWN and separating the surface and body wave contributions in order to better represent Green's function experimentally retrieved.

Observation of two-dimensional Faraday waves in extremely shallow depth.

PubMed

Li, Xiaochen; Yu, Zhengyue; Liao, Shijun

2015-09-01

A family of two-dimensional Faraday waves in extremely shallow depth (1 mm to 2 mm) of absolute ethanol are observed experimentally using a Hele-Shaw cell that vibrates vertically. The same phenomena are not observed by means of water, ethanol solution, and silicone oil. These Faraday waves are quite different from the traditional ones. These phenomena are helpful to deepen and enrich our understandings about Faraday waves, and besides provide a challenging problem for computational fluid dynamics.

Intermediate energy proton-deuteron elastic scattering

NASA Technical Reports Server (NTRS)

Wilson, J. W.

1973-01-01

A fully symmetrized multiple scattering series is considered for the description of proton-deuteron elastic scattering. An off-shell continuation of the experimentally known twobody amplitudes that retains the exchange symmeteries required for the calculation is presented. The one boson exchange terms of the two body amplitudes are evaluated exactly in this off-shell prescription. The first two terms of the multiple scattering series are calculated explicitly whereas multiple scattering effects are obtained as minimum variance estimates from the 146-MeV data of Postma and Wilson. The multiple scattering corrections indeed consist of low order partial waves as suggested by Sloan based on model studies with separable interactions. The Hamada-Johnston wave function is shown consistent with the data for internucleon distances greater than about 0.84 fm.

Comparison of Shuttle Imaging Radar-B ocean wave image spectra with linear model predictions based on aircraft measurements

NASA Technical Reports Server (NTRS)

Monaldo, Frank M.; Lyzenga, David R.

1988-01-01

During October 1984, coincident Shuttle Imaging Radar-B synthetic aperture radar (SAR) imagery and wave measurements from airborne instrumentation were acquired. The two-dimensional wave spectrum was measured by both a radar ocean-wave spectrometer and a surface-contour radar aboard the aircraft. In this paper, two-dimensional SAR image intensity variance spectra are compared with these independent measures of ocean wave spectra to verify previously proposed models of the relationship between such SAR image spectra and ocean wave spectra. The results illustrate both the functional relationship between SAR image spectra and ocean wave spectra and the limitations imposed on the imaging of short-wavelength, azimuth-traveling waves.

Elastic wave induced by friction as a signature of human skin ageing and gender effect.

PubMed

Djaghloul, M; Morizot, F; Zahouani, H

2016-08-01

In this work, we propose an innovative approach based on a rotary tribometer coupled with laser velocimetry for measuring the elastic wave propagation on the skin. The method is based on a dynamic contact with the control of the normal force (Fn ), the contact length and speed. During the test a quantification of the friction force is produced. The elastic wave generated by friction is measured at the surface of the skin 35 mm from the source of friction exciter. In order to quantify the spectral range and the energy property of the wave generated, we have used laser velocimetry whose spot laser diameter is 120 μm, which samples the elastic wave propagation at a frequency which may reach 100 kHz. In this configuration, the speaker is the friction exciter and the listener the laser velocimetry. In order to perform non-invasive friction tests, the normal stress has been set to 0.3 N and the rotary velocity to 3 revolutions per second, which involves a sliding velocity of 63 mm/s. This newly developed innovative tribometer has been used for the analysis of the elastic wave propagation induced by friction on human skin during chronological ageing and gender effect. Measurements in vivo have been made on 60 healthy men and women volunteers, aged from 25 to 70. The results concerning the energy of the elastic wave signature induced by friction show a clear difference between the younger and older groups in the range of a low band of frequencies (0-200 Hz). The gender effect was marked by a 20% decrease in the energy of elastic wave propagation in the female group. © 2015 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.

TH-A-207B-01: Basics and Current Implementations of Ultrasound Imaging of Shear Wave Speed and Elasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, S.

Imaging of tissue elastic properties is a relatively new and powerful approach to one of the oldest and most important diagnostic tools. Imaging of shear wave speed with ultrasound is has been added to most high-end ultrasound systems. Understanding this exciting imaging mode aiding its most effective use in medicine can be a rewarding effort for medical physicists and other medical imaging and treatment professionals. Assuring consistent, quantitative measurements across the many ultrasound systems in a typical imaging department will constitute a major step toward realizing the great potential of this technique and other quantitative imaging. This session will targetmore » these two goals with two presentations. A. Basics and Current Implementations of Ultrasound Imaging of Shear Wave Speed and Elasticity - Shigao Chen, Ph.D. Learning objectives-To understand: Introduction: Importance of tissue elasticity measurement Strain vs. shear wave elastography (SWE), beneficial features of SWE The link between shear wave speed and material properties, influence of viscosity Generation of shear waves External vibration (Fibroscan) ultrasound radiation force Point push Supersonic push (Aixplorer) Comb push (GE Logiq E9) Detection of shear waves Motion detection from pulse-echo ultrasound Importance of frame rate for shear wave imaging Plane wave imaging detection How to achieve high effective frame rate using line-by-line scanners Shear wave speed calculation Time to peak Random sample consensus (RANSAC) Cross correlation Sources of bias and variation in SWE Tissue viscosity Transducer compression or internal pressure of organ Reflection of shear waves at boundaries B. Elasticity Imaging System Biomarker Qualification and User Testing of Systems – Brian Garra, M.D. Learning objectives-To understand: Goals Review the need for quantitative medical imaging Provide examples of quantitative imaging biomarkers Acquaint the participant with the purpose of the RSNA Quantitative Imaging Biomarker Alliance and the need for such an organization Review the QIBA process for creating a quantitative biomarker Summarize steps needed to verify adherence of site, operators, and imaging systems to a QIBA profile Underlying Premise and Assumptions Objective, quantifiable results are needed to enhance the value of diagnostic imaging in clinical practice Reasons for quantification Evidence based medicine requires objective, not subjective observer data Computerized decision support tools (eg CAD) generally require quantitative input. Quantitative, reproducible measures are more easily used to develop personalized molecular medical diagnostic and treatment systems What is quantitative imaging? Definition from Imaging Metrology Workshop The Quantitative Imaging Biomarker Alliance Formation 2008 Mission Structure Example Imaging Biomarkers Being Explored Biomarker Selection Groundwork Draft Protocol for imaging and data evaluation QIBA Profile Drafting Equipment and Site Validation Technical Clinical Site and Equipment QA and Compliance Checking Ultrasound Elasticity Estimation Biomarker US Elasticity Estimation Background Current Status and Problems Biomarker Selection-process and outcome US SWS for Liver Fibrosis Biomarker Work Groundwork Literature search and analysis results Phase I phantom testing-Elastic phantoms Phase II phantom testing-Viscoelastic phantoms Digital Simulated Data Protocol and Profile Drafting Protocol: based on UPICT and existing literature and standards bodies protocols Profile-Current claims, Manufacturer specific appendices What comes after the profile Profile Validation Technical validation Clinical validation QA and Compliance Possible approaches Site Operator testing Site protocol re-evaluation Imaging system Manufacturer testing and attestation User acceptance testing and periodic QA Phantom Tests Digital Phantom Based Testing Standard QA Testing Remediation Schemes Profile Evolution Towards additional applications Towards higher accuracy and precision Supported in part by NIH contract HHSN268201300071C from NIBIB. Collaboration with GE Global Research, no personal support.; S. Chen, Some technologies described in this presentation have been licensed. Mayo Clinic and Dr. Chen have financial interests these technologies.« less

Constitutive relations in multidimensional isotropic elasticity and their restrictions to subspaces of lower dimensions

NASA Astrophysics Data System (ADS)

Georgievskii, D. V.

2017-07-01

The mechanical meaning and the relationships among material constants in an n-dimensional isotropic elastic medium are discussed. The restrictions of the constitutive relations (Hooke's law) to subspaces of lower dimension caused by the conditions that an m-dimensional strain state or an m-dimensional stress state (1 ≤ m < n) is realized in the medium. Both the terminology and the general idea of the mathematical construction are chosen by analogy with the case n = 3 and m = 2, which is well known in the classical plane problem of elasticity theory. The quintuples of elastic constants of the same medium that enter both the n-dimensional relations and the relations written out for any m-dimensional restriction are expressed in terms of one another. These expressions in terms of the known constants, for example, of a three-dimensional medium, i.e., the classical elastic constants, enable us to judge the material properties of this medium immersed in a space of larger dimension.

Properties of seismic absorption induced reflections

NASA Astrophysics Data System (ADS)

Zhao, Haixia; Gao, Jinghuai; Peng, Jigen

2018-05-01

Seismic reflections at an interface are often regarded as the variation of the acoustic impedance (product of seismic velocity and density) in a medium. In fact, they can also be generated due to the difference in absorption of the seismic energy. In this paper, we investigate the properties of such reflections. Based on the diffusive-viscous wave equation and elastic diffusive-viscous wave equation, we investigate the dependency of the reflection coefficients on frequency, and their variations with incident angles. Numerical results at a boundary due to absorption contrasts are compared with those resulted from acoustic impedance variation. It is found that, the reflection coefficients resulted from absorption depend significantly on the frequency especially at lower frequencies, but vary very slowly at small incident angles. At the higher frequencies, the reflection coefficients of diffusive-viscous wave and elastic diffusive-viscous wave are close to those of acoustic and elastic cases, respectively. On the other hand, the reflections caused by acoustic impedance variation are independent of frequency but vary distinctly with incident angles before the critical angle. We also investigate the difference between the seismograms generated in the two different media. The numerical results show that the amplitudes of these reflected waves are attenuated and their phases are shifted. However, the reflections obtained by acoustic impedance contrast, show no significant amplitude attenuation and phase shift.

Elastic and acoustic wavefield decompositions and application to reverse time migrations

NASA Astrophysics Data System (ADS)

Wang, Wenlong

P- and S-waves coexist in elastic wavefields, and separation between them is an essential step in elastic reverse-time migrations (RTMs). Unlike the traditional separation methods that use curl and divergence operators, which do not preserve the wavefield vector component information, we propose and compare two vector decomposition methods, which preserve the same vector components that exist in the input elastic wavefield. The amplitude and phase information is automatically preserved, so no amplitude or phase corrections are required. The decoupled propagation method is extended from elastic to viscoelastic wavefields. To use the decomposed P and S vector wavefields and generate PP and PS images, we create a new 2D migration context for isotropic, elastic RTM which includes PS vector decomposition; the propagation directions of both incident and reflected P- and S-waves are calculated directly from the stress and particle velocity definitions of the decomposed P- and S-wave Poynting vectors. Then an excitation-amplitude image condition that scales the receiver wavelet by the source vector magnitude produces angle-dependent images of PP and PS reflection coefficients with the correct polarities, polarization, and amplitudes. It thus simplifies the process of obtaining PP and PS angle-domain common-image gathers (ADCIGs); it is less effort to generate ADCIGs from vector data than from scalar data. Besides P- and S-waves decomposition, separations of up- and down-going waves are also a part of processing of multi-component recorded data and propagating wavefields. A complex trace based up/down separation approach is extended from acoustic to elastic, and combined with P- and S-wave decomposition by decoupled propagation. This eliminates the need for a Fourier transform over time, thereby significantly reducing the storage cost and improving computational efficiency. Wavefield decomposition is applied to both synthetic elastic VSP data and propagating wavefield snapshots. Poynting vectors obtained from the particle-velocity and stress fields after P/S and up/down decompositions are much more accurate than those without. The up/down separation algorithm is also applicable in acoustic RTMs, where both (forward-time extrapolated) source and (reverse-time extrapolated) receiver wavefields are decomposed into up-going and down-going parts. Together with the crosscorrelation imaging condition, four images (down-up, up-down, up-up and down-down) are generated, which facilitate the analysis of artifacts and the imaging ability of the four images. Artifacts may exist in all the decomposed images, but their positions and types are different. The causes of artifacts in different images are explained and illustrated with sketches and numerical tests.

Spin-wave energy dispersion of a frustrated spin-½ Heisenberg antiferromagnet on a stacked square lattice.

PubMed

Majumdar, Kingshuk

2011-03-23

The effects of interlayer coupling and spatial anisotropy on the spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-½ Heisenberg antiferromagnet (HAFM) are investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM have similar qualitative features to the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for the strength of the interlayer coupling, spatial anisotropy parameter, and magnetic frustration.

Propagation of elastic wave in nanoporous material with distributed cylindrical nanoholes

NASA Astrophysics Data System (ADS)

Qiang, FangWei; Wei, PeiJun; Liu, XiQiang

2013-08-01

The effective propagation constants of plane longitudinal and shear waves in nanoporous material with random distributed parallel cylindrical nanoholes are studied. The surface elastic theory is used to consider the surface stress effects and to derive the nontraditional boundary condition on the surface of nanoholes. The plane wave expansion method is used to obtain the scattering waves from the single nanohole. The multiple scattering effects are taken into consideration by summing the scattered waves from all scatterers and performing the configuration averaging of random distributed scatterers. The effective propagation constants of coherent waves along with the associated dynamic effective elastic modulus are numerically evaluated. The influences of surface stress are discussed based on the numerical results.

Berni Alder and Phase Transitions in Two Dimensions

NASA Astrophysics Data System (ADS)

Kosterlitz, J. Michael

I do not know Berni Alder as a person, but I feel that I know him well through his seminal paper "Phase Transition in Elastic Disks𠇍 by B. J. Alder and T. E. Wainwright [1962], which was essential in motivating David Thouless and myself to think about phase transitions in two dimensional systems with a continuous symmetry. In the early 1970's, the conventional wisdom was that a crystalline solid could not exist in a two dimensional world because of the rigorous Mermin-Wagner theorem prohibiting true long range translational order at any non-zero temperature. This contradiction was settled by the theory of dislocation mediated melting to an intermediate hexatic phase followed by a second transition to the isotropic fluid at a higher temperature. This scenario, with its associated sophisticated theory, seemed to settle the controversy of two dimensional melting once and for all. However, in our elation at understanding the fundamental physics and the essential excitations of melting in 2D, we had all forgotten that the early work of Berni Alder also showed that this melting involved a weak first order transition while theory now predicted melting by two successive continuous transitions with no discontinuity in area at the critical pressure. This discrepancy could be hand waved away by arguing that Berni's system was far too small and his computers far too slow so that the areal discontinuity could be due to finite size effects or to failing to equilibrate the system. Experiments were not able to resolve the order of the transitions, but seemed to agree quantitatively with theory…

Investigating the thermally induced acoustoelastic effect in isotropic media with Lamb waves

PubMed Central

Dodson, Jacob C.; Inman, Daniel J.

2014-01-01

Elastic wave velocities in metallic structures are affected by variations in environmental conditions such as changing temperature. This paper extends the theory of acoustoelasticity by allowing thermally induced strains in unconstrained isotropic media, and it experimentally examines the velocity variation of Lamb waves in aluminum plates (AL-6061) due to isothermal temperature deviations. This paper presents both thermally induced acoustoelastic constants and thermally varying effective Young's modulus and Poisson's ratio which include the third order elastic material constants. The experimental thermal sensitivity of the phase velocity (∂vP/∂θ) for both the symmetric and antisymmetric modes are bounded by two theories, the acoustoelastic Lamb wave theory with thermo-acoustoelastic tensors and the thermoelastic Lamb wave theory using an effective thermo-acoustoelastic moduli. This paper shows the theoretical thermally induced acoustoelastic Lamb wave thermal sensitivity (∂vP/∂θ) is an upper bound approximation of the experimental thermal changes, but the acoustoelastic Lamb wave theory is not valid for predicting the antisymmetric (A0) phase velocity at low frequency-thickness values, <1.55 MHz mm for various temperatures. PMID:25373955

The Fundamental Structure and the Reproduction of Spiral Wave in a Two-Dimensional Excitable Lattice.

PubMed

Qian, Yu; Zhang, Zhaoyang

2016-01-01

In this paper we have systematically investigated the fundamental structure and the reproduction of spiral wave in a two-dimensional excitable lattice. A periodically rotating spiral wave is introduced as the model to reproduce spiral wave artificially. Interestingly, by using the dominant phase-advanced driving analysis method, the fundamental structure containing the loop structure and the wave propagation paths has been revealed, which can expose the periodically rotating orbit of spiral tip and the charity of spiral wave clearly. Furthermore, the fundamental structure is utilized as the core for artificial spiral wave. Additionally, the appropriate parameter region, in which the artificial spiral wave can be reproduced, is studied. Finally, we discuss the robustness of artificial spiral wave to defects.

Governing equations for 1D opto-mechanical vibrations of elastic cubical micro-resonators

NASA Astrophysics Data System (ADS)

Sobhani, Hassan; Zohrabi, Mehdi

2018-03-01

In this paper by employing the Lagrangian method, the effect of the radiation pressure on the coupling between the optical and mechanical modes in an elastic cavity is surveyed. The radiation pressure couldn't be considered as an external force because the electromagnetic waves are non-separable part of the elastic media. Due to the deformation of elastic media, the electromagnetic waves is modified as a result of the element velocity. To consider the electromagnetic evolution, it is preferred to employ the Lagrangian method instead of the second Newton's law. Here, using an elastic frame, governing equations on opto-mechanical oscillations in an elastic media are derived. In a specific case, by comparing the results to the other methods, it shown that this method is more accurate because the exchange of electromagnetic waves by regarding the movement of the elastic media due to deform is considered.

New Experimental Setup for High-Pressure High-Temperature Gigahertz Ultrasonic Interferometry

NASA Astrophysics Data System (ADS)

Kantor, A. P.; Kantor, I. Y.; Dubrovinsky, L. S.; Jacobsen, S. D.

2005-12-01

The only direct information about Earth's interior comes from seismological observations of sound wave velocities. In order to create compositional and mineralogical model from seismological data knowledge of the elastic properties and crystal chemistry of minerals is necessary. Gigahertz ultrasonic interferometry (GUI) is a relatively new tool used to measure single-crystal compressional and shear-wave travel times, which are converted to sound velocities and elastic moduli for direct application to problems in geophysics. Although possibility of simultaneous high-pressure and high-temperature GUI measurements in diamond anvil cell was demonstrated before up to temperature of 250°C, in situ pressure measurements were not possible. We developed new experimental setup for simultaneous GUI and pressure determination using a ruby fluorescence gouge. A diamond anvil cell is equipped with a miniature internal resistive heater with thermocouple fixed at a very small distance from the sample chamber. DAC is mounted at the rotating stage with 5 degrees of freedom (XYZ and two tilting degrees), that can be fixed in three different positions: on top of a P-buffer rod for compressional wave velocities measurement, on top of S-buffer rod for shear wave velocities measurement and under the microscope, equipped with laser and portable high-resolution spectrometer for ruby fluorescence measurement. DAC under high temperature could be moved between these three positions, and independent pressure, temperature, S and P wave velocities measurements could be done simultaneously at each data point. In addition to single-crystal elasticity measurements, ability of GUI for elasticity measurements of liquids was demonstrated. Compressional wave velocities in liquid argon were measured at high pressures and temperatures, showing the ability of GUI for studies equation of state of a liquid.

Directional ocean wave measurements in a coastal setting using a focused array imaging radar

DOE Office of Scientific and Technical Information (OSTI.GOV)

Frasier, S.J.; Liu, Y.; Moller, D.

1995-03-01

A unique focused array imaging Doppler radar was used to measure directional spectra of ocean surface waves in a nearshore experiment performed on the North Carolina Outer Banks. Radar images of the ocean surface`s Doppler velocity were used to generate two dimensional spectra of the radial component of the ocean surface velocity field. These are compared to simultaneous in-situ measurements made by a nearby array of submerged pressure sensors. Analysis of the resulting two-dimensional spectra include comparisons of dominant wave lengths, wave directions, and wave energy accounting for relative differences in water depth at the measurement locations. Limited estimates ofmore » the two-dimensional surface displacement spectrum are derived from the radar data. The radar measurements are analogous to those of interferometric synthetic aperture radars (INSAR), and the equivalent INSAR parameters are shown. The agreement between the remote and in-situ measurements suggests that an imaging Doppler radar is effective for these wave measurements at near grazing incidence angles.« less

Transversally periodic solitary gravity–capillary waves

PubMed Central

Milewski, Paul A.; Wang, Zhan

2014-01-01

When both gravity and surface tension effects are present, surface solitary water waves are known to exist in both two- and three-dimensional infinitely deep fluids. We describe here solutions bridging these two cases: travelling waves which are localized in the propagation direction and periodic in the transverse direction. These transversally periodic gravity–capillary solitary waves are found to be of either elevation or depression type, tend to plane waves below a critical transverse period and tend to solitary lumps as the transverse period tends to infinity. The waves are found numerically in a Hamiltonian system for water waves simplified by a cubic truncation of the Dirichlet-to-Neumann operator. This approximation has been proved to be very accurate for both two- and three-dimensional computations of fully localized gravity–capillary solitary waves. The stability properties of these waves are then investigated via the time evolution of perturbed wave profiles. PMID:24399922

Emergence of charge density waves and a pseudogap in single-layer TiTe 2

DOE PAGES

Chen, P.; Pai, Woei Wu; Chan, Y. -H.; ...

2017-09-11

Two-dimensional materials constitute a promising platform for developing nanoscale devices and systems. Their physical properties can be very different from those of the corresponding three-dimensional materials because of extreme quantum confinement and dimensional reduction. Here in this paper we report a study of TiTe 2 from the single-layer to the bulk limit. Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy and spectroscopy, we observed the emergence of a (2 × 2) charge density wave order in single-layer TiTe 2 with a transition temperature of 92 ± 3 K. Also observed was a pseudogap of about 28 meV at the Fermimore » level at 4.2 K. Surprisingly, no charge density wave transitions were observed in two-layer and multi-layer TiTe 2 , despite the quasi-two-dimensional nature of the material in the bulk. The unique charge density wave phenomenon in the single layer raises intriguing questions that challenge the prevailing thinking about the mechanisms of charge density wave formation.« less

Locating S-wave sources for the SPE-5 explosion using time reversal methods and a close-in, 1000 sensor network

NASA Astrophysics Data System (ADS)

Myers, S. C.; Pitarka, A.; Mellors, R. J.

2016-12-01

The Source Physics Experiment (SPE) is producing new data to study the generation of seismic waves from explosive sources. Preliminary results show that far-field S-waves are generated both within the non-elastic volume surrounding explosive sources and by P- to S-wave scattering. The relative contribution of non-elastic phenomenology and elastic-wave scattering to far-field S-waves has been debated for decades, and numerical simulations based on the SPE experiments are addressing this question. The match between observed and simulated data degrades with event-station distance and with increasing time in each seismogram. This suggests that a more accurate model of subsurface elastic properties could result in better agreement between observed and simulated seismograms. A detailed model of subsurface structure has been developed using geologic maps and the extensive database of borehole logs, but uncertainty in structural details remains high. The large N instrument deployment during the SPE-5 experiment offers an opportunity to use time-reversal techniques to back project the wave field into the subsurface to locate significant sources of scattered energy. The large N deployment was nominally 1000, 5 Hz sensors (500 Z and 500 3C geophones) deployed in a roughly rectangular array to the south and east of the SPE-5 shot. Sensor spacing was nominally 50 meters in the interior portion of the array and 100 meters in the outer region, with two dense lines at 25 m spacing. The array covers the major geologic boundary between the Yucca Flat basin and the granitic Climax Stock in which the SPE experiments have been conducted. Improved mapping of subsurface scatterers is expected to result in better agreement between simulated and observed seismograms and aid in our understanding of S-wave generation from explosions. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.

Cubic nonlinearity in shear wave beams with different polarizations

PubMed Central

Wochner, Mark S.; Hamilton, Mark F.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.

2008-01-01

A coupled pair of nonlinear parabolic equations is derived for the two components of the particle motion perpendicular to the axis of a shear wave beam in an isotropic elastic medium. The equations account for both quadratic and cubic nonlinearity. The present paper investigates, analytically and numerically, effects of cubic nonlinearity in shear wave beams for several polarizations: linear, elliptical, circular, and azimuthal. Comparisons are made with effects of quadratic nonlinearity in compressional wave beams. PMID:18529167

Monetary Policy Rules, Supply Shocks, and the Price-Level Elasticity of Aggregate Demand: A Graphical Examination.

ERIC Educational Resources Information Center

Kyer, Ben L.; Maggs, Gary E.

1995-01-01

Utilizes two-dimensional price and output graphs to demonstrate the way that the price-level elasticity of aggregate demand affects alternative monetary policy rules designed to cope with random aggregate supply shocks. Includes graphs illustrating price-level, real Gross Domestic Product (GDP), nominal GDP, and nominal money supply targeting.…

Uncertainty principles for inverse source problems for electromagnetic and elastic waves

NASA Astrophysics Data System (ADS)

Griesmaier, Roland; Sylvester, John

2018-06-01

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.

Numerical simulation of boundary layers. Part 2: Ribbon-induced transition in Blasius flow

NASA Technical Reports Server (NTRS)

Spalart, P.; Yang, K. S.

1986-01-01

The early three-dimensional stages of transition in Blasius boundary layers are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and random low-amplitude three-dimensional disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wave number increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. Agreement with experimental and theoretical results is discussed.

Distribution of soap molecules in flowing soap films

NASA Astrophysics Data System (ADS)

Kim, Ildoo; Sane, Aakash; Mandre, Shreyas

Flowing soap films are useful tools to simulate two-dimensional flows. The Marangoni elasticity due to the presence of soap molecules not only stabilizes the soap film but also imparts it compressibility to the two-dimensional flow in the soap film. Therefore, it is desirable to measure the surface concentration cs of soap molecules to understand the physics flowing soap films. In this study, we present an indirect measurement of cs, by making a direct measurement of the surface tension and the Marangoni elasticity. Using a two-stage model for soap distribution in the flows, the range of cs is calculated for different thickness and the soap solution concentration. Our model shows that the soap film will have the same cs for the range of parameters in popular use and in agreements with experimental data.

Variations in lithospheric thickness on Venus

NASA Technical Reports Server (NTRS)

Johnson, C. L.; Sandwell, David T.

1992-01-01

Recent analyses of Magellan data have indicated many regions exhibiting topograhic flexure. On Venus, flexure is associated predominantly with coronae and the chasmata with Aphrodite Terra. Modeling of these flexural signatures allows the elastic and mechanical thickness of the lithosphere to be estimated. In areas where the lithosphere is flexed beyond its elastic limit the saturation moment provides information on the strength of the lithosphere. Modeling of 12 flexural features on Venus has indicated lithospheric thicknesses comparable with terrestrial values. This has important implications for the venusian heat budget. Flexure of a thin elastic plate due simultaneously to a line load on a continuous plate and a bending moment applied to the end of a broken plate is considered. The mean radius and regional topographic gradient are also included in the model. Features with a large radius of curvature were selected so that a two-dimensional approximation could be used. Comparisons with an axisymmetric model were made for some features to check the validity of the two-dimensional assumption. The best-fit elastic thickness was found for each profile crossing a given flexural feature. In addition, the surface stress and bending moment at the first zero crossing of each profile were also calculated. Flexural amplitudes and elastic thicknesses obtained for 12 features vary significantly. Three examples of the model fitting procedures are discussed.

Two-dimensional topological superconducting phases emerged from d-wave superconductors in proximity to antiferromagnets

NASA Astrophysics Data System (ADS)

Zhu, Guo-Yi; Wang, Ziqiang; Zhang, Guang-Ming

2017-05-01

Motivated by the recent observations of nodeless superconductivity in the monolayer CuO2 grown on the Bi2Sr2CaCu2O8+δ substrates, we study the two-dimensional superconducting (SC) phases described by the two-dimensional t\\text-J model in proximity to an antiferromagnetic (AF) insulator. We found that i) the nodal d-wave SC state can be driven via a continuous transition into a nodeless d-wave pairing state by the proximity-induced AF field. ii) The energetically favorable pairing states in the strong field regime have extended s-wave symmetry and can be nodal or nodeless. iii) Between the pure d-wave and s-wave paired phases, there emerge two topologically distinct SC phases with (s+\\text{i}d) symmetry, i.e., the weak and strong pairing phases, and the weak pairing phase is found to be a Z 2 topological superconductor protected by valley symmetry, exhibiting robust gapless nonchiral edge modes. These findings strongly suggest that the high-T c superconductors in proximity to antiferromagnets can realize fully gapped symmetry-protected topological SC.

Flow Visualization by Elastic Light Scattering in the Boundary Layer of a Supersonic Flow

NASA Technical Reports Server (NTRS)

Herring, G. C.; Hillard, Mervin E., Jr.

2000-01-01

We demonstrate instantaneous flow visualization of the boundary layer region of a Mach 2.5 supersonic flow over a flat plate that is interacting with an impinging shock wave. Tests were performed in the Unitary Plan Wind Tunnel (UPWT) at NASA Langley Research Center. The technique is elastic light scattering using 10-nsec laser pulses at 532 nm. We emphasize that no seed material of any kind, including water (H2O), is purposely added to the flow. The scattered light comes from a residual impurity that normally exists in the flow medium after the air drying process. Thus, the technique described here differs from the traditional vapor-screen method, which is typically accomplished by the addition of extra H2O vapor to the airflow. The flow is visualized with a series of thin two-dimensional light sheets (oriented perpendicular to the streamwise direction) that are located at several positions downstream of the leading edge of the model. This geometry allows the direct observation of the unsteady flow structure in the spanwise dimension of the model and also allows the indirect observation of the boundary layer growth in the streamwise dimension.

Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain.

PubMed

Tirry, Wim; Schryvers, Dominique

2009-09-01

Ni-Ti is one of the most popular shape-memory alloys, a phenomenon resulting from a martensitic transformation. Commercial Ni-Ti-based alloys are often thermally treated to contain Ni(4)Ti(3) precipitates. The presence of these precipitates can introduce an extra transformation step related to the so-called R-phase. It is believed that the strain field surrounding the precipitates, caused by the matrix-precipitate lattice mismatch, lies at the origin of this intermediate transformation step. Atomic-resolution transmission electron microscopy in combination with geometrical phase analysis is used to measure the elastic strain field surrounding these precipitates. By combining measurements from two different crystallographic directions, the three-dimensional strain matrix is determined from two-dimensional measurements. Comparison of the measured strain matrix to the eigenstrain of the R-phase shows that both are very similar and that the introduction of the R-phase might indeed compensate the elastic strain introduced by the precipitate.

Linking a completely three-dimensional nanostrain to a structural transformation eigenstrain

NASA Astrophysics Data System (ADS)

Tirry, Wim; Schryvers, Dominique

2009-09-01

Ni-Ti is one of the most popular shape-memory alloys, a phenomenon resulting from a martensitic transformation. Commercial Ni-Ti-based alloys are often thermally treated to contain Ni4Ti3 precipitates. The presence of these precipitates can introduce an extra transformation step related to the so-called R-phase. It is believed that the strain field surrounding the precipitates, caused by the matrix-precipitate lattice mismatch, lies at the origin of this intermediate transformation step. Atomic-resolution transmission electron microscopy in combination with geometrical phase analysis is used to measure the elastic strain field surrounding these precipitates. By combining measurements from two different crystallographic directions, the three-dimensional strain matrix is determined from two-dimensional measurements. Comparison of the measured strain matrix to the eigenstrain of the R-phase shows that both are very similar and that the introduction of the R-phase might indeed compensate the elastic strain introduced by the precipitate.

Elastic energy distribution in bi-material lithosphere: implications for shear zone formation

NASA Astrophysics Data System (ADS)

So, B.; Yuen, D. A.

2013-12-01

Shear instability in the lithosphere can cause mechanical rupturing such as slab detachment and deep focus earthquake. Recent studies reported that bi-material interface, which refers to sharp elastic modulus contrast, plays an important role in triggering the instability [So and Yuen et al., 2012, GJI]. In present study, we performed two-dimensional numerical simulations to investigate the distribution of thermal-mechanical energy within the bi-material lithosphere. Under the far-field constant compression exerted on the domain, a larger elastic energy is accumulated into the compliant part than stiff medium. For instance, the compliant part has two times greater elastic energy density than surrounding stiff part, when the elastic modulus contrast between two different parts is five. Although these elastic energies in both parts are conversed into thermal energies after plastic yielding, denser elastic energy in the compliant is released more efficiently. This leads to efficient strength weakening and the subsequent ductile shear zone in the compliant part. We propose that strong shear heating occurs in lithosphere with the bi-material interface due to locally non-uniform distribution of the energy around the interface.

Time-resolved seismic tomography detects magma intrusions at Mount Etna.

PubMed

Patanè, D; Barberi, G; Cocina, O; De Gori, P; Chiarabba, C

2006-08-11

The continuous volcanic and seismic activity at Mount Etna makes this volcano an important laboratory for seismological and geophysical studies. We used repeated three-dimensional tomography to detect variations in elastic parameters during different volcanic cycles, before and during the October 2002-January 2003 flank eruption. Well-defined anomalous low P- to S-wave velocity ratio volumes were revealed. Absent during the pre-eruptive period, the anomalies trace the intrusion of volatile-rich (>/=4 weight percent) basaltic magma, most of which rose up only a few months before the onset of eruption. The observed time changes of velocity anomalies suggest that four-dimensional tomography provides a basis for more efficient volcano monitoring and short- and midterm eruption forecasting of explosive activity.

Numerical Study of a Three Dimensional Interaction between two bow Shock Waves and the Aerodynamic Heating on a Wedge Shaped Nose Cone

NASA Astrophysics Data System (ADS)

Wu, N.; Wang, J. H.; Shen, L.

2017-03-01

This paper presents a numerical investigation on the three-dimensional interaction between two bow shock waves in two environments, i.e. ground high-enthalpy wind tunnel test and real space flight, using Fluent 15.0. The first bow shock wave, also called induced shock wave, which is generated by the leading edge of a hypersonic vehicle. The other bow shock wave can be deemed objective shock wave, which is generated by the cowl clip of hypersonic inlet, and in this paper the inlet is represented by a wedge shaped nose cone. The interaction performances including flow field structures, aerodynamic pressure and heating are analyzed and compared between the ground test and the real space flight. Through the analysis and comparison, we can find the following important phenomena: 1) Three-dimensional complicated flow structures appear in both cases, but only in the real space flight condition, a local two-dimensional type IV interaction appears; 2) The heat flux and pressure in the interaction region are much larger than those in the no-interaction region in both cases, but the peak values of the heat flux and pressure in real space flight are smaller than those in ground test. 3) The interaction region on the objective surface are different in the two cases, and there is a peak value displacement of 3 mm along the stagnation line.

Control of spiral waves and turbulent states in a cardiac model by travelling-wave perturbations

NASA Astrophysics Data System (ADS)

Wang, Peng-Ye; Xie, Ping; Yin, Hua-Wei

2003-06-01

We propose a travelling-wave perturbation method to control the spatiotemporal dynamics in a cardiac model. It is numerically demonstrated that the method can successfully suppress the wave instability (alternans in action potential duration) in the one-dimensional case and convert spiral waves and turbulent states to the normal travelling wave states in the two-dimensional case. An experimental scheme is suggested which may provide a new design for a cardiac defibrillator.

Signatures of extra dimensions in gravitational waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Andriot, David; Gómez, Gustavo Lucena, E-mail: andriotphysics@gmail.com, E-mail: glucenag@aei.mpg.de

2017-06-01

Considering gravitational waves propagating on the most general 4+ N -dimensional space-time, we investigate the effects due to the N extra dimensions on the four-dimensional waves. All wave equations are derived in general and discussed. On Minkowski{sub 4} times an arbitrary Ricci-flat compact manifold, we find: a massless wave with an additional polarization, the breathing mode, and extra waves with high frequencies fixed by Kaluza-Klein masses. We discuss whether these two effects could be observed.

Foam metal metamaterial panel for mechanical waves isolation

NASA Astrophysics Data System (ADS)

Hua, Lei; Sun, Hongwei; Gu, Jinliang

2016-04-01

This paper presents modeling, analysis techniques and experiment of foam metal metamaterial panel for Broadband Vibration Absorption. For a unit cell of an infinite foam metal metamaterial panel, governing equations are derived using the extended Hamilton principle. The concepts of negative effective mass and stiffness and how the spring-mass-damper subsystems create a stopband are explained in detail. Numerical simulations reveal that the actual working mechanism of the proposed metamaterial panel is based on the concept of conventional mechanical vibration absorbers. It uses the incoming elastic wave in the panel to resonate the integrated membrane-mass-damper absorbers to vibrate in their optical mode at frequencies close to but above their local resonance frequencies to create shear forces and bending moments to straighten the panel and stop the wave propagation. Moreover, a two-dimension acoustic foam metal metamaterial panel consisting of lumped mass and elastic membrane is proposed in the lab. We do experiments on the model and The results validate the concept and show that, for two-dimension acoustic foam metal metamaterial panel do exist two vibration modes. For the wave absorption, the mass of each cell should be considered in the design. With appropriate design calculations, the proposed two-dimension acoustic foam metal metamaterial panel can be used for absorption of low-frequency waves and hence expensive micro-manufacturing techniques are not needed for design and manufacturing of such foam metal metamaterial panel for low-frequency waves absorption/isolation.

Topological guiding of elastic waves in phononic metamaterials based on 2D pentamode structures.

PubMed

Guo, Yuning; Dekorsy, Thomas; Hettich, Mike

2017-12-22

A topological state with protected propagation of elastic waves is achieved by appropriately engineering a phononic metamaterial based on 2D pentamode structures in silicon. Gapless edge states in the designed structure, which are characterized by pseudospin-dependent transport, provide backscattering-immune propagation of the elastic wave along bend paths. The role of the states responsible for forward and backward transfer can be interchanged by design.

Laser-ultrasound spectroscopy apparatus and method with detection of shear resonances for measuring anisotropy, thickness, and other properties

DOEpatents

Levesque, Daniel; Moreau, Andre; Dubois, Marc; Monchalin, Jean-Pierre; Bussiere, Jean; Lord, Martin; Padioleau, Christian

2000-01-01

Apparatus and method for detecting shear resonances includes structure and steps for applying a radiation pulse from a pulsed source of radiation to an object to generate elastic waves therein, optically detecting the elastic waves generated in the object, and analyzing the elastic waves optically detected in the object. These shear resonances, alone or in combination with other information, may be used in the present invention to improve thickness measurement accuracy and to determine geometrical, microstructural, and physical properties of the object. At least one shear resonance in the object is detected with the elastic waves optically detected in the object. Preferably, laser-ultrasound spectroscopy is utilized to detect the shear resonances.

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

The exact thermal rotational spectrum of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

NASA Technical Reports Server (NTRS)

Reimers, J. R.; Heller, E. J.

1985-01-01

The exact thermal rotational spectrum of a two-dimensional rigid rotor is obtained using Gaussian wave packet dynamics. The spectrum is obtained by propagating, without approximation, infinite sets of Gaussian wave packets. These sets are constructed so that collectively they have the correct periodicity, and indeed, are coherent states appropriate to this problem. Also, simple, almost classical, approximations to full wave packet dynamics are shown to give results which are either exact or very nearly exact. Advantages of the use of Gaussian wave packet dynamics over conventional linear response theory are discussed.

Numerical study on wave loads and motions of two ships advancing in waves by using three-dimensional translating-pulsating source

NASA Astrophysics Data System (ADS)

Xu, Yong; Dong, Wen-Cai

2013-08-01

A frequency domain analysis method based on the three-dimensional translating-pulsating (3DTP) source Green function is developed to investigate wave loads and free motions of two ships advancing on parallel course in waves. Two experiments are carried out respectively to measure the wave loads and the freemotions for a pair of side-byside arranged ship models advancing with an identical speed in head regular waves. For comparison, each model is also tested alone. Predictions obtained by the present solution are found in favorable agreement with the model tests and are more accurate than the traditional method based on the three dimensional pulsating (3DP) source Green function. Numerical resonances and peak shift can be found in the 3DP predictions, which result from the wave energy trapped in the gap between two ships and the extremely inhomogeneous wave load distribution on each hull. However, they can be eliminated by 3DTP, in which the speed affects the free surface and most of the wave energy can be escaped from the gap. Both the experiment and the present prediction show that hydrodynamic interaction effects on wave loads and free motions are significant. The present solver may serve as a validated tool to predict wave loads and motions of two vessels under replenishment at sea, and may help to evaluate the hydrodynamic interaction effects on the ships safety in replenishment operation.

Optimal determination of the elastic constants of composite materials from ultrasonic wave-speed measurements

NASA Astrophysics Data System (ADS)

Castagnède, Bernard; Jenkins, James T.; Sachse, Wolfgang; Baste, Stéphane

1990-03-01

A method is described to optimally determine the elastic constants of anisotropic solids from wave-speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree-three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double-iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Hybrid dispersive media with controllable wave propagation: A new take on smart materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bergamini, Andrea E., E-mail: andrea.bergamini@empa.ch; Zündel, Manuel; Flores Parra, Edgar A.

In this paper, we report on the wave transmission characteristics of a hybrid one dimensional (1D) medium. The hybrid characteristic is the result of the coupling between a 1D mechanical waveguide in the form of an elastic beam, supporting the propagation of transverse waves and a discrete electrical transmission line, consisting of a series of inductors connected to ground through capacitors. The capacitors correspond to a periodic array of piezoelectric patches that are bonded to the beam and that couple the two waveguides. The coupling leads to a hybrid medium that is characterized by a coincidence condition for the frequency/wavenumbermore » value corresponding to the intersection of the branches of the two waveguides. In the frequency range centered at coincidence, the hybrid medium features strong attenuation of wave motion as a result of the energy transfer towards the electrical transmission line. This energy transfer, and the ensuing attenuation of wave motion, is alike the one obtained through internal resonating units of the kind commonly used in metamaterials. However, the distinct shape of the dispersion curves suggests how this energy transfer is not the result of a resonance and is therefore fundamentally different. This paper presents the numerical investigation of the wave propagation in the considered media, it illustrates experimental evidence of wave transmission characteristics and compares the performance of the considered configuration with that of internal resonating metamaterials. In addition, the ability to conveniently tune the dispersion properties of the electrical transmission line is exploited to adapt the periodicity of the domain and to investigate diatomic periodic configurations that are characterized by a richer dispersion spectrum and broader bandwidth of wave attenuation at coincidence. The medium consisting of mechanical, piezoelectric, and analog electronic elements can be easily interfaced to digital devices to offer a novel approach to smart materials.« less

Wave propagation in viscoelastic horns using a fractional calculus rheology model

NASA Astrophysics Data System (ADS)

Margulies, Timothy

2003-10-01

The complex mechanical behavior of materials are characterized by fluid and solid models with fractional calculus differentials to relate stress and strain fields. Fractional derivatives have been shown to describe the viscoelastic stress from polymer chain theory for molecular solutions [Rouse and Sittel, J. Appl. Phys. 24, 690 (1953)]. Here the propagation of infinitesimal waves in one dimensional horns with a small cross-sectional area change along the longitudinal axis are examined. In particular, the linear, conical, exponential, and catenoidal shapes are studied. The wave amplitudes versus frequency are solved analytically and predicted with mathematical computation. Fractional rheology data from Bagley [J. Rheol. 27, 201 (1983); Bagley and Torvik, J. Rheol. 30, 133 (1986)] are incorporated in the simulations. Classical elastic and fluid ``Webster equations'' are recovered in the appropriate limits. Horns with real materials that employ fractional calculus representations can be modeled to examine design trade-offs for engineering or for scientific application.

A 3D staggered-grid finite difference scheme for poroelastic wave equation

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai

2014-10-01

Three dimensional numerical modeling has been a viable tool for understanding wave propagation in real media. The poroelastic media can better describe the phenomena of hydrocarbon reservoirs than acoustic and elastic media. However, the numerical modeling in 3D poroelastic media demands significantly more computational capacity, including both computational time and memory. In this paper, we present a 3D poroelastic staggered-grid finite difference (SFD) scheme. During the procedure, parallel computing is implemented to reduce the computational time. Parallelization is based on domain decomposition, and communication between processors is performed using message passing interface (MPI). Parallel analysis shows that the parallelized SFD scheme significantly improves the simulation efficiency and 3D decomposition in domain is the most efficient. We also analyze the numerical dispersion and stability condition of the 3D poroelastic SFD method. Numerical results show that the 3D numerical simulation can provide a real description of wave propagation.

Reflection of acoustic wave from the elastic seabed with an overlying gassy poroelastic layer

NASA Astrophysics Data System (ADS)

Chen, Weiyun; Wang, Zhihua; Zhao, Kai; Chen, Guoxing; Li, Xiaojun

2015-10-01

Based on the multiphase poroelasticity theory, the reflection characteristics of an obliquely incident acoustic wave upon a plane interface between overlying water and a gassy marine sediment layer with underlying elastic solid seabed are investigated. The sandwiched gassy layer is modelled as a porous material with finite thickness, which is saturated by two compressible and viscous fluids (liquid and gas). The closed-form expression for the amplitude ratio of the reflected wave, called reflection coefficient, is derived theoretically according to the boundary conditions at the upper and lower interfaces in our proposed model. Using numerical calculation, the influences of layer thickness, incident angle, wave frequency and liquid saturation of sandwiched porous layer on the reflection coefficient are analysed, respectively. It is revealed that the reflection coefficient is closely associated with incident angle and sandwiched layer thickness. Moreover, in different frequency ranges, the dependence of the wave reflection characteristics on moisture (or gas) variations in the intermediate marine sediment layer is distinguishing.

Visualising elastic anisotropy: theoretical background and computational implementation

NASA Astrophysics Data System (ADS)

Nordmann, J.; Aßmus, M.; Altenbach, H.

2018-02-01

In this article, we present the technical realisation for visualisations of characteristic parameters of the fourth-order elasticity tensor, which is classified by three-dimensional symmetry groups. Hereby, expressions for spatial representations of uc(Young)'s modulus and bulk modulus as well as plane representations of shear modulus and uc(Poisson)'s ratio are derived and transferred into a comprehensible form to computer algebra systems. Additionally, we present approaches for spatial representations of both latter parameters. These three- and two-dimensional representations are implemented into the software MATrix LABoratory. Exemplary representations of characteristic materials complete the present treatise.

Observations of experimental and numerical waveforms of piezoelectric signals generated in bovine cancellous bone by ultrasound waves

NASA Astrophysics Data System (ADS)

Hosokawa, Atsushi

2018-07-01

Experimental and numerical waveforms of piezoelectric signals generated in the bovine cancellous bone by ultrasound waves at 1.0 MHz were observed. The experimental observations were performed using a “piezoelectric cell (PE-cell)”, in which an air-saturated cancellous bone specimen was electrically shielded. The PE-cell was used to receive burst ultrasound waves. The numerical observations were performed using a piezoelectric finite-difference time-domain (PE-FDTD) method, which was an elastic FDTD method with piezoelectric constitutive equations. The cancellous bone model was reconstructed from the three-dimensional X-ray microcomputed tomographic image of the specimen used in the experiments. Both experimental and numerical results showed that the repetitive piezoelectric signals could be generated by the multireflected ultrasound waves within the cancellous bone specimen. Moreover, it was shown that the output piezoelectric signal in the PE-cell could be the overlap of the local signals in the trabecular elements at various depths (or thicknesses) in the cancellous bone specimen.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, P.; Pai, Woei Wu; Chan, Y. -H.

Two-dimensional materials constitute a promising platform for developing nanoscale devices and systems. Their physical properties can be very different from those of the corresponding three-dimensional materials because of extreme quantum confinement and dimensional reduction. Here in this paper we report a study of TiTe 2 from the single-layer to the bulk limit. Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy and spectroscopy, we observed the emergence of a (2 × 2) charge density wave order in single-layer TiTe 2 with a transition temperature of 92 ± 3 K. Also observed was a pseudogap of about 28 meV at the Fermimore » level at 4.2 K. Surprisingly, no charge density wave transitions were observed in two-layer and multi-layer TiTe 2 , despite the quasi-two-dimensional nature of the material in the bulk. The unique charge density wave phenomenon in the single layer raises intriguing questions that challenge the prevailing thinking about the mechanisms of charge density wave formation.« less

A k-space method for large-scale models of wave propagation in tissue.

PubMed

Mast, T D; Souriau, L P; Liu, D L; Tabei, M; Nachman, A I; Waag, R C

2001-03-01

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

WE-E-9A-01: Ultrasound Elasticity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Emelianov, S; Hall, T; Bouchard, R

2014-06-15

Principles and techniques of ultrasound-based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitativemore » Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained. Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging. Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force-based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement and imaging can contribute to diagnosis of breast and prostate cancer, staging of liver fibrosis, age estimation of deep veinous fhrombosis, confirmation of thermal lesions in the liver after RF ablation.« less

The Simple Lamb Wave Analysis to Characterize Concrete Wide Beams by the Practical MASW Test

PubMed Central

Lee, Young Hak; Oh, Taekeun

2016-01-01

In recent years, the Lamb wave analysis by the multi-channel analysis of surface waves (MASW) for concrete structures has been an effective nondestructive evaluation, such as the condition assessment and dimension identification by the elastic wave velocities and their reflections from boundaries. This study proposes an effective Lamb wave analysis by the practical application of MASW to concrete wide beams in an easy and simple manner in order to identify the dimension and elastic wave velocity (R-wave) for the condition assessment (e.g., the estimation of elastic properties). This is done by identifying the zero-order antisymmetric (A0) and first-order symmetric (S1) modes among multimodal Lamb waves. The MASW data were collected on eight concrete wide beams and compared to the actual depth and to the pressure (P-) wave velocities collected for the same specimen. Information is extracted from multimodal Lamb wave dispersion curves to obtain the elastic stiffness parameters and the thickness of the concrete structures. Due to the simple and cost-effective procedure associated with the MASW processing technique, the characteristics of several fundamental modes in the experimental Lamb wave dispersion curves could be measured. Available reference data are in good agreement with the parameters that were determined by our analysis scheme. PMID:28773562

Wrinkle-like slip pulse on a fault between different materials

USGS Publications Warehouse

Andrews, D.J.; Ben-Zion, Y.

1997-01-01

Pulses of slip velocity can propagate on a planar interface governed by a constant coefficient of friction, where the interface separates different elastic materials. Such pulses have been found in two-dimensional plane strain finite difference calculations of slip on a fault between elastic media with wave speeds differing by 20%. The self-sustaining propagation of the slip pulse arises from interaction between normal and tangential deformation that exists only with a material contrast. These calculations confirm the prediction of Weertman [1980] that a dislocation propagating steadily along a material interface has a tensile change of normal traction with the same pulse shape as slip velocity. The self-sustaining pulse is associated with a rapid transition from a head wave traveling along the interface with the S wave speed of the faster material, to an opposite polarity body wave traveling with the slower S speed. Slip occurs during the reversal of normal particle velocity. The pulse can propagate in a region with constant coefficient of friction and an initial stress state below the frictional criterion. Propagation occurs in only one direction, the direction of slip in the more compliant medium, with rupture velocity near the slower S wave speed. Displacement is larger in the softer medium, which is displaced away from the fault during the passage of the slip pulse. Motion is analogous to a propagating wrinkle in a carpet. The amplitude of slip remains approximately constant during propagation, but the pulse width decreases and the amplitudes of slip velocity and stress change increase. The tensile change of normal traction increases until absolute normal traction reaches zero. The pulse can be generated as a secondary effect of a drop of shear stress in an asperity. The pulse shape is unstable, and the initial slip pulse can change during propagation into a collection of sharper pulses. Such a pulse enables slip to occur with little loss of energy to friction, while at the same time increasing irregularity of stress and slip at the source. Copyright 1997 by the American Geophysical Union.

Geometric charges in theories of elasticity and plasticity

NASA Astrophysics Data System (ADS)

Moshe, Michael

The mechanics of many natural systems is governed by localized sources of stresses. Examples include ''plastic events'' that occur in amorphous solids under external stress, defects formation in crystalline material, and force-dipoles applied by cells adhered to an elastic substrate. Recent developments in a geometric formulation of elasticity theory paved the way for a unifying mathematical description of such singular sources of stress, as ''elastic charges''. In this talk I will review basic results in this emerging field, focusing on the geometry and mechanics of elastic charges in two-dimensional solid bodies. I will demonstrate the applicability of this new approach in three different problems: failure of an amorphous solid under load, mechanics of Kirigami, and wrinkle patterns in geometrically-incompatible elastic sheets.

Regional Detection of Decoupled Explosions, Yield Estimation from Surface Waves, Two-Dimensional Source Effects, Three-Dimensional Earthquake Modeling and Automated Magnitude Measures

DTIC Science & Technology

1980-07-01

41 3.2 EXPERIMENTAL DETERMINATION OF THE DEPENDENCE OF RAYLEIGH WAVE AMPLITUDE ON PROPERTIES OF THE SOURCE MATERIAL ...Surface Wave Observations ...... ................ 48 3.3.3 Surface Wave Dependence on Source Material Properties ..... ................ .. 51 SYSTEMS...with various aspects of the problem of estimating yield from single station recordings of surface waves. The material in these four summaries has been

TH-A-207B-02: QIBA Ultrasound Elasticity Imaging System Biomarker Qualification and User Testing of Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garra, B.

Imaging of tissue elastic properties is a relatively new and powerful approach to one of the oldest and most important diagnostic tools. Imaging of shear wave speed with ultrasound is has been added to most high-end ultrasound systems. Understanding this exciting imaging mode aiding its most effective use in medicine can be a rewarding effort for medical physicists and other medical imaging and treatment professionals. Assuring consistent, quantitative measurements across the many ultrasound systems in a typical imaging department will constitute a major step toward realizing the great potential of this technique and other quantitative imaging. This session will targetmore » these two goals with two presentations. A. Basics and Current Implementations of Ultrasound Imaging of Shear Wave Speed and Elasticity - Shigao Chen, Ph.D. Learning objectives-To understand: Introduction: Importance of tissue elasticity measurement Strain vs. shear wave elastography (SWE), beneficial features of SWE The link between shear wave speed and material properties, influence of viscosity Generation of shear waves External vibration (Fibroscan) ultrasound radiation force Point push Supersonic push (Aixplorer) Comb push (GE Logiq E9) Detection of shear waves Motion detection from pulse-echo ultrasound Importance of frame rate for shear wave imaging Plane wave imaging detection How to achieve high effective frame rate using line-by-line scanners Shear wave speed calculation Time to peak Random sample consensus (RANSAC) Cross correlation Sources of bias and variation in SWE Tissue viscosity Transducer compression or internal pressure of organ Reflection of shear waves at boundaries B. Elasticity Imaging System Biomarker Qualification and User Testing of Systems – Brian Garra, M.D. Learning objectives-To understand: Goals Review the need for quantitative medical imaging Provide examples of quantitative imaging biomarkers Acquaint the participant with the purpose of the RSNA Quantitative Imaging Biomarker Alliance and the need for such an organization Review the QIBA process for creating a quantitative biomarker Summarize steps needed to verify adherence of site, operators, and imaging systems to a QIBA profile Underlying Premise and Assumptions Objective, quantifiable results are needed to enhance the value of diagnostic imaging in clinical practice Reasons for quantification Evidence based medicine requires objective, not subjective observer data Computerized decision support tools (eg CAD) generally require quantitative input. Quantitative, reproducible measures are more easily used to develop personalized molecular medical diagnostic and treatment systems What is quantitative imaging? Definition from Imaging Metrology Workshop The Quantitative Imaging Biomarker Alliance Formation 2008 Mission Structure Example Imaging Biomarkers Being Explored Biomarker Selection Groundwork Draft Protocol for imaging and data evaluation QIBA Profile Drafting Equipment and Site Validation Technical Clinical Site and Equipment QA and Compliance Checking Ultrasound Elasticity Estimation Biomarker US Elasticity Estimation Background Current Status and Problems Biomarker Selection-process and outcome US SWS for Liver Fibrosis Biomarker Work Groundwork Literature search and analysis results Phase I phantom testing-Elastic phantoms Phase II phantom testing-Viscoelastic phantoms Digital Simulated Data Protocol and Profile Drafting Protocol: based on UPICT and existing literature and standards bodies protocols Profile-Current claims, Manufacturer specific appendices What comes after the profile Profile Validation Technical validation Clinical validation QA and Compliance Possible approaches Site Operator testing Site protocol re-evaluation Imaging system Manufacturer testing and attestation User acceptance testing and periodic QA Phantom Tests Digital Phantom Based Testing Standard QA Testing Remediation Schemes Profile Evolution Towards additional applications Towards higher accuracy and precision Supported in part by NIH contract HHSN268201300071C from NIBIB. Collaboration with GE Global Research, no personal support.; S. Chen, Some technologies described in this presentation have been licensed. Mayo Clinic and Dr. Chen have financial interests these technologies.« less

An IBEM solution to the scattering of plane SH-waves by a lined tunnel in elastic wedge space

NASA Astrophysics Data System (ADS)

Liu, Zhongxian; Liu, Lei

2015-02-01

The indirect boundary element method (IBEM) is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and efficiently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.

Velocity sensitivity of seismic body waves to the anisotropic parameters of a TTI-medium

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, Stewart

2008-09-01

We formulate the derivatives of the phase and group velocities for each of the anisotropic parameters in a tilted transversely isotropic medium (TTI-medium). This is a common geological model in seismic exploration and has five elastic moduli or related Thomsen parameters and two orientation angles defining the axis of symmetry of the rock. We present two independent methods to compute the derivatives and examine the formulae with real anisotropic rocks. The formulations and numerical computations do not encounter any singularity problem when applied to the two quasi shear waves, which is a problem with other approaches. The two methods yield the same results, which show in a quantitative way the sensitivity behaviour of the phase and the group velocities to all of the elastic moduli or Thomsen's anisotropic parameters as well as the orientation angles in the 2D and 3D cases. One can recognize the dominant (strong effect) and weak (or 'dummy') parameters for the three seismic body-wave modes (qP, qSV, qSH) and their effective domains over the whole range of phase-slowness directions. These sensitivity patterns indicate the possibility of nonlinear kinematic inversion with the three wave modes for determining the anisotropic parameters and imaging an anisotropic medium.

One-dimensional wave propagation in particulate suspensions

NASA Technical Reports Server (NTRS)

Rochelle, S. G.; Peddieson, J., Jr.

1976-01-01

One-dimensional small-amplitude wave motion in a two-phase system consisting of an inviscid gas and a cloud of suspended particles is analyzed using a continuum theory of suspensions. Laplace transform methods are used to obtain several approximate solutions. Properties of acoustic wave motion in particulate suspensions are inferred from these solutions.

Feasibility of Using Elastic Wave Velocity Monitoring for Early Warning of Rainfall-Induced Slope Failure

PubMed Central

Chen, Yulong; Irfan, Muhammad; Uchimura, Taro; Zhang, Ke

2018-01-01

Rainfall-induced landslides are one of the most widespread slope instability phenomena posing a serious risk to public safety worldwide so that their temporal prediction is of great interest to establish effective warning systems. The objective of this study is to determine the effectiveness of elastic wave velocities in the surface layer of the slope in monitoring, prediction and early warning of landslide. The small-scale fixed and varied, and large-scale slope model tests were conducted. Analysis of the results has established that the elastic wave velocity continuously decreases in response of moisture content and deformation and there was a distinct surge in the decrease rate of wave velocity when failure was initiated. Based on the preliminary results of this analysis, the method using the change in elastic wave velocity proves superior for landslide early warning and suggests that a warning be issued at switch of wave velocity decrease rate. PMID:29584699

A Study for Anisotropic Wavefield Analysis with Elastic Layered Models

NASA Astrophysics Data System (ADS)

Yoneki, R.; Mikada, H.; Takekawa, J.

2015-12-01

Subsurface materials are generally anisotropic due to complicated geological conditions, for example, sedimentary materials, fractures reflecting various stress conditions in the past and present in the subsurface. There are many studies on seismic wave propagation in TI (transversely isotropic) and orthorhombic media (e.g., Thomsen, 1986; Alkhalifah, 2000; Bansal and Sen, 2008). In most of those studies, the magnitude of anisotropy is assumed to be weak. Therefore, it may be not appropriate to apply their theories directly to strongly anisotropic subsurface media in seismic exploration. It is necessary to understand the effects of the anisotropy on the behavior of seismic wave propagation in strongly anisotropic media in the seismic exploration. In this study, we investigate the influence of strong anisotropy on received seismic waveforms using three-dimensional numerical models, and verified capability of detecting subsurface anisotropy. Our numerical models contain an isotropic and an anisotropic (VTI, transversely isotropic media with vertical symmetry axis) layer, respectively, in the isotropic background subsurface. Since the difference between the two models is only the anisotropy in the vertical propagation velocity, we could look at the influence of anisotropy in the residual wavefield that is the difference in the observed wavefields of two models. We analyzed the orbital motions of the residual wavefield to see what kind of wave motions the waveforms show. We found that the residual waveforms generated by the anisotropic layer include the orbital motions of shear waves right after the first arrival, i.e., mode conversion from the compressional waves due to the anisotropy. The residual waveforms could be exploited to estimate both the order of anisotropy and the thickness of anisotropic layer in subsurface.

Analytical solution for the transient wave propagation of a buried cylindrical P-wave line source in a semi-infinite elastic medium with a fluid surface layer

NASA Astrophysics Data System (ADS)

Shan, Zhendong; Ling, Daosheng

2018-02-01

This article develops an analytical solution for the transient wave propagation of a cylindrical P-wave line source in a semi-infinite elastic solid with a fluid layer. The analytical solution is presented in a simple closed form in which each term represents a transient physical wave. The Scholte equation is derived, through which the Scholte wave velocity can be determined. The Scholte wave is the wave that propagates along the interface between the fluid and solid. To develop the analytical solution, the wave fields in the fluid and solid are defined, their analytical solutions in the Laplace domain are derived using the boundary and interface conditions, and the solutions are then decomposed into series form according to the power series expansion method. Each item of the series solution has a clear physical meaning and represents a transient wave path. Finally, by applying Cagniard's method and the convolution theorem, the analytical solutions are transformed into the time domain. Numerical examples are provided to illustrate some interesting features in the fluid layer, the interface and the semi-infinite solid. When the P-wave velocity in the fluid is higher than that in the solid, two head waves in the solid, one head wave in the fluid and a Scholte wave at the interface are observed for the cylindrical P-wave line source.

The Fundamental Structure and the Reproduction of Spiral Wave in a Two-Dimensional Excitable Lattice

PubMed Central

Qian, Yu; Zhang, Zhaoyang

2016-01-01

In this paper we have systematically investigated the fundamental structure and the reproduction of spiral wave in a two-dimensional excitable lattice. A periodically rotating spiral wave is introduced as the model to reproduce spiral wave artificially. Interestingly, by using the dominant phase-advanced driving analysis method, the fundamental structure containing the loop structure and the wave propagation paths has been revealed, which can expose the periodically rotating orbit of spiral tip and the charity of spiral wave clearly. Furthermore, the fundamental structure is utilized as the core for artificial spiral wave. Additionally, the appropriate parameter region, in which the artificial spiral wave can be reproduced, is studied. Finally, we discuss the robustness of artificial spiral wave to defects. PMID:26900841

Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations.

PubMed

Ghodsi, Hossein; Darvish, Kurosh

2016-10-01

Collagen fibril is a major component of connective tissues such as bone, tendon, blood vessels, and skin. The mechanical properties of this highly hierarchical structure are greatly influenced by the presence of covalent cross-links between individual collagen molecules. This study investigates the viscoelastic behavior of a collagen lysine-lysine cross-link based on creep simulations with applied forces in the range or 10 to 2000pN using steered molecular dynamics (SMD). The viscoelastic model of the cross-link was combined with a system composed by two segments of adjacent collagen molecules hence representing a reduced viscoelastic model for a simplified micro-fibril. It was found that the collagen micro-fibril assembly had a steady-state Young׳s modulus ranging from 2.24 to 3.27GPa, which is in agreement with reported experimental measurements. The propagation of longitudinal force wave along the molecule was implemented by adding a delay element to the model. The force wave speed was found to be correlated with the speed of one-dimensional elastic waves in rods. The presented reduced model with three degrees of freedom can serve as a building block for developing models of the next level of hierarchy, i.e., a collagen fibril. Copyright © 2016 Elsevier Ltd. All rights reserved.

The transmission or scattering of elastic waves by an inhomogeneity of simple geometry: A comparison of theories

NASA Technical Reports Server (NTRS)

Sheu, Y. C.; Fu, L. S.

1983-01-01

The extended method of equivalent inclusions is applied to study the specific wave problems: (1) the transmission of elastic waves in an infinite medium containing a layer of inhomogeneity, and (2) the scattering of elastic waves in an infinite medium containing a perfect spherical inhomogeneity. Eigenstrains are expanded as a geometric series and a method of integration based on the inhomogeneous Helmholtz operator is adopted. This study compares results, obtained by using limited number of terms in the eigenstrain expansion, with exact solutions for the layer problem and that for a perfect sphere.

Probing flexible thermoplastic thin films on a substrate using ultrasonic waves to retrieve mechanical moduli and density: Inverse problem

NASA Astrophysics Data System (ADS)

Lazri, H.; Ogam, E.; Amar, B.; Fellah, Z. E. A.; Sayoud, N.; Boumaiza, Y.

2018-05-01

Flexible, supple thermoplastic thin films (PVB and PET) placed on elastic substrates were probed using ultrasonic waves to identify their mechanical moduli and density. The composite medium immersed in a fluid host medium (water) was excited using a 50 Mhz transducer operating at normal incidence in reflection mode. Elastic wave propagation data from the stratified medium was captured in the host medium as scattered field. These data were used along with theoretical fluid-solid interaction forward models for stratified-media developed using elasticity theory, to solve an inverse problem for the recovery of the model parameters of the thin films. Two configurations were modeled, one considering the substrate as a semi-infinite elastic medium and the second the substrate having a finite thickness and flanked by a semi-infinite host medium. Transverse slip for the sliding interface between the films and substrate was chosen. This was found to agree with the experiments whereby the thin films were just placed on the substrate without bonding. The inverse problems for the recovery of the mechanical parameters were successful in retrieving the thin films’ parameters under the slip boundary condition. The possible improvements to the new method for the characterization of thin films are discussed.

Classifying bilinear differential equations by linear superposition principle

NASA Astrophysics Data System (ADS)

Zhang, Lijun; Khalique, Chaudry Masood; Ma, Wen-Xiu

2016-09-01

In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota bilinear equations possessing this specific sub-class of N-wave solutions is presented. We apply this result to find N-wave solutions to the (2+1)-dimensional KP equation, a (3+1)-dimensional generalized Kadomtsev-Petviashvili (KP) equation, a (3+1)-dimensional generalized BKP equation and the (2+1)-dimensional BKP equation. The inverse question, i.e., constructing Hirota Bilinear equations possessing N-wave solutions, is considered and a refined 3-step algorithm is proposed. As examples, we construct two very general kinds of Hirota bilinear equations of order 4 possessing N-wave solutions among which one satisfies dispersion relation and another does not satisfy dispersion relation.

Dynamic acousto-elastic testing of concrete with a coda-wave probe: comparison with standard linear and nonlinear ultrasonic techniques.

PubMed

Shokouhi, Parisa; Rivière, Jacques; Lake, Colton R; Le Bas, Pierre-Yves; Ulrich, T J

2017-11-01

The use of nonlinear acoustic techniques in solids consists in measuring wave distortion arising from compliant features such as cracks, soft intergrain bonds and dislocations. As such, they provide very powerful nondestructive tools to monitor the onset of damage within materials. In particular, a recent technique called dynamic acousto-elasticity testing (DAET) gives unprecedented details on the nonlinear elastic response of materials (classical and non-classical nonlinear features including hysteresis, transient elastic softening and slow relaxation). Here, we provide a comprehensive set of linear and nonlinear acoustic responses on two prismatic concrete specimens; one intact and one pre-compressed to about 70% of its ultimate strength. The two linear techniques used are Ultrasonic Pulse Velocity (UPV) and Resonance Ultrasound Spectroscopy (RUS), while the nonlinear ones include DAET (fast and slow dynamics) as well as Nonlinear Resonance Ultrasound Spectroscopy (NRUS). In addition, the DAET results correspond to a configuration where the (incoherent) coda portion of the ultrasonic record is used to probe the samples, as opposed to a (coherent) first arrival wave in standard DAET tests. We find that the two visually identical specimens are indistinguishable based on parameters measured by linear techniques (UPV and RUS). On the contrary, the extracted nonlinear parameters from NRUS and DAET are consistent and orders of magnitude greater for the damaged specimen than those for the intact one. This compiled set of linear and nonlinear ultrasonic testing data including the most advanced technique (DAET) provides a benchmark comparison for their use in the field of material characterization. Copyright © 2017 Elsevier B.V. All rights reserved.

The high temperature impact response of tungsten and chromium

NASA Astrophysics Data System (ADS)

Zaretsky, E. B.; Kanel, G. I.

2017-09-01

The evolution of elastic-plastic shock waves has been studied in pure polycrystalline tungsten and chromium at room and elevated temperatures over propagation distances ranging from 0.05 to 3 mm (tungsten) and from 0.1 to 2 mm (chromium). The use of fused silica windows in all but one experiment with chromium and in several high temperature experiments with tungsten led to the need for performing shock and optic characterization of these windows over the 300-1200 K temperature interval. Experiments with tungsten and chromium samples showed that annealing of the metals transforms the initial ramping elastic wave into a jump-like wave, substantially increasing the Hugoniot elastic limits of the metals. With increased annealing time, the spall strength of the two metals slightly increases. Both at room and at high temperatures, the elastic precursor in the two metals decays in two distinct regimes. At propagation distances smaller than ˜1 mm (tungsten) or ˜0.5 mm (chromium), decay is fast, with the dislocation motion and multiplication being controlled by phonon viscous drag. At greater distances, the rate of decay becomes much lower, with control of the plastic deformation being passed to the thermally activated generation and motion of dislocation double-kinks. The stress at which this transition takes place virtually coincides with the Peierls stress τP of the active glide system. Analysis of the annealing effects in both presently and previously studied BCC metals (i.e., Ta, V, Nb, Mo, W, and Cr) and of the dependencies of their normalized Peierls stresses τP(θ) /τP(0 ) on the normalized temperature θ=T /Tm allows one to conclude that the non-planar, split into several glide planes, structure of the dislocation core in these metals is mainly responsible for their plastic deformation features.

Scale-dependent effects on wave propagation in magnetically affected single/double-layered compositionally graded nanosize beams

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza

2018-04-01

This article deals with the wave propagation analysis of single/double layered functionally graded (FG) size-dependent nanobeams in elastic medium and subjected to a longitudinal magnetic field employing nonlocal elasticity theory. Material properties of nanobeam change gradually according to the sigmoid function. Applying an analytical solution, the acoustical and optical dispersion relations are explored for various wave number, nonlocality parameter, material composition, elastic foundation constants, and magnetic field intensity. It is found that frequency and phase velocity of waves propagating in S-FGM nanobeam are significantly affected by these parameters. Also, presence of cut-off and escape frequencies in wave propagation analysis of embedded S-FGM nanobeams is investigated.