Connectivity as an alternative to boundary integral equations: Construction of bases

PubMed Central

Herrera, Ismael; Sabina, Federico J.

1978-01-01

In previous papers Herrera developed a theory of connectivity that is applicable to the problem of connecting solutions defined in different regions, which occurs when solving partial differential equations and many problems of mechanics. In this paper we explain how complete connectivity conditions can be used to replace boundary integral equations in many situations. We show that completeness is satisfied not only in steady-state problems such as potential, reduced wave equation and static and quasi-static elasticity, but also in time-dependent problems such as heat and wave equations and dynamical elasticity. A method to obtain bases of connectivity conditions, which are independent of the regions considered, is also presented. PMID:16592522

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.

Finite Difference Modeling of Wave Progpagation in Acoustic TiltedTI Media

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

Zhang, Linbin; Rector III, James W.; Hoversten, G. Michael

2005-03-21

Based on an acoustic assumption (shear wave velocity is zero) and a dispersion relation, we derive an acoustic wave equation for P-waves in tilted transversely isotropic (TTI) media (transversely isotropic media with a tilted symmetry axis). This equation has fewer parameters than an elastic wave equation in TTI media and yields an accurate description of P-wave traveltimes and spreading-related attenuation. Our TTI acoustic wave equation is a fourth-order equation in time and space. We demonstrate that the acoustic approximation allows the presence of shear waves in the solution. The substantial differences in traveltime and amplitude between data created using VTImore » and TTI assumptions is illustrated in examples.« less

Bulk solitary waves in elastic solids

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.

2015-10-01

A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the duct-like polymer shell and proved, that there is no tensile area behind the wave, the bulk soliton propagates on a distance many times longer than its wave length, while both its shape and amplitude remain unchanged. We demonstrated recently how the strain solitons can be used for non-destructive testing (NDT) of laminated composites, used nowadays for various applications, e.g., in microelectronics, aerospace and automotive industries, and bulk strain solitons are among prospective instruments for NDT. Being aimed to propose the bulk strain solitons as an instrument for NDT in solids, we studied numerically the evolution of them in various wave guides with local defects, and shown that the strain soliton undergoes changes in amplitude, phase shift and the shape, that are distinctive and can be estimated. To sum up, now we are able to propose a new NDT technique, based on bulk strain soliton propagation in structural elements.

On the eigenfrequencies of elastic shear waves propagating in an inhomogeneous layer

NASA Astrophysics Data System (ADS)

Khachatryan, V. M.

2018-04-01

In this work, we consider the problem of eigenfrequencies of elastic shear waves propagating in a layer whose Young’s modulus and density are functions of the longitudinal coordinate. Taking into account the material inhomogeneity makes the problem of the eigenfrequencies of the waves propagating in the layer more complicated. In this paper, the problem of pure shear is considered. To solve the problem, we use an integral formula which allows us to represent the general solution of the original equation with variable coefficients in terms of the general solution of the accompanying equation with constant coefficients.

Seismic waves in a self-gravitating planet

NASA Astrophysics Data System (ADS)

Brazda, Katharina; de Hoop, Maarten V.; Hörmann, Günther

2013-04-01

The elastic-gravitational equations describe the propagation of seismic waves including the effect of self-gravitation. We rigorously derive and analyze this system of partial differential equations and boundary conditions for a general, uniformly rotating, elastic, but aspherical, inhomogeneous, and anisotropic, fluid-solid earth model, under minimal assumptions concerning the smoothness of material parameters and geometry. For this purpose we first establish a consistent mathematical formulation of the low regularity planetary model within the framework of nonlinear continuum mechanics. Using calculus of variations in a Sobolev space setting, we then show how the weak form of the linearized elastic-gravitational equations directly arises from Hamilton's principle of stationary action. Finally we prove existence and uniqueness of weak solutions by the method of energy estimates and discuss additional regularity properties.

Equivalent Quantum Equations in a System Inspired by Bouncing Droplets Experiments

NASA Astrophysics Data System (ADS)

Borghesi, Christian

2017-07-01

In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy (and momentum) of the concretion, naturally defined from the energy (and momentum) density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas.

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

Mathematical Modeling of Torsional Surface Wave Propagation in a Non-Homogeneous Transverse Isotropic Elastic Solid Semi-Infinite Medium Under a Layer

NASA Astrophysics Data System (ADS)

Sethi, M.; Sharma, A.; Vasishth, A.

2017-05-01

The present paper deals with the mathematical modeling of the propagation of torsional surface waves in a non-homogeneous transverse isotropic elastic half-space under a rigid layer. Both rigidities and density of the half-space are assumed to vary inversely linearly with depth. Separation of variable method has been used to get the analytical solutions for the dispersion equation of the torsional surface waves. Also, the effects of nonhomogeneities on the phase velocity of torsional surface waves have been shown graphically. Also, dispersion equations have been derived for some particular cases, which are in complete agreement with some classical results.

Stability of post-fertilization traveling waves

NASA Astrophysics Data System (ADS)

Flores, Gilberto; Plaza, Ramón G.

This paper studies the stability of a family of traveling wave solutions to the system proposed by Lane et al. [D.C. Lane, J.D. Murray, V.S. Manoranjan, Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs, IMA J. Math. Appl. Med. Biol. 4 (4) (1987) 309-331], to model a pair of mechanochemical phenomena known as post-fertilization waves on eggs. The waves consist of an elastic deformation pulse on the egg's surface, and a free calcium concentration front. The family is indexed by a coupling parameter measuring contraction stress effects on the calcium concentration. This work establishes the spectral, linear and nonlinear orbital stability of these post-fertilization waves for small values of the coupling parameter. The usual methods for the spectral and evolution equations cannot be applied because of the presence of mixed partial derivatives in the elastic equation. Nonetheless, exponential decay of the directly constructed semigroup on the complement of the zero eigenspace is established. We show that small perturbations of the waves yield solutions to the nonlinear equations decaying exponentially to a phase-modulated traveling wave.

Wave chaos in the elastic disk.

PubMed

Sondergaard, Niels; Tanner, Gregor

2002-12-01

The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study, in particular, the eigenfrequencies of an elastic disk with free boundaries and their connection to periodic rays inside the circular domain. Even though the problem is separable, wave mixing between the shear and pressure component of the wave field at the boundary leads to an effective stochastic part in the ray dynamics. This introduces phenomena typically associated with classical chaos as, for example, an exponential increase in the number of periodic orbits. Classically, the problem can be decomposed into an integrable part and a simple binary Markov process. Similarly, the wave equation can, in the high-frequency limit, be mapped onto a quantum graph. Implications of this result for the level statistics are discussed. Furthermore, a periodic trace formula is derived from the scattering matrix based on the inside-outside duality between eigenmodes and scattering solutions and periodic orbits are identified by Fourier transforming the spectral density.

A Numerical Method for Predicting Rayleigh Surface Wave Velocity in Anisotropic Crystals (Postprint)

DTIC Science & Technology

2017-09-05

generalized version of the equations are very difficult to derive, even in symbolic math languages such as Mathematica. As a result, the equations are...formalism, Math . Mech. Solids 9 (1) (2004) 5–15. [8] M. Destrade, The explicit secular equation for surface acoustic waves in monoclinic elastic crystals...Q. J. Mech. Appl. Math . 55 (2) (2002) 297–311. [10] D. Taylor, Surface waves in anisotropic media: the secular equation and its numerical solution

Iterative image reconstruction in elastic inhomogenous media with application to transcranial photoacoustic tomography

NASA Astrophysics Data System (ADS)

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

2017-03-01

Photoacoustic computed tomography (PACT) is an emerging computed 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 a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT brain imaging is to compensate for aberrations in the measured data due to the propagation of the photoacoustic wavefields 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 medium. In this study, an iterative image reconstruction method for 3D transcranial PACT is developed based on the elastic wave equation. To accomplish this, a forward model based on a finite-difference time-domain discretization of the elastic wave equation is established. Subsequently, gradient-based methods are employed for computing penalized least squares estimates of the initial source distribution that produced the measured photoacoustic data. The developed reconstruction algorithm is validated and investigated through computer-simulation studies.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter.

PubMed

Fovargue, Daniel E; Mitran, Sorin; Smith, Nathan B; Sankin, Georgy N; Simmons, Walter N; Zhong, Pei

2013-08-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model.

Experimentally validated multiphysics computational model of focusing and shock wave formation in an electromagnetic lithotripter

PubMed Central

Fovargue, Daniel E.; Mitran, Sorin; Smith, Nathan B.; Sankin, Georgy N.; Simmons, Walter N.; Zhong, Pei

2013-01-01

A multiphysics computational model of the focusing of an acoustic pulse and subsequent shock wave formation that occurs during extracorporeal shock wave lithotripsy is presented. In the electromagnetic lithotripter modeled in this work the focusing is achieved via a polystyrene acoustic lens. The transition of the acoustic pulse through the solid lens is modeled by the linear elasticity equations and the subsequent shock wave formation in water is modeled by the Euler equations with a Tait equation of state. Both sets of equations are solved simultaneously in subsets of a single computational domain within the BEARCLAW framework which uses a finite-volume Riemann solver approach. This model is first validated against experimental measurements with a standard (or original) lens design. The model is then used to successfully predict the effects of a lens modification in the form of an annular ring cut. A second model which includes a kidney stone simulant in the domain is also presented. Within the stone the linear elasticity equations incorporate a simple damage model. PMID:23927200

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.

Reflection of electromagnetic wave from the boundary of the piezoelectric half-space with cubic symmetry

NASA Astrophysics Data System (ADS)

Berberyan, A. Kh; Garakov, V. G.

2018-04-01

A large number of works have been devoted to investigation of the influence of the piezoelectric properties of a material on the propagation of elastic waves [1–3]. Herewith, the quasi-static piezoelasticity model was mainly used. In the problem of an electromagnetic wave reflection from an elastic medium with piezoelectric properties, it is necessary to consider hyperbolic equations [4].

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.

In-plane time-harmonic elastic wave motion and resonance phenomena in a layered phononic crystal with periodic cracks.

PubMed

Golub, Mikhail V; Zhang, Chuanzeng

2015-01-01

This paper presents an elastodynamic analysis of two-dimensional time-harmonic elastic wave propagation in periodically multilayered elastic composites, which are also frequently referred to as one-dimensional phononic crystals, with a periodic array of strip-like interior or interface cracks. The transfer matrix method and the boundary integral equation method in conjunction with the Bloch-Floquet theorem are applied to compute the elastic wave fields in the layered periodic composites. The effects of the crack size, spacing, and location, as well as the incidence angle and the type of incident elastic waves on the wave propagation characteristics in the composite structure are investigated in details. In particular, the band-gaps, the localization and the resonances of elastic waves are revealed by numerical examples. In order to understand better the wave propagation phenomena in layered phononic crystals with distributed cracks, the energy flow vector of Umov and the corresponding energy streamlines are visualized and analyzed. The numerical results demonstrate that large energy vortices obstruct elastic wave propagation in layered phononic crystals at resonance frequencies. They occur before the cracks reflecting most of the energy transmitted by the incoming wave and disappear when the problem parameters are shifted from the resonant ones.

Exact Analytical Solutions for Elastodynamic Impact

DTIC Science & Technology

2015-11-30

corroborated by derivation of exact discrete solutions from recursive equations for the impact problems. 15. SUBJECT TERMS One-dimensional impact; Elastic...wave propagation; Laplace transform; Floor function; Discrete solutions 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18...impact Elastic wave propagation Laplace transform Floor function Discrete solutionsWe consider the one-dimensional impact problem in which a semi

Transformation of Elastic Wave Energy to the Energy of Motion of Bodies

NASA Astrophysics Data System (ADS)

Vesnitskiĭ, A. I.; Lisenkova, E. E.

2002-01-01

The motion of a body along an elastic guide under the effect of an incident wave is considered. An equation describing the longitudinal motion of a body along an arbitrary guide is derived from the laws governing the energy and momentum variations for the case when the incident wave generates a single reflected wave. The equations that describe the motion of a body along a string and along a beam corresponding to the Bernoulli-Euler model are considered as examples. The process of the body acceleration along a beam of the aforementioned type is investigated. For the subcritical velocities, the law governing the motion of the body and the ratio of the kinetic energy variation to the energy supplied to the body are determined.

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.

Implementation of perfectly matched layers in an arbitrary geometrical boundary for elastic wave modelling

NASA Astrophysics Data System (ADS)

Gao, Hongwei; Zhang, Jianfeng

2008-09-01

The perfectly matched layer (PML) absorbing boundary condition is incorporated into an irregular-grid elastic-wave modelling scheme, thus resulting in an irregular-grid PML method. We develop the irregular-grid PML method using the local coordinate system based PML splitting equations and integral formulation of the PML equations. The irregular-grid PML method is implemented under a discretization of triangular grid cells, which has the ability to absorb incident waves in arbitrary directions. This allows the PML absorbing layer to be imposed along arbitrary geometrical boundaries. As a result, the computational domain can be constructed with smaller nodes, for instance, to represent the 2-D half-space by a semi-circle rather than a rectangle. By using a smooth artificial boundary, the irregular-grid PML method can also avoid the special treatments to the corners, which lead to complex computer implementations in the conventional PML method. We implement the irregular-grid PML method in both 2-D elastic isotropic and anisotropic media. The numerical simulations of a VTI lamb's problem, wave propagation in an isotropic elastic medium with curved surface and in a TTI medium demonstrate the good behaviour of the irregular-grid PML method.

Single-wave-number representation of nonlinear energy spectrum in elastic-wave turbulence of the Föppl-von Kármán equation: energy decomposition analysis and energy budget.

PubMed

Yokoyama, Naoto; Takaoka, Masanori

2014-12-01

A single-wave-number representation of a nonlinear energy spectrum, i.e., a stretching-energy spectrum, is found in elastic-wave turbulence governed by the Föppl-von Kármán (FvK) equation. The representation enables energy decomposition analysis in the wave-number space and analytical expressions of detailed energy budgets in the nonlinear interactions. We numerically solved the FvK equation and observed the following facts. Kinetic energy and bending energy are comparable with each other at large wave numbers as the weak turbulence theory suggests. On the other hand, stretching energy is larger than the bending energy at small wave numbers, i.e., the nonlinearity is relatively strong. The strong correlation between a mode a(k) and its companion mode a(-k) is observed at the small wave numbers. The energy is input into the wave field through stretching-energy transfer at the small wave numbers, and dissipated through the quartic part of kinetic-energy transfer at the large wave numbers. Total-energy flux consistent with energy conservation is calculated directly by using the analytical expression of the total-energy transfer, and the forward energy cascade is observed clearly.

Bulk Nonlinear Elastic Strain Waves in a Bilayer Coaxial Cylindrical Rod

NASA Astrophysics Data System (ADS)

Gula, I. A.; Samsonov, A. M.

2017-12-01

The problem of the propagation of long nonlinear elastic strain waves in a bilayer coaxial cylindrical rod with an ideal contact between the layers has been considered. Expressions for transverse displacements through longitudinal displacements have been derived. The former satisfies free boundary conditions and continuity conditions for displacements and stresses at the interlayer interface with the desired accuracy. It has been shown how these expressions generalize the well-known plane-section and Love hypotheses for an isotropic homogeneous rod. An equation for the propagation of a nonlinearly elastic strain longitudinal wave has been derived, and its particular solution in the form of a solitary traveling wave has been studied.

Plane Evanescent Waves and Interface Waves

NASA Astrophysics Data System (ADS)

Luppé, F.; Conoir, J. M.; El Kettani, M. Ech-Cherif; Lenoir, O.; Izbicki, J. L.; Duclos, J.; Poirée, B.

The evanescent plane wave formalism is used to obtain the characteristic equation of the normal vibration modes of a plane elastic solid embedded in a perfect fluid. Simple drawings of the real and imaginary parts of complex wave vectors make quite clear the choice of the Riemann sheets on which the roots of the characteristic equation are to be looked for. The generalized Rayleigh wave and the Scholte - Stoneley wave are then described. The same formalism is used to describe Lamb waves on an elastic plane plate immersed in water. The damping, due to energy leaking in the fluid, is shown to be directly given by the projection of evanescence vectors on the interface. Measured values of the damping coefficient are in good agreement with those derived from calculations. The width of the angular resonances associated to Lamb waves or Rayleigh waves is also directly related to this same evanescence vectors projection, as well as the excitation coefficient of a given Lamb wave excited by a plane incident wave. This study shows clearly the strong correlation between the resonance point of view and the wave one in plane interface problems.

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

Transformation elastodynamics and cloaking for flexural waves

NASA Astrophysics Data System (ADS)

Colquitt, D. J.; Brun, M.; Gei, M.; Movchan, A. B.; Movchan, N. V.; Jones, I. S.

2014-12-01

The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general form of the partial differential equation is not invariant with respect to the cloaking transformation. The significant result of this paper is the analysis of the transformed equation and its interpretation in the framework of the linear theory of pre-stressed plates. The paper provides a formal framework for transformation elastodynamics as applied to elastic plates. Furthermore, an algorithm is proposed for designing a broadband square cloak for flexural waves, which employs a regularised push-out transformation. Illustrative numerical examples show high accuracy and efficiency of the proposed cloaking algorithm. In particular, a physical configuration involving a perturbation of an interference pattern generated by two coherent sources is presented. It is demonstrated that the perturbation produced by a cloaked defect is negligibly small even for such a delicate interference pattern.

Alternative stable qP wave equations in TTI media with their applications for reverse time migration

NASA Astrophysics Data System (ADS)

Zhou, Yang; Wang, Huazhong; Liu, Wenqing

2015-10-01

Numerical instabilities may arise if the spatial variation of symmetry axis is handled improperly when implementing P-wave modeling and reverse time migration in heterogeneous tilted transversely isotropic (TTI) media, especially in the cases where fast changes exist in TTI symmetry axis’ directions. Based on the pseudo-acoustic approximation to anisotropic elastic wave equations in Cartesian coordinates, alternative second order qP (quasi-P) wave equations in TTI media are derived in this paper. Compared with conventional stable qP wave equations, the proposed equations written in stress components contain only spatial derivatives of wavefield variables (stress components) and are free from spatial derivatives involving media parameters. These lead to an easy and efficient implementation for stable P-wave modeling and imaging. Numerical experiments demonstrate the stability and computational efficiency of the presented equations in complex TTI media.

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.

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.

Evolution of nonlinear waves in a blood-filled artery with an aneurysm

NASA Astrophysics Data System (ADS)

Nikolova, E. V.; Jordanov, I. P.; Dimitrova, Z. I.; Vitanov, N. K.

2017-10-01

We discuss propagation of traveling waves in a blood-filled hyper-elastic artery with a local dilatation (an aneurysm). The processes in the injured artery are modeled by an equation of the motion of the arterial wall and by equations of the motion of the fluid (the blood). Taking into account the specific arterial geometry and applying the reductive perturbation method in long-wave approximation we reduce the model equations to a version of the perturbed Korteweg-de Vries kind equation with variable coefficients. Exact traveling-wave solutions of this equation are obtained by the modified method of simplest equation where the differential equation of Abel is used as a simplest equation. A particular case of the obtained exact solution is numerically simulated and discussed from the point of view of arterial disease mechanics.

Elastic guided wave propagation in electrical cables.

PubMed

Mateo, Carlos; Talavera, Juan A; Muñoz, Antonio

2007-07-01

This article analyzes the propagation modes of ultrasound waves inside an electrical cable in order to assess its behavior as an acoustic transmission channel. A theoretical model for propagation of elastic waves in electric power cables is presented. The power cables are represented as viscoelastic-layered cylindrical structures with a copper core and a dielectric cover. The model equations then have been applied and numerically resolved for this and other known structures such as solid and hollow cylinders. The results are compared with available data from other models. Several experimental measures were carried out and were compared with results from the numerical simulations. Experimental and simulated results showed a significant difference between elastic wave attenuation inside standard versus bare, low-voltage power cables.

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.

Reflection coefficient of qP, qS and SH at a plane boundary between viscoelastic TTI media

NASA Astrophysics Data System (ADS)

Wang, Hongwei; Peng, Suping

2016-01-01

This paper introduces a calculation method for the effective elastic stiffness tensor matrix of the viscous-elastic TTI medium based on the Chapman theory. We then obtain the phase velocity formula and seismic wave polarization formula of the viscous-elastic TTI medium, by solving the Christoffel equation; solve the phase angle of reflection and transmission wave through the numerical method in accordance with the wave slowness ellipsoid; on the basis of this assumption, and assuming that qP, qS and SH waves occurred simultaneously at the viscous-elastic anisotropic interface, establish the sixth-order Zoeppritz equation in accordance with the boundary conditions; establish the models for the upper and lower media which are viscous-elastic HTI, TTI, etc., on the basis of the sixth-order Zoeppritz equation; and study the impact of fracture dip angle, azimuth angle and frequency on the reflection coefficient. From this we obtain the following conclusions: the reflection coefficient can identify the fracture strike and dip when any information pertaining to the media is unknown; dispersion phenomenon is obvious on the axial plane of symmetry and weakened in the plane vertical to the axial plane of symmetry; the vertical-incidence longitudinal wave can stimulate the qS wave when the dip angle is not 0° or 90° under the condition of coincidence between the symmetry planes of the upper and lower media; when the symmetry planes of the upper and lower media do not coincide and the dip angle is not 0° or 90°, then the vertical-incidence qP will stimulate the qS and SH waves at the same time; the dip angle can cause the reflection coefficient curve to have a more obvious dispersion phenomenon, while the included angle between the symmetry planes of the upper and lower media will weaken the dispersion except SH; and the intercept of reflection coefficient is affected by the fracture dip and included angle between the symmetry planes of the upper and lower media.

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.

Quantum revival for elastic waves in thin plate

NASA Astrophysics Data System (ADS)

Dubois, Marc; Lefebvre, Gautier; Sebbah, Patrick

2017-05-01

Quantum revival is described as the time-periodic reconstruction of a wave packet initially localized in space and time. This effect is expected in finite-size systems which exhibit commensurable discrete spectrum such as the infinite quantum well. Here, we report on the experimental observation of full and fractional quantum revival for classical waves in a two dimensional cavity. We consider flexural waves propagating in thin plates, as their quadratic dispersion at low frequencies mimics the dispersion relation of quantum systems governed by Schrödinger equation. Time-dependent excitation and measurement are performed at ultrasonic frequencies and reveal a periodic reconstruction of the initial elastic wave packet.

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.

Shear waves in elastic medium with void pores welded between vertically inhomogeneous and anisotropic magnetoelastic semi-infinite media

NASA Astrophysics Data System (ADS)

Gupta, Shishir; Ahmed, Mostaid; Pramanik, Abhijit

2017-03-01

The paper intends to study the propagation of horizontally polarized shear waves in an elastic medium with void pores constrained between a vertically inhomogeneous and an anisotropic magnetoelastic semi-infinite media. Elasto-dynamical equations of elastic medium with void pores and magnetoelastic solid have been employed to investigate the shear wave propagation in the proposed three-layered earth model. Method of separation of variables has been incorporated to deduce the dispersion relation. All possible special cases have been envisaged and they fairly comply with the corresponding results for classical cases. The role of inhomogeneity parameter, thickness of layer, angle with which the wave crosses the magnetic field and anisotropic magnetoelastic coupling parameter for three different materials has been elucidated and represented by graphs using MATHEMATICA.

An Analysis of an Implicit Factored Scheme for Simulating Shock Waves

DTIC Science & Technology

1988-05-01

can cope with a wide range of boundary conditions and equations of state, For modelling -( shock waves in solids, elastic- plastic terms must also be...positive caracteristic speeds. One-sided schemes have superior dissipative and dispersive properties compared to those of centered schemes (Steger and...Elastic- plastic con. ditions must be- incorporated into the problem and usually the addition of suitable bource or sink terms to c-’ustion (1

Spacetime representation of topological phononics

NASA Astrophysics Data System (ADS)

Deymier, Pierre A.; Runge, Keith; Lucas, Pierre; Vasseur, Jérôme O.

2018-05-01

Non-conventional topology of elastic waves arises from breaking symmetry of phononic structures either intrinsically through internal resonances or extrinsically via application of external stimuli. We develop a spacetime representation based on twistor theory of an intrinsic topological elastic structure composed of a harmonic chain attached to a rigid substrate. Elastic waves in this structure obey the Klein–Gordon and Dirac equations and possesses spinorial character. We demonstrate the mapping between straight line trajectories of these elastic waves in spacetime and the twistor complex space. The twistor representation of these Dirac phonons is related to their topological and fermion-like properties. The second topological phononic structure is an extrinsic structure composed of a one-dimensional elastic medium subjected to a moving superlattice. We report an analogy between the elastic behavior of this time-dependent superlattice, the scalar quantum field theory and general relativity of two types of exotic particle excitations, namely temporal Dirac phonons and temporal ghost (tachyonic) phonons. These phonons live on separate sides of a two-dimensional frequency space and are delimited by ghost lines reminiscent of the conventional light cone. Both phonon types exhibit spinorial amplitudes that can be measured by mapping the particle behavior to the band structure of elastic waves.

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

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

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

Yu, Xin, E-mail: yuxin@buaa.edu.cn; Sun, Zhi-Yuan

Under investigation in this paper is a nonautonomous Kadomtsev–Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Parabola solitons for the nonautonomous KP equation in fluids and plasmas

NASA Astrophysics Data System (ADS)

Yu, Xin; Sun, Zhi-Yuan

2016-04-01

Under investigation in this paper is a nonautonomous Kadomtsev-Petviashvili (KP) equation in fluids and plasmas. The integrability of this equation is examined via the Painlevé analysis and its multi-soliton solutions are constructed. A constraint is proposed to ensure the existence of parabola solitons for such KP equation. Based on the constructed solutions, the solitonic propagation and interaction, including the elastic interaction, inelastic interaction and soliton resonance for parabola solitons, are discussed. The results might be useful for shallow water wave and rogue wave.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) – a simplified treatment of interfaces

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

Martin, Bradley, E-mail: brma7253@colorado.edu; Fornberg, Bengt, E-mail: Fornberg@colorado.edu

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy formore » the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.« less

A finite difference method for a coupled model of wave propagation in poroelastic materials.

PubMed

Zhang, Yang; Song, Limin; Deffenbaugh, Max; Toksöz, M Nafi

2010-05-01

A computational method for time-domain multi-physics simulation of wave propagation in a poroelastic medium is presented. The medium is composed of an elastic matrix saturated with a Newtonian fluid, and the method operates on a digital representation of the medium where a distinct material phase and properties are specified at each volume cell. The dynamic response to an acoustic excitation is modeled mathematically with a coupled system of equations: elastic wave equation in the solid matrix and linearized Navier-Stokes equation in the fluid. Implementation of the solution is simplified by introducing a common numerical form for both solid and fluid cells and using a rotated-staggered-grid which allows stable solutions without explicitly handling the fluid-solid boundary conditions. A stability analysis is presented which can be used to select gridding and time step size as a function of material properties. The numerical results are shown to agree with the analytical solution for an idealized porous medium of periodically alternating solid and fluid layers.

Seismic modeling with radial basis function-generated finite differences (RBF-FD) - a simplified treatment of interfaces

NASA Astrophysics Data System (ADS)

Martin, Bradley; Fornberg, Bengt

2017-04-01

In a previous study of seismic modeling with radial basis function-generated finite differences (RBF-FD), we outlined a numerical method for solving 2-D wave equations in domains with material interfaces between different regions. The method was applicable on a mesh-free set of data nodes. It included all information about interfaces within the weights of the stencils (allowing the use of traditional time integrators), and was shown to solve problems of the 2-D elastic wave equation to 3rd-order accuracy. In the present paper, we discuss a refinement of that method that makes it simpler to implement. It can also improve accuracy for the case of smoothly-variable model parameter values near interfaces. We give several test cases that demonstrate the method solving 2-D elastic wave equation problems to 4th-order accuracy, even in the presence of smoothly-curved interfaces with jump discontinuities in the model parameters.

Determination of the effective transverse coherence of the neutron wave packet as employed in reflectivity investigations of condensed-matter structures. II. Analysis of elastic scattering using energy-gated wave packets with an application to neutron reflection from ruled gratings

NASA Astrophysics Data System (ADS)

Berk, N. F.

2014-03-01

We present a general approach to analyzing elastic scattering for those situations where the incident beam is prepared as an incoherent ensemble of wave packets of a given arbitrary shape. Although wave packets, in general, are not stationary solutions of the Schrödinger equation, the analysis of elastic scattering data treats the scattering as a stationary-state problem. We thus must gate the wave packet, coherently distorting its shape in a manner consistent with the elastic condition. The resulting gated scattering amplitudes (e.g., reflection coefficients) thus are weighted coherent sums of the constituent plane-wave scattering amplitudes, with the weights determined by the shape of the incident wave packet as "filtered" by energy gating. We develop the gating formalism in general and apply it to the problem of neutron scattering from ruled gratings described by Majkrzak et al. in a companion paper. The required exact solution of the associated problem of plane-wave reflection from gratings also is derived.

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

A spectral hybridizable discontinuous Galerkin method for elastic-acoustic wave propagation

NASA Astrophysics Data System (ADS)

Terrana, S.; Vilotte, J. P.; Guillot, L.

2018-04-01

We introduce a time-domain, high-order in space, hybridizable discontinuous Galerkin (DG) spectral element method (HDG-SEM) for wave equations in coupled elastic-acoustic media. The method is based on a first-order hyperbolic velocity-strain formulation of the wave equations written in conservative form. This method follows the HDG approach by introducing a hybrid unknown, which is the approximation of the velocity on the elements boundaries, as the only globally (i.e. interelement) coupled degrees of freedom. In this paper, we first present a hybridized formulation of the exact Riemann solver at the element boundaries, taking into account elastic-elastic, acoustic-acoustic and elastic-acoustic interfaces. We then use this Riemann solver to derive an explicit construction of the HDG stabilization function τ for all the above-mentioned interfaces. We thus obtain an HDG scheme for coupled elastic-acoustic problems. This scheme is then discretized in space on quadrangular/hexahedral meshes using arbitrary high-order polynomial basis for both volumetric and hybrid fields, using an approach similar to the spectral element methods. This leads to a semi-discrete system of algebraic differential equations (ADEs), which thanks to the structure of the global conservativity condition can be reformulated easily as a classical system of first-order ordinary differential equations in time, allowing the use of classical explicit or implicit time integration schemes. When an explicit time scheme is used, the HDG method can be seen as a reformulation of a DG with upwind fluxes. The introduction of the velocity hybrid unknown leads to relatively simple computations at the element boundaries which, in turn, makes the HDG approach competitive with the DG-upwind methods. Extensive numerical results are provided to illustrate and assess the accuracy and convergence properties of this HDG-SEM. The approximate velocity is shown to converge with the optimal order of k + 1 in the L2-norm, when element polynomials of order k are used, and to exhibit the classical spectral convergence of SEM. Additional inexpensive local post-processing in both the elastic and the acoustic case allow to achieve higher convergence orders. The HDG scheme provides a natural framework for coupling classical, continuous Galerkin SEM with HDG-SEM in the same simulation, and it is shown numerically in this paper. As such, the proposed HDG-SEM can combine the efficiency of the continuous SEM with the flexibility of the HDG approaches. Finally, more complex numerical results, inspired from real geophysical applications, are presented to illustrate the capabilities of the method for wave propagation in heterogeneous elastic-acoustic media with complex geometries.

A first-order k-space model for elastic wave propagation in heterogeneous media.

PubMed

Firouzi, K; Cox, B T; Treeby, B E; Saffari, N

2012-09-01

A pseudospectral model of linear elastic wave propagation is described based on the first order stress-velocity equations of elastodynamics. k-space adjustments to the spectral gradient calculations are derived from the dyadic Green's function solution to the second-order elastic wave equation and used to (a) ensure the solution is exact for homogeneous wave propagation for timesteps of arbitrarily large size, and (b) also allows larger time steps without loss of accuracy in heterogeneous media. The formulation in k-space allows the wavefield to be split easily into compressional and shear parts. A perfectly matched layer (PML) absorbing boundary condition was developed to effectively impose a radiation condition on the wavefield. The staggered grid, which is essential for accurate simulations, is described, along with other practical details of the implementation. The model is verified through comparison with exact solutions for canonical examples and further examples are given to show the efficiency of the method for practical problems. The efficiency of the model is by virtue of the reduced point-per-wavelength requirement, the use of the fast Fourier transform (FFT) to calculate the gradients in k space, and larger time steps made possible by the k-space adjustments.

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

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

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

Sano, Yukio; Abe, Akihisa; Tokushima, Koji

The aim of this study is to examine the difference between shock temperatures predicted by an equation for temperature inside a steady wave front and the Walsh-Christian equation. Calculations are for yttria-doped tetragonal zirconia, which shows an elastic-plastic and a phase transition: Thus the shock waves treated are multiple structure waves composed of one to three steady wave fronts. The evaluated temperature was 3350K at the minimum specific volume of 0.1175 cm{sup 3}/g (or maximum Hugoniot shock pressure of 140GPa) considered in the present examination, while the temperature predicted by the Walsh-Christian equation under identical conditions was 2657K. The causemore » of the large temperature discrepancy is considered to be that the present model treats nonequilibrium states inside steady waves.« less

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.

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.

Dissipation-preserving spectral element method for damped seismic wave equations

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai; Wang, Yushun

2017-12-01

This article describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems, which has superior behaviors in long-time stability and dissipation preservation. To reveal the intrinsic dissipative properties of the model equations, we first reformulate the original systems in their equivalent conformal multi-symplectic structures and derive the corresponding conformal symplectic conservation laws. We thereafter separate each system into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed conformal symplectic method. A relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh wave in elastic wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic methods in both the attenuating homogeneous and heterogeneous media.

Second Order Accurate Finite Difference Methods

DTIC Science & Technology

1984-08-20

34Nonlinear Modulation of Torsional Waves in Elastic Rods," 3. Phys. Soc. Japan, V. 42, No. 6, pp. 2056-2064, 1977. 10. S. S. Antman and T. Liu. "Travelling...waves in a circular rod. The equations have been solved for coupling effects in torsional and longitudinal waves. Antman and Liu (10) have studied

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Soliton solutions to the fifth-order Korteweg-de Vries equation and their applications to surface and internal water waves

NASA Astrophysics Data System (ADS)

Khusnutdinova, K. R.; Stepanyants, Y. A.; Tranter, M. R.

2018-02-01

We study solitary wave solutions of the fifth-order Korteweg-de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.).

Propagation and attenuation of Rayleigh waves in generalized thermoelastic media

NASA Astrophysics Data System (ADS)

Sharma, M. D.

2014-01-01

This study considers the propagation of Rayleigh waves in a generalized thermoelastic half-space with stress-free plane boundary. The boundary has the option of being either isothermal or thermally insulated. In either case, the dispersion equation is obtained in the form of a complex irrational expression due to the presence of radicals. This dispersion equation is rationalized into a polynomial equation, which is solvable, numerically, for exact complex roots. The roots of the dispersion equation are obtained after removing the extraneous zeros of this polynomial equation. Then, these roots are filtered out for the inhomogeneous propagation of waves decaying with depth. Numerical examples are solved to analyze the effects of thermal properties of elastic materials on the dispersion of existing surface waves. For these thermoelastic Rayleigh waves, the behavior of elliptical particle motion is studied inside and at the surface of the medium. Insulation of boundary does play a significant role in changing the speed, amplitude, and polarization of Rayleigh waves in thermoelastic media.

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.

Nonlinear to Linear Elastic Code Coupling in 2-D Axisymmetric Media.

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

Preston, Leiph

Explosions within the earth nonlinearly deform the local media, but at typical seismological observation distances, the seismic waves can be considered linear. Although nonlinear algorithms can simulate explosions in the very near field well, these codes are computationally expensive and inaccurate at propagating these signals to great distances. A linearized wave propagation code, coupled to a nonlinear code, provides an efficient mechanism to both accurately simulate the explosion itself and to propagate these signals to distant receivers. To this end we have coupled Sandia's nonlinear simulation algorithm CTH to a linearized elastic wave propagation code for 2-D axisymmetric media (axiElasti)more » by passing information from the nonlinear to the linear code via time-varying boundary conditions. In this report, we first develop the 2-D axisymmetric elastic wave equations in cylindrical coordinates. Next we show how we design the time-varying boundary conditions passing information from CTH to axiElasti, and finally we demonstrate the coupling code via a simple study of the elastic radius.« less

Viscoelastic Waves Simulation in a Blocky Medium with Fluid-Saturated Interlayers Using High-Performance Computing

NASA Astrophysics Data System (ADS)

Sadovskii, Vladimir; Sadovskaya, Oxana

2017-04-01

A thermodynamically consistent approach to the description of linear and nonlinear wave processes in a blocky medium, which consists of a large number of elastic blocks interacting with each other via pliant interlayers, is proposed. The mechanical properties of interlayers are defined by means of the rheological schemes of different levels of complexity. Elastic interaction between the blocks is considered in the framework of the linear elasticity theory [1]. The effects of viscoelastic shear in the interblock interlayers are taken into consideration using the Pointing-Thomson rheological scheme. The model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. On the basis of the Biot equations for a fluid-saturated porous medium, a new mathematical model of a blocky medium is worked out, in which the interlayers provide a convective fluid motion due to the external perturbations. The collapse of pores is modeled within the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact [2], which is used to describe the behavior of materials with different resistance to tension and compression. Thermodynamic consistency of the equations in interlayers with the equations in blocks guarantees fulfillment of the energy conservation law for a blocky medium in a whole, i.e. kinetic and potential energy of the system is the sum of kinetic and potential energies of the blocks and interlayers. As a result of discretization of the equations of the model, robust computational algorithm is constructed, that is stable because of the thermodynamic consistency of the finite difference equations at a discrete level. The splitting method by the spatial variables and the Godunov gap decay scheme are used in the blocks, the dissipationless finite difference Ivanov scheme is applied in the interlayers. The parallel program is designed, using the MPI technology. By means of this software, nonlinear wave processes in the case of initial rotation of the central block in a rock mass as well as in the case of concentrated couple stress load, applied at the boundary of a rock mass, are analyzed. Results of computations on the multiprocessor computer systems demonstrate the strong anisotropy of a blocky medium. This work was supported by the Complex Fundamental Research Program no. II.2P "Integration and Development" of Siberian Branch of the Russian Academy of Sciences. References 1. Sadovskii V.M., Sadovskaya O.V. Modeling of Elastic Waves in a Blocky Medium Based on Equations of the Cosserat Continuum // Wave Motion. 2015. V. 52. P. 138-150. 2. Sadovskaya O., Sadovskii V. Mathematical Modeling in Mechanics of Granular Materials. Ser.: Advanced Structured Materials, V. 21. Heidelberg - New York - Dordrecht - London, Springer, 2012. 390 p.

Enabling real-time ultrasound imaging of soft tissue mechanical properties by simplification of the shear wave motion equation.

PubMed

Engel, Aaron J; Bashford, Gregory R

2015-08-01

Ultrasound based shear wave elastography (SWE) is a technique used for non-invasive characterization and imaging of soft tissue mechanical properties. Robust estimation of shear wave propagation speed is essential for imaging of soft tissue mechanical properties. In this study we propose to estimate shear wave speed by inversion of the first-order wave equation following directional filtering. This approach relies on estimation of first-order derivatives which allows for accurate estimations using smaller smoothing filters than when estimating second-order derivatives. The performance was compared to three current methods used to estimate shear wave propagation speed: direct inversion of the wave equation (DIWE), time-to-peak (TTP) and cross-correlation (CC). The shear wave speed of three homogeneous phantoms of different elastic moduli (gelatin by weight of 5%, 7%, and 9%) were measured with each method. The proposed method was shown to produce shear speed estimates comparable to the conventional methods (standard deviation of measurements being 0.13 m/s, 0.05 m/s, and 0.12 m/s), but with simpler processing and usually less time (by a factor of 1, 13, and 20 for DIWE, CC, and TTP respectively). The proposed method was able to produce a 2-D speed estimate from a single direction of wave propagation in about four seconds using an off-the-shelf PC, showing the feasibility of performing real-time or near real-time elasticity imaging with dedicated hardware.

A Unified Treatment of the Acoustic and Elastic Scattered Waves from Fluid-Elastic Media

NASA Astrophysics Data System (ADS)

Denis, Max Fernand

In this thesis, contributions are made to the numerical modeling of the scattering fields from fluid-filled poroelastic materials. Of particular interest are highly porous materials that demonstrate strong contrast to the saturating fluid. A Biot's analysis of porous medium serves as the starting point of the elastic-solid and pore-fluid governing equations of motion. The longitudinal scattering waves of the elastic-solid mode and the pore-fluid mode are modeled by the Kirchhoff-Helmholtz integral equation. The integral equation is evaluated using a series approximation, describing the successive perturbation of the material contrasts. To extended the series' validity into larger domains, rational fraction extrapolation methods are employed. The local Pade□ approximant procedure is a technique that allows one to extrapolate from a scattered field of small contrast into larger values, using Pade□ approximants. To ensure the accuracy of the numerical model, comparisons are made with the exact solution of scattering from a fluid sphere. Mean absolute error analyses, yield convergent and accurate results. In addition, the numerical model correctly predicts the Bragg peaks for a periodic lattice of fluid spheres. In the case of trabecular bones, the far-field scattering pressure attenuation is a superposition of the elastic-solid mode and the pore-fluid mode generated waves from the surrounding fluid and poroelastic boundaries. The attenuation is linearly dependent with frequency between 0.2 and 0.6MHz. The slope of the attenuation is nonlinear with porosity, and does not reflect the mechanical properties of the trabecular bone. The attenuation shows the anisotropic effects of the trabeculae structure. Thus, ultrasound can possibly be employed to non-invasively predict the principal structural orientation of trabecular bones.

A parametric analysis of waves propagating in a porous solid saturated by a three-phase fluid.

PubMed

Santos, Juan E; Savioli, Gabriela B

2015-11-01

This paper presents an analysis of a model for the propagation of waves in a poroelastic solid saturated by a three-phase viscous, compressible fluid. The constitutive relations and the equations of motion are stated first. Then a plane wave analysis determines the phase velocities and attenuation coefficients of the four compressional waves and one shear wave that propagate in this type of medium. A procedure to compute the elastic constants in the constitutive relations is defined next. Assuming the knowledge of the shear modulus of the dry matrix, the other elastic constants in the stress-strain relations are determined by employing ideal gedanken experiments generalizing those of Biot's theory for single-phase fluids. These experiments yield expressions for the elastic constants in terms of the properties of the individual solid and fluids phases. Finally the phase velocities and attenuation coefficients of all waves are computed for a sample of Berea sandstone saturated by oil, gas, and water.

Observation of shock transverse waves in elastic media.

PubMed

Catheline, S; Gennisson, J-L; Tanter, M; Fink, M

2003-10-17

We report the first experimental observation of a shock transverse wave propagating in an elastic medium. This observation was possible because the propagation medium, a soft solid, allows one to reach a very high Mach number. In this extreme configuration, the shock formation is observed over a distance of less than a few wavelengths, thanks to a prototype of an ultrafast scanner (that acquires 5000 frames per second). A comparison of these new experimental data with theoretical predictions, based on a modified Burger's equation, shows good agreement.

Elastic parabolic equation and normal mode solutions for seismo-acoustic propagation in underwater environments with ice covers.

PubMed

Collis, Jon M; Frank, Scott D; Metzler, Adam M; Preston, Kimberly S

2016-05-01

Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.

Volterra integral equation-factorisation method and nucleus-nucleus elastic scattering

NASA Astrophysics Data System (ADS)

Laha, U.; Majumder, M.; Bhoi, J.

2018-04-01

An approximate solution for the nuclear Hulthén plus atomic Hulthén potentials is constructed by solving the associated Volterra integral equation by series substitution method. Within the framework of supersymmetry-inspired factorisation method, this solution is exploited to construct higher partial wave interactions. The merit of our approach is examined by computing elastic scattering phases of the α {-}α system by the judicious use of phase function method. Reasonable agreements in phase shifts are obtained with standard data.

Solitons, Bäcklund transformation and Lax pair for a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation in the fluid/plasma mechanics

NASA Astrophysics Data System (ADS)

Lan, Zhong-Zhou; Gao, Yi-Tian; Yang, Jin-Wei; Su, Chuan-Qi; Wang, Qi-Min

2016-09-01

Under investigation in this paper is a (2+1)-dimensional B-type Kadomtsev-Petviashvili equation for the shallow water wave in a fluid or electrostatic wave potential in a plasma. Bilinear form, Bäcklund transformation and Lax pair are derived based on the binary Bell polynomials. Multi-soliton solutions are constructed via the Hirota’s method. Propagation and interaction of the solitons are illustrated graphically: (i) Through the asymptotic analysis, elastic and inelastic interactions between the two solitons are discussed analytically and graphically, respectively. The elastic interaction, amplitudes, velocities and shapes of the two solitons remain unchanged except for a phase shift. However, in the area of the inelastic interaction, amplitudes of the two solitons have a linear superposition. (ii) Elastic interactions among the three solitons indicate that the properties of the elastic interactions among the three solitons are similar to those between the two solitons. Moreover, oblique and overtaking interactions between the two solitons are displayed. Oblique interactions among the three solitons and interactions among the two parallel solitons and a single one are presented as well. (iii) Inelastic-elastic interactions imply that the interaction between the inelastic region and another one is elastic.

Role of surface elasticity in the drainage of soap films

NASA Astrophysics Data System (ADS)

Sonin, A. A.; Bonfillon, A.; Langevin, D.

1993-10-01

We present measurements of the thinning velocity of circular horizontal soap films made from dilute surfactant solutions (around the critical micellar concentration). We have solved numerically the hydrodynamic equations for the drainage process. After data fitting, we deduce the values of the elasticities of the surfactant monolayer that stabilizes the soap film. These elasticity values have been compared to elasticities obtained independently from the study of waves at the surface of the solution. The comparison reveals the importance of surface convection in the drainage process and demonstrates the important role of surface elasticity.

Stress Wave Propagation in Viscoelastic-Plastic Rock-Like Materials.

PubMed

Lang, Liu; Song, Ki-Il; Zhai, Yue; Lao, Dezheng; Lee, Hang-Lo

2016-05-17

Rock-like materials are composites that can be regarded as a mixture composed of elastic, plastic, and viscous components. They exhibit viscoelastic-plastic behavior under a high-strain-rate loading according to element model theory. This paper presents an analytical solution for stress wave propagation in viscoelastic-plastic rock-like materials under a high-strain-rate loading and verifies the solution through an experimental test. A constitutive equation of viscoelastic-plastic rock-like materials was first established, and then kinematic and kinetic equations were then solved to derive the analytic solution for stress wave propagation in viscoelastic-plastic rock-like materials. An experimental test using the SHPB (Split Hopkinson Pressure Bar) for a concrete specimen was conducted to obtain a stress-strain curve under a high-strain-rate loading. Inverse analysis based on differential evolution was conducted to estimate undetermined variables for constitutive equations. Finally, the relationship between the attenuation factor and the strain rate in viscoelastic-plastic rock-like materials was investigated. According to the results, the frequency of the stress wave, viscosity coefficient, modulus of elasticity, and density play dominant roles in the attenuation of the stress wave. The attenuation decreases with increasing strain rate, demonstrating strongly strain-dependent attenuation in viscoelastic-plastic rock-like materials.

An optimization-based approach for solving a time-harmonic multiphysical wave problem with higher-order schemes

NASA Astrophysics Data System (ADS)

Mönkölä, Sanna

2013-06-01

This study considers developing numerical solution techniques for the computer simulations of time-harmonic fluid-structure interaction between acoustic and elastic waves. The focus is on the efficiency of an iterative solution method based on a controllability approach and spectral elements. We concentrate on the model, in which the acoustic waves in the fluid domain are modeled by using the velocity potential and the elastic waves in the structure domain are modeled by using displacement. Traditionally, the complex-valued time-harmonic equations are used for solving the time-harmonic problems. Instead of that, we focus on finding periodic solutions without solving the time-harmonic problems directly. The time-dependent equations can be simulated with respect to time until a time-harmonic solution is reached, but the approach suffers from poor convergence. To overcome this challenge, we follow the approach first suggested and developed for the acoustic wave equations by Bristeau, Glowinski, and Périaux. Thus, we accelerate the convergence rate by employing a controllability method. The problem is formulated as a least-squares optimization problem, which is solved with the conjugate gradient (CG) algorithm. Computation of the gradient of the functional is done directly for the discretized problem. A graph-based multigrid method is used for preconditioning the CG algorithm.

Stress Wave Propagation in Viscoelastic-Plastic Rock-Like Materials

PubMed Central

Lang, Liu; Song, KI-IL; Zhai, Yue; Lao, Dezheng; Lee, Hang-Lo

2016-01-01

Rock-like materials are composites that can be regarded as a mixture composed of elastic, plastic, and viscous components. They exhibit viscoelastic-plastic behavior under a high-strain-rate loading according to element model theory. This paper presents an analytical solution for stress wave propagation in viscoelastic-plastic rock-like materials under a high-strain-rate loading and verifies the solution through an experimental test. A constitutive equation of viscoelastic-plastic rock-like materials was first established, and then kinematic and kinetic equations were then solved to derive the analytic solution for stress wave propagation in viscoelastic-plastic rock-like materials. An experimental test using the SHPB (Split Hopkinson Pressure Bar) for a concrete specimen was conducted to obtain a stress-strain curve under a high-strain-rate loading. Inverse analysis based on differential evolution was conducted to estimate undetermined variables for constitutive equations. Finally, the relationship between the attenuation factor and the strain rate in viscoelastic-plastic rock-like materials was investigated. According to the results, the frequency of the stress wave, viscosity coefficient, modulus of elasticity, and density play dominant roles in the attenuation of the stress wave. The attenuation decreases with increasing strain rate, demonstrating strongly strain-dependent attenuation in viscoelastic-plastic rock-like materials. PMID:28773500

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.

Local recovery of the compressional and shear speeds from the hyperbolic DN map

NASA Astrophysics Data System (ADS)

Stefanov, Plamen; Uhlmann, Gunther; Vasy, Andras

2018-01-01

We study the isotropic elastic wave equation in a bounded domain with boundary. We show that local knowledge of the Dirichlet-to-Neumann map determines uniquely the speed of the p-wave locally if there is a strictly convex foliation with respect to it, and similarly for the s-wave speed.

Scattering of elastic waves by a spheroidal inclusion

NASA Astrophysics Data System (ADS)

Johnson, Lane R.

2018-03-01

An analytical solution is presented for scattering of elastic waves by prolate and oblate spheroidal inclusions. The problem is solved in the frequency domain where separation of variables leads to a solution involving spheroidal wave functions of the angular and radial kind. Unlike the spherical problem, the boundary equations remain coupled with respect to one of the separation indices. Expanding the angular spheroidal wave functions in terms of associated Legendre functions and using their orthogonality properties leads to a set of linear equations that can be solved to simultaneously obtain solutions for all coupled modes of both scattered and interior fields. To illustrate some of the properties of the spheroidal solution, total scattering cross-sections for P, SV and SH plane waves incident at an oblique angle on a prolate spheroid, an oblate spheroid and a sphere are compared. The waveforms of the scattered field exterior to the inclusion are calculated for these same incident waves. The waveforms scattered by a spheroid are strongly dependent upon the angle of incidence, are different for incident SV and SH waves and are asymmetrical about the centre of the spheroid with the asymmetry different for prolate and oblate spheroids.

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.

Wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes with surface and nonlocal effects

NASA Astrophysics Data System (ADS)

Zhen, Ya-Xin

2017-02-01

In this paper, the transverse wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes is investigated based on nonlocal elasticity theory with consideration of surface effect. The governing equation is formulated utilizing nonlocal Euler-Bernoulli beam theory and Kelvin-Voigt model. Explicit wave dispersion relation is developed and wave phase velocities and frequencies are obtained. The effect of the fluid flow velocity, structural damping, surface effect, small scale effects and tube diameter on the wave propagation properties are discussed with different wave numbers. The wave frequency increases with the increase of fluid flow velocity, but decreases with the increases of tube diameter and wave number. The effect of surface elasticity and residual surface tension is more significant for small wave number and tube diameter. For larger values of wave number and nonlocal parameters, the real part of frequency ratio raises.

Structure-preserving spectral element method in attenuating seismic wave modeling

NASA Astrophysics Data System (ADS)

Cai, Wenjun; Zhang, Huai

2016-04-01

This work describes the extension of the conformal symplectic method to solve the damped acoustic wave equation and the elastic wave equations in the framework of the spectral element method. The conformal symplectic method is a variation of conventional symplectic methods to treat non-conservative time evolution problems which has superior behaviors in long-time stability and dissipation preservation. To construct the conformal symplectic method, we first reformulate the damped acoustic wave equation and the elastic wave equations in their equivalent conformal multi-symplectic structures, which naturally reveal the intrinsic properties of the original systems, especially, the dissipation laws. We thereafter separate each structures into a conservative Hamiltonian system and a purely dissipative ordinary differential equation system. Based on the splitting methodology, we solve the two subsystems respectively. The dissipative one is cheaply solved by its analytic solution. While for the conservative system, we combine a fourth-order symplectic Nyström method in time and the spectral element method in space to cover the circumstances in realistic geological structures involving complex free-surface topography. The Strang composition method is adopted thereby to concatenate the corresponding two parts of solutions and generate the completed numerical scheme, which is conformal symplectic and can therefore guarantee the numerical stability and dissipation preservation after a large time modeling. Additionally, a relative larger Courant number than that of the traditional Newmark scheme is found in the numerical experiments in conjunction with a spatial sampling of approximately 5 points per wavelength. A benchmark test for the damped acoustic wave equation validates the effectiveness of our proposed method in precisely capturing dissipation rate. The classical Lamb problem is used to demonstrate the ability of modeling Rayleigh-wave propagation. More comprehensive numerical experiments are presented to investigate the long-time simulation, low dispersion and energy conservation properties of the conformal symplectic method in both the attenuating homogeneous and heterogeneous mediums.

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.

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.

Effect of surface-related Rayleigh and multiple waves on velocity reconstruction with time-domain elastic FWI

NASA Astrophysics Data System (ADS)

Fang, Jinwei; Zhou, Hui; Zhang, Qingchen; Chen, Hanming; Wang, Ning; Sun, Pengyuan; Wang, Shucheng

2018-01-01

It is critically important to assess the effectiveness of elastic full waveform inversion (FWI) algorithms when FWI is applied to real land seismic data including strong surface and multiple waves related to the air-earth boundary. In this paper, we review the realization of the free surface boundary condition in staggered-grid finite-difference (FD) discretization of elastic wave equation, and analyze the impact of the free surface on FWI results. To reduce inputs/outputs (I/O) operations in gradient calculation, we adopt the boundary value reconstruction method to rebuild the source wavefields during the backward propagation of the residual data. A time-domain multiscale inversion strategy is conducted by using a convolutional objective function, and a multi-GPU parallel programming technique is used to accelerate our elastic FWI further. Forward simulation and elastic FWI examples without and with considering the free surface are shown and analyzed, respectively. Numerical results indicate that no free surface incorporated elastic FWI fails to recover a good inversion result from the Rayleigh wave contaminated observed data. By contrast, when the free surface is incorporated into FWI, the inversion results become better. We also discuss the dependency of the Rayleigh waveform incorporated FWI on the accuracy of initial models, especially the accuracy of the shallow part of the initial models.

The structure of shock wave in a gas consisting of ideally elastic, rigid spherical molecules

NASA Technical Reports Server (NTRS)

Cheremisin, F. G.

1972-01-01

Principal approaches are examined to the theoretical study of the shock layer structure. The choice of a molecular model is discussed and three procedures are formulated. These include a numerical calculation method, solution of the kinetic relaxation equation, and solution of the Boltzmann equation.

Elastic constants of calcite

USGS Publications Warehouse

Peselnick, L.; Robie, R.A.

1962-01-01

The recent measurements of the elastic constants of calcite by Reddy and Subrahmanyam (1960) disagree with the values obtained independently by Voigt (1910) and Bhimasenachar (1945). The present authors, using an ultrasonic pulse technique at 3 Mc and 25??C, determined the elastic constants of calcite using the exact equations governing the wave velocities in the single crystal. The results are C11=13.7, C33=8.11, C44=3.50, C12=4.82, C13=5.68, and C14=-2.00, in units of 1011 dyncm2. Independent checks of several of the elastic constants were made employing other directions and polarizations of the wave velocities. With the exception of C13, these values substantially agree with the data of Voigt and Bhimasenachar. ?? 1962 The American Institute of Physics.

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.

An Approach to Study Elastic Vibrations of Fractal Cylinders

NASA Astrophysics Data System (ADS)

Steinberg, Lev; Zepeda, Mario

2016-11-01

This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

Application of ANNs approach for wave-like and heat-like equations

NASA Astrophysics Data System (ADS)

Jafarian, Ahmad; Baleanu, Dumitru

2017-12-01

Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

Modeling of plasticity and fracture of metals at shock loading

NASA Astrophysics Data System (ADS)

Mayer, A. E.; Khishchenko, K. V.; Levashov, P. R.; Mayer, P. N.

2013-05-01

In this paper, we present a model of dislocation plasticity and fracture of metals, which in combination with the wide-range equation of state and the continuum mechanics equations is a necessary component for simulation of the shock-wave loading. We take into account immobilization of dislocations and nucleation of micro-voids in weakened zones of substance; this is distinguished feature of the present version of the model. Accounting of the dislocations immobilization provides a better description of the unloading wave structure, while the detailed consideration of processes in the weakened zones expands the domain of applicability of fracture model to higher strain rates. We compare our results with the experimental data for the shock loading of aluminum, copper, and nickel samples; the comparison indicates satisfactory description of the elastic precursor, unloading wave, and spall pulse. Using the model, we investigate intently the early stage of the shock formation in solids; it is found out that the elastic precursor is formed even for a strong shock wave, and initially the precursor has very large amplitude and propagation velocity.

Elastic properties of gas hydrate-bearing sediments

USGS Publications Warehouse

Lee, M.W.; Collett, T.S.

2001-01-01

Downhole-measured compressional- and shear-wave velocities acquired in the Mallik 2L-38 gas hydrate research well, northwestern Canada, reveal that the dominant effect of gas hydrate on the elastic properties of gas hydrate-bearing sediments is as a pore-filling constituent. As opposed to high elastic velocities predicted from a cementation theory, whereby a small amount of gas hydrate in the pore space significantly increases the elastic velocities, the velocity increase from gas hydrate saturation in the sediment pore space is small. Both the effective medium theory and a weighted equation predict a slight increase of velocities from gas hydrate concentration, similar to the field-observed velocities; however, the weighted equation more accurately describes the compressional- and shear-wave velocities of gas hydrate-bearing sediments. A decrease of Poisson's ratio with an increase in the gas hydrate concentration is similar to a decrease of Poisson's ratio with a decrease in the sediment porosity. Poisson's ratios greater than 0.33 for gas hydrate-bearing sediments imply the unconsolidated nature of gas hydrate-bearing sediments at this well site. The seismic characteristics of gas hydrate-bearing sediments at this site can be used to compare and evaluate other gas hydrate-bearing sediments in the Arctic.

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

NASA Technical Reports Server (NTRS)

Crandall, S. H.; Nigam, A. K.

1973-01-01

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Magneto-thermo-elastokinetics of geometrically nonlinear laminated composite plates. Part 2: vibration and wave propagation

NASA Technical Reports Server (NTRS)

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

2005-01-01

In Part 1 of this paper, the governing equations of geometrically nonlinear, anisotropic composite plates incorporating magneto-thermo-elastic effects have been derived. In order to gain insight into the implications of a number of geometrical and physical features of the system. three special cases are investigated: (i) free vibration of a plate strip immersed in a transversal magnetic field; (ii) free vibration of the plate strip immersed in an axial magnetic field; (iii) magneto-elastic wave propagations of an infinite plate. Within each of these cases, a prescribed uniform thermal field is considered. Special coupling characteristics between the magnetic and elastic fields are put into evidence. Extensive numerical investigations are conducted and pertinent conclusions which highlight the various effects induced by the magneto-elastic couplings and the finite electroconductivity, are outlined.

Hybridizable discontinuous Galerkin method for the 2-D frequency-domain elastic wave equations

NASA Astrophysics Data System (ADS)

Bonnasse-Gahot, Marie; Calandra, Henri; Diaz, Julien; Lanteri, Stéphane

2018-04-01

Discontinuous Galerkin (DG) methods are nowadays actively studied and increasingly exploited for the simulation of large-scale time-domain (i.e. unsteady) seismic wave propagation problems. Although theoretically applicable to frequency-domain problems as well, their use in this context has been hampered by the potentially large number of coupled unknowns they incur, especially in the 3-D case, as compared to classical continuous finite element methods. In this paper, we address this issue in the framework of the so-called hybridizable discontinuous Galerkin (HDG) formulations. As a first step, we study an HDG method for the resolution of the frequency-domain elastic wave equations in the 2-D case. We describe the weak formulation of the method and provide some implementation details. The proposed HDG method is assessed numerically including a comparison with a classical upwind flux-based DG method, showing better overall computational efficiency as a result of the drastic reduction of the number of globally coupled unknowns in the resulting discrete HDG system.

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.

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.

Effect of surface wave propagation in a four-layered oceanic crust model

NASA Astrophysics Data System (ADS)

Paul, Pasupati; Kundu, Santimoy; Mandal, Dinbandhu

2017-12-01

Dispersion of Rayleigh type surface wave propagation has been discussed in four-layered oceanic crust. It includes a sandy layer over a crystalline elastic half-space and over it there are two more layers—on the top inhomogeneous liquid layer and under it a liquid-saturated porous layer. Frequency equation is obtained in the form of determinant. The effects of the width of different layers as well as the inhomogeneity of liquid layer, sandiness of sandy layer on surface waves are depicted and shown graphically by considering all possible case of the particular model. Some special cases have been deduced, few special cases give the dispersion equation of Scholte wave and Stoneley wave, some of which have already been discussed elsewhere.

Thermo-elastic wave model of the photothermal and photoacoustic signal

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

Meja, P.; Steiger, B.; Delsanto, P.P.

1996-12-31

By means of the thermo-elastic wave equation the dynamical propagation of mechanical stress and temperature can be described and applied to model the photothermal and photoacoustic signal. Analytical solutions exist only in particular cases. Using massively parallel computers it is possible to simulate the photothermal and photoacoustic signal in a most sufficient way. In this paper the method of local interaction simulation approach (LISA) is presented and selected examples of its application are given. The advantages of this method, which is particularly suitable for parallel processing, consist in reduced computation time and simple description of the photoacoustic signal in opticalmore » materials. The present contribution introduces the authors model, the formalism and some results in the 1 D case for homogeneous nonattenuative materials. The photoacoustic wave can be understood as a wave with locally limited displacement. This displacement corresponds to a temperature variation. Both variables are usually measured in photoacoustics and photothermal measurements. Therefore the temperature and displacement dependence on optical, elastic and thermal constants is analysed.« less

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.

Derivation of Nonlinear Wave Equation for Flexural Motions of AN Elastic Beam Travelling in AN Air-Filled Tube

NASA Astrophysics Data System (ADS)

Sugimoto, N.; Kugo, K.; Watanabe, Y.

2002-07-01

Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.

Wave-induced fluid flow in random porous media: Attenuation and dispersion of elastic waves

NASA Astrophysics Data System (ADS)

Müller, Tobias M.; Gurevich, Boris

2005-05-01

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed. .

Numerical Modeling of Electroacoustic Logging Including Joule Heating

NASA Astrophysics Data System (ADS)

Plyushchenkov, Boris D.; Nikitin, Anatoly A.; Turchaninov, Victor I.

It is well known that electromagnetic field excites acoustic wave in a porous elastic medium saturated with fluid electrolyte due to electrokinetic conversion effect. Pride's equations describing this process are written in isothermal approximation. Update of these equations, which allows to take influence of Joule heating on acoustic waves propagation into account, is proposed here. This update includes terms describing the initiation of additional acoustic waves excited by thermoelastic stresses and the heat conduction equation with right side defined by Joule heating. Results of numerical modeling of several problems of propagation of acoustic waves excited by an electric field source with and without consideration of Joule heating effect in their statements are presented. From these results, it follows that influence of Joule heating should be taken into account at the numerical simulation of electroacoustic logging and at the interpretation of its log data.

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.

Spectral modification of seismic waves propagating through solids exhibiting a resonance frequency: a 1-D coupled wave propagation-oscillation model

NASA Astrophysics Data System (ADS)

Frehner, Marcel; Schmalholz, Stefan M.; Podladchikov, Yuri

2009-02-01

A 1-D model is presented that couples the microscale oscillations of non-wetting fluid blobs in a partially saturated poroelastic medium with the macroscale wave propagation through the elastic skeleton. The fluid oscillations are caused by surface tension forces that act as the restoring forces driving the oscillations. The oscillations are described mathematically with the equation for a linear oscillator and the wave propagation is described with the 1-D elastic wave equation. Coupling is done using Hamilton's variational principle for continuous systems. The resulting linear system of two partial differential equations is solved numerically with explicit finite differences. Numerical simulations are used to analyse the effect of solids exhibiting internal oscillations, and consequently a resonance frequency, on seismic waves propagating through such media. The phase velocity dispersion relation shows a higher phase velocity in the high-frequency limit and a lower phase velocity in the low-frequency limit. At the resonance frequency a singularity in the dispersion relation occurs. Seismic waves can initiate oscillations of the fluid by transferring energy from solid to fluid at the resonance frequency. Due to this transfer, the spectral amplitude of the solid particle velocity decreases at the resonance frequency. After initiation, the oscillatory movement of the fluid continuously transfers energy at the resonance frequency back to the solid. Therefore, the spectral amplitude of the solid particle velocity is increased at the resonance frequency. Once initiated, fluid oscillations decrease in amplitude with increasing time. Consequently, the spectral peak of the solid particle velocity at the resonance frequency decreases with time.

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.

Polariton resonances in multilayered piezoelectric superlattices

NASA Astrophysics Data System (ADS)

Piliposyan, D.

2018-04-01

Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-length superlattice with identical piezoelectric materials in a unit cell are considered in the framework of the full system of Maxwell’s electrodynamic equations. In the long wavelength region, coupling between electro-magnetic and elastic waves creates frequency band gaps. It is shown that for piezoelectric superlattice at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell. The results of the paper may be useful in design of narrow band filters or multi-channel piezoelectric filters.

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.

Modeling of wave processes in blocky media with porous and fluid-saturated interlayers

NASA Astrophysics Data System (ADS)

Sadovskii, Vladimir M.; Sadovskaya, Oxana V.; Lukyanov, Alexander A.

2017-09-01

The wave processes in blocky media are analyzed by applying different mathematical models, wherein the elastic blocks interact with each other via pliant interlayers with the complex mechanical properties. Four versions of constitutive equations are considered. In the first version, an elastic interaction between the blocks is simulated within the framework of linear elasticity theory, and the model of elastic-plastic interlayers is constructed to take into account the appearance of irreversible deformation of interlayers at short time intervals. In the second one, the effects of viscoelastic shear in the interblock interlayers are taken into the consideration using the Poynting-Thomson rheological scheme. In the third option, the model of an elastic porous material is used in the interlayers, where the pores collapse if an abrupt compressive stress is applied. In the fourth case, the model of a fluid-saturated material with open pores is examined based on Biot's equations. The collapse of pores is modeled by the generalized rheological approach, wherein the mechanical properties of a material are simulated using four rheological elements. Three of them are the traditional elastic, viscous and plastic elements, the fourth element is the so-called rigid contact, which is used to describe the behavior of materials with the different resistance to tension and compression. It was shown that the thermodynamically consistent model is provided, which means that the energy balance equation is fulfilled for an entire blocky structure, where the kinetic and potential energy of the system is the sum of the kinetic and potential energies of the blocks and interlayers. Under numerical implementation of the interlayers models, the dissipationless finite difference Ivanov's method was used. The splitting method by spatial variables in the combination with the Godunov gap decay scheme was applied in the blocks. As a result, robust and stable computational algorithms are built and tested. Using MPI technology, the parallel software was designed for the modeling of wave processes in 2D setting. The numerical results are presented, discussed and future studies are outlined.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Hydroelectromechanical modelling of a piezoelectric wave energy converter

NASA Astrophysics Data System (ADS)

Renzi, E.

2016-11-01

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

Tube wave signatures in cylindrically layered poroelastic media computed with spectral method

NASA Astrophysics Data System (ADS)

Karpfinger, Florian; Gurevich, Boris; Valero, Henri-Pierre; Bakulin, Andrey; Sinha, Bikash

2010-11-01

This paper describes a new algorithm based on the spectral method for the computation of Stoneley wave dispersion and attenuation propagating in cylindrical structures composed of fluid, elastic and poroelastic layers. The spectral method is a numerical method which requires discretization of the structure along the radial axis using Chebyshev points. To approximate the differential operators of the underlying differential equations, we use spectral differentiation matrices. After discretizing equations of motion along the radial direction, we can solve the problem as a generalized algebraic eigenvalue problem. For a given frequency, calculated eigenvalues correspond to the wavenumbers of different modes. The advantage of this approach is that it can very efficiently analyse structures with complicated radial layering composed of different fluid, solid and poroelastic layers. This work summarizes the fundamental equations, followed by an outline of how they are implemented in the numerical spectral schema. The interface boundary conditions are then explained for fluid/porous, elastic/porous and porous interfaces. Finally, we discuss three examples from borehole acoustics. The first model is a fluid-filled borehole surrounded by a poroelastic formation. The second considers an additional elastic layer sandwiched between the borehole and the formation, and finally a model with radially increasing permeability is considered.

Wave propagation through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces.

PubMed

Jiao, Fengyu; Wei, Peijun; Li, Yueqiu

2018-01-01

Reflection and transmission of plane waves through a flexoelectric piezoelectric slab sandwiched by two piezoelectric half-spaces are studied in this paper. The secular equations in the flexoelectric piezoelectric material are first derived from the general governing equation. Different from the classical piezoelectric medium, there are five kinds of coupled elastic waves in the piezoelectric material with the microstructure effects taken into consideration. The state vectors are obtained by the summation of contributions from all possible partial waves. The state transfer equation of flexoelectric piezoelectric slab is derived from the motion equation by the reduction of order, and the transfer matrix of flexoelectric piezoelectric slab is obtained by solving the state transfer equation. By using the continuous conditions at the interface and the approach of partition matrix, we get the resultant algebraic equations in term of the transfer matrix from which the reflection and transmission coefficients can be calculated. The amplitude ratios and further the energy flux ratios of various waves are evaluated numerically. The numerical results are shown graphically and are validated by the energy conservation law. Based on these numerical results, the influences of two characteristic lengths of microstructure and the flexoelectric coefficients on the wave propagation are discussed. Copyright © 2017 Elsevier B.V. All rights reserved.

High-frequency homogenization for travelling waves in periodic media.

PubMed

Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

2016-07-01

We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

The Complex-Step-Finite-Difference method

NASA Astrophysics Data System (ADS)

Abreu, Rafael; Stich, Daniel; Morales, Jose

2015-07-01

We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.

Mechanical and Thermophysical Properties of Cubic Rock-Salt AlN Under High Pressure

NASA Astrophysics Data System (ADS)

Lebga, Noudjoud; Daoud, Salah; Sun, Xiao-Wei; Bioud, Nadhira; Latreche, Abdelhakim

2018-03-01

Density functional theory, density functional perturbation theory, and the Debye model have been used to investigate the structural, elastic, sound velocity, and thermodynamic properties of AlN with cubic rock-salt structure under high pressure, yielding the equilibrium structural parameters, equation of state, and elastic constants of this interesting material. The isotropic shear modulus, Pugh ratio, and Poisson's ratio were also investigated carefully. In addition, the longitudinal, transverse, and average elastic wave velocities, phonon contribution to the thermal conductivity, and interesting thermodynamic properties were predicted and analyzed in detail. The results demonstrate that the behavior of the elastic wave velocities under increasing hydrostatic pressure explains the hardening of the corresponding phonons. Based on the elastic stability criteria under pressure, it is found that AlN with cubic rock-salt structure is mechanically stable, even at pressures up to 100 GPa. Analysis of the Pugh ratio and Poisson's ratio revealed that AlN with cubic rock-salt structure behaves in brittle manner.

Scattering of Lamb waves by cracks in a composite graphite fiber-reinforced epoxy plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu K.; Shah, Arvind

1990-01-01

Recent investigations of space construction techniques have explored the used of composite materials in the construction of space stations and platforms. These composites offer superior strength to weight ratio and are thermally stable. For example, a composite material being considered is laminates of graphite fibers in an epoxy matrix. The overall effective elastic constants of such a medium can be calculated from fiber and matrix properties by using an effective modulus theory as shown in Datta, el. al. The investigation of propagation and scattering of elastic waves in composite materials is necessary in order to develop an ability to characterize cracks and predict the reliability of composite structures. The objective of this investigation is the characterization of a surface breaking crack by ultrasonic techniques. In particular, the use of Lamb waves for this purpose is studied here. The Lamb waves travel through the plate, encountering a crack, and scatter. Of interest is the modeling of the scattered wave in terms of the Lamb wave modes. The direct problem of propagation and scattering of Lamb waves by a surface breaking crack has been analyzed. This would permit an experimentalist to characterize the crack by comparing the measured response to the analytical model. The plate is assumed to be infinite in the x and y directions with a constant thickness in the z direction. The top and bottom surfaces are traction free. Solving the governing wave equations and using the stress-free boundary conditions results in the dispersion equation. This equation yields the guided modes in the homogeneous plate. The theoretical model is a hybrid method that combines analytical and finite elements techniques to describe the scattered displacements. A finite region containing the defects is discretized by finite elements. Outside the local region, the far field solution is expressed as a Fourier summation of the guided modes obtained from the dispersion equation. Continuity of tractions and displacements at the boundaries of the two regions provides the necessary equations to determine the expansion coefficients and the nodal displacements. In the hybrid method used here these defects can be of arbitrary shapes as well as inclusions of different materials.

Biot-Gassmann theory for velocities of gas hydrate-bearing sediments

USGS Publications Warehouse

Lee, M.W.

2002-01-01

Elevated elastic velocities are a distinct physical property of gas hydrate-bearing sediments. A number of velocity models and equations (e.g., pore-filling model, cementation model, effective medium theories, weighted equations, and time-average equations) have been used to describe this effect. In particular, the weighted equation and effective medium theory predict reasonably well the elastic properties of unconsolidated gas hydrate-bearing sediments. A weakness of the weighted equation is its use of the empirical relationship of the time-average equation as one element of the equation. One drawback of the effective medium theory is its prediction of unreasonably higher shear-wave velocity at high porosities, so that the predicted velocity ratio does not agree well with the observed velocity ratio. To overcome these weaknesses, a method is proposed, based on Biot-Gassmann theories and assuming the formation velocity ratio (shear to compressional velocity) of an unconsolidated sediment is related to the velocity ratio of the matrix material of the formation and its porosity. Using the Biot coefficient calculated from either the weighted equation or from the effective medium theory, the proposed method accurately predicts the elastic properties of unconsolidated sediments with or without gas hydrate concentration. This method was applied to the observed velocities at the Mallik 2L-39 well, Mackenzie Delta, Canada.

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.

Nonlinear Elastic Plate in a Flow of Gas: Recent Results and Conjectures

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

Chueshov, Igor, E-mail: chueshov@karazin.ua; Dowell, Earl H., E-mail: dowell@duke.edu; Lasiecka, Irena, E-mail: lasiecka@memphis.edu

2016-06-15

We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of the discussion here is on the interesting mathematical aspects of physical phenomena occurring in aeroelasticity, such as flutter and divergence. This leads to a partial differential equation treatment of issues such as well-posedness of finite energy solutions, and long-time (asymptotic) behavior. The latter includes theory of asymptotic stability, convergence to equilibria, and to global attracting sets. We complete the discussion with several well knownmore » observations and conjectures based on experimental/numerical studies.« less

Study of the exact analytical solution of the equation of longitudinal waves in a liquid with account of its relaxation properties

NASA Astrophysics Data System (ADS)

Kudinov, I. V.; Kudinov, V. A.

2013-09-01

A mathematical model of elastic vibrations of an incompressible liquid has been developed based on the hypothesis on the finite velocity of propagation of field potentials in this liquid. A hyperbolic equation of vibrations of such a liquid with account of its relaxation properties has been obtained. An exact analytical solution of this equation has been found and investigated in detail.

The effect of shear stress on solitary waves in arteries.

PubMed

Demiray, H

1997-09-01

In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.

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.

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

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

Petersson, N. Anders; Sjogreen, Bjorn

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

DOE PAGES

Petersson, N. Anders; Sjogreen, Bjorn

2017-04-18

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high ordermore » accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.« less

Nonlinear surface elastic modes in crystals

NASA Astrophysics Data System (ADS)

Gorentsveig, V. I.; Kivshar, Yu. S.; Kosevich, A. M.; Syrkin, E. S.

1990-03-01

The influence of nonlinearity on shear horizontal surface elastic waves in crystals is described on the basis of the effective nonlinear Schrödinger equation. It is shown that the corresponding solutions form a set of surface modes and the simplest mode coincides with the solution proposed by Mozhaev. The higher order modes have internal frequencies caused by the nonlinearity. All these modes decay in the crystal as uoexp(- z/ zo) atz≫ zo- u o-1 ( z is the distance from the crystal surface, uo the wave amplitude at the surface). The creation of the modes from a localized surface excitation has a threshold. The stability of the modes is discussed.

Antiplane wave scattering from a cylindrical cavity in pre-stressed nonlinear elastic media

PubMed Central

Shearer, Tom; Parnell, William J.; Abrahams, I. David

2015-01-01

The effect of a longitudinal stretch and a pressure-induced inhomogeneous radial deformation on the scattering of antiplane elastic waves from a cylindrical cavity is determined. Three popular nonlinear strain energy functions are considered: the neo-Hookean, the Mooney–Rivlin and a two-term Arruda–Boyce model. A new method is developed to analyse and solve the governing wave equations. It exploits their properties to determine an asymptotic solution in the far-field, which is then used to derive a boundary condition to numerically evaluate the equations local to the cavity. This method could be applied to any linear ordinary differential equation whose inhomogeneous coefficients tend to a constant as its independent variable tends to infinity. The effect of the pre-stress is evaluated by considering the scattering cross section. A longitudinal stretch is found to decrease the scattered power emanating from the cavity, whereas a compression increases it. The effect of the pressure difference depends on the strain energy function employed. For a Mooney–Rivlin material, a cavity inflation increases the scattered power and a deflation decreases it; for a neo-Hookean material, the scattering cross section is unaffected by the radial deformation; and for a two-term Arruda–Boyce material, both inflation and deflation are found to decrease the scattered power. PMID:26543398

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.

Mechanical circulator for elastic waves by using the nonreciprocity of flexible rotating rings

NASA Astrophysics Data System (ADS)

Beli, Danilo; Silva, Priscilla Brandão; Arruda, José Roberto de França

2018-01-01

Circulators have a wide range of applications in wave manipulation. They provide a nonreciprocal response by breaking the time-reversal symmetry. In the mechanical field, nonlinear isolators and ferromagnetic circulators can be used for this objective. However, they require high power and high volumes. Herein, a flexible rotating ring is used to break the time-reversal symmetry as a result of the combined effect of Coriolis acceleration and material damping. Complete asymmetry of oscillating and evanescent components of wavenumbers is achieved. The elastic ring produces a nonreciprocal response that is used to design a three port mechanical circulator. The rotational speed for maximum transmission in one port and isolation in the other one is determined using analytical equations. A spectral element formulation is used to compute the complex dispersion diagrams and the forced response. Waveguides that support longitudinal and flexural waves are investigated. In this case, the ring nonreciprocity is modulated by the waveguide reciprocal response and the transmission coefficients can be affected. The proposed device is compact, nonferromagnetic, and may open new directions for elastic wave manipulation.

Gassmann Theory Applies to Nanoporous Media

NASA Astrophysics Data System (ADS)

Gor, Gennady Y.; Gurevich, Boris

2018-01-01

Recent progress in extraction of unconventional hydrocarbon resources has ignited the interest in the studies of nanoporous media. Since many thermodynamic and mechanical properties of nanoscale solids and fluids differ from the analogous bulk materials, it is not obvious whether wave propagation in nanoporous media can be described using the same framework as in macroporous media. Here we test the validity of Gassmann equation using two published sets of ultrasonic measurements for a model nanoporous medium, Vycor glass, saturated with two different fluids, argon, and n-hexane. Predictions of the Gassmann theory depend on the bulk and shear moduli of the dry samples, which are known from ultrasonic measurements and the bulk moduli of the solid and fluid constituents. The solid bulk modulus can be estimated from adsorption-induced deformation or from elastic effective medium theory. The fluid modulus can be calculated according to the Tait-Murnaghan equation at the solvation pressure in the pore. Substitution of these parameters into the Gassmann equation provides predictions consistent with measured data. Our findings set up a theoretical framework for investigation of fluid-saturated nanoporous media using ultrasonic elastic wave propagation.

Nucleon-nucleon interactions from dispersion relations: Elastic partial waves

NASA Astrophysics Data System (ADS)

Albaladejo, M.; Oller, J. A.

2011-11-01

We consider nucleon-nucleon (NN) interactions from chiral effective field theory. In this work we restrict ourselves to the elastic NN scattering. We apply the N/D method to calculate the NN partial waves taking as input the one-pion exchange discontinuity along the left-hand cut. This discontinuity is amenable to a chiral power counting as discussed by Lacour, Oller, and Meißner [Ann. Phys. (NY)APNYA60003-491610.1016/j.aop.2010.06.012 326, 241 (2011)], with one-pion exchange as its leading order contribution. The resulting linear integral equation for a partial wave with orbital angular momentum ℓ≥2 is solved in the presence of ℓ-1 constraints, so as to guarantee the right behavior of the D- and higher partial waves near threshold. The calculated NN partial waves are based on dispersion relations and are independent of regulator. This method can also be applied to higher orders in the calculation of the discontinuity along the left-hand cut and extended to triplet coupled partial waves.

Wave-packet continuum-discretization approach to ion-atom collisions including rearrangement: Application to differential ionization in proton-hydrogen scattering

NASA Astrophysics Data System (ADS)

Abdurakhmanov, I. B.; Bailey, J. J.; Kadyrov, A. S.; Bray, I.

2018-03-01

In this work, we develop a wave-packet continuum-discretization approach to ion-atom collisions that includes rearrangement processes. The total scattering wave function is expanded using a two-center basis built from wave-packet pseudostates. The exact three-body Schrödinger equation is converted into coupled-channel differential equations for time-dependent expansion coefficients. In the asymptotic region these time-dependent coefficients represent transition amplitudes for all processes including elastic scattering, excitation, ionization, and electron capture. The wave-packet continuum-discretization approach is ideal for differential ionization studies as it allows one to generate pseudostates with arbitrary energies and distribution. The approach is used to calculate the double differential cross section for ionization in proton collisions with atomic hydrogen. Overall good agreement with experiment is obtained for all considered cases.

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

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

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.

Asymptotic expansions and solitons of the Camassa-Holm - nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Mylonas, I. K.; Ward, C. B.; Kevrekidis, P. G.; Rothos, V. M.; Frantzeskakis, D. J.

2017-12-01

We study a deformation of the defocusing nonlinear Schrödinger (NLS) equation, the defocusing Camassa-Holm NLS, hereafter referred to as CH-NLS equation. We use asymptotic multiscale expansion methods to reduce this model to a Boussinesq-like equation, which is then subsequently approximated by two Korteweg-de Vries (KdV) equations for left- and right-traveling waves. We use the soliton solution of the KdV equation to construct approximate solutions of the CH-NLS system. It is shown that these solutions may have the form of either dark or antidark solitons, namely dips or humps on top of a stable continuous-wave background. We also use numerical simulations to investigate the validity of the asymptotic solutions, study their evolution, and their head-on collisions. It is shown that small-amplitude dark and antidark solitons undergo quasi-elastic collisions.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

Propagation of mechanical waves through a stochastic medium with spherical symmetry

NASA Astrophysics Data System (ADS)

Avendaño, Carlos G.; Reyes, J. Adrián

2018-01-01

We theoretically analyze the propagation of outgoing mechanical waves through an infinite isotropic elastic medium possessing spherical symmetry whose Lamé coefficients and density are spatial random functions characterized by well-defined statistical parameters. We derive the differential equation that governs the average displacement for a system whose properties depend on the radial coordinate. We show that such an equation is an extended version of the well-known Bessel differential equation whose perturbative additional terms contain coefficients that depend directly on the squared noise intensities and the autocorrelation lengths in an exponential decay fashion. We numerically solve the second order differential equation for several values of noise intensities and autocorrelation lengths and compare the corresponding displacement profiles with that of the exact analytic solution for the case of absent inhomogeneities.

Model Parameterization and P-wave AVA Direct Inversion for Young's Impedance

NASA Astrophysics Data System (ADS)

Zong, Zhaoyun; Yin, Xingyao

2017-05-01

AVA inversion is an important tool for elastic parameters estimation to guide the lithology prediction and "sweet spot" identification of hydrocarbon reservoirs. The product of the Young's modulus and density (named as Young's impedance in this study) is known as an effective lithology and brittleness indicator of unconventional hydrocarbon reservoirs. Density is difficult to predict from seismic data, which renders the estimation of the Young's impedance inaccurate in conventional approaches. In this study, a pragmatic seismic AVA inversion approach with only P-wave pre-stack seismic data is proposed to estimate the Young's impedance to avoid the uncertainty brought by density. First, based on the linearized P-wave approximate reflectivity equation in terms of P-wave and S-wave moduli, the P-wave approximate reflectivity equation in terms of the Young's impedance is derived according to the relationship between P-wave modulus, S-wave modulus, Young's modulus and Poisson ratio. This equation is further compared to the exact Zoeppritz equation and the linearized P-wave approximate reflectivity equation in terms of P- and S-wave velocities and density, which illustrates that this equation is accurate enough to be used for AVA inversion when the incident angle is within the critical angle. Parameter sensitivity analysis illustrates that the high correlation between the Young's impedance and density render the estimation of the Young's impedance difficult. Therefore, a de-correlation scheme is used in the pragmatic AVA inversion with Bayesian inference to estimate Young's impedance only with pre-stack P-wave seismic data. Synthetic examples demonstrate that the proposed approach is able to predict the Young's impedance stably even with moderate noise and the field data examples verify the effectiveness of the proposed approach in Young's impedance estimation and "sweet spots" evaluation.

Collision of Identical Solitary Waves in Hertzian Chains

NASA Astrophysics Data System (ADS)

Sen, Surajit; Manciu, Marian; Hurd, Alan J.

2000-03-01

We consider a chain of elastic beads, which repel upon contact according to the non-linear Hertz potential. We further assume that the chain is under zero loading, i.e., the grains have zero initial overlap. We show via careful numerical solution of the equations of motion that an impulse propagates as a solitary wave and that the collision of identical solitary waves propagating in opposite directions along the chain spawns a hierarchy of multiple weak solitary waves [1]. [1] M. Manciu, S. Sen and A.J. Hurd, Phys Lett A (submitted).

Wave-equation migration velocity inversion using passive seismic sources

NASA Astrophysics Data System (ADS)

Witten, B.; Shragge, J. C.

2015-12-01

Seismic monitoring at injection sites (e.g., CO2 sequestration, waste water disposal, hydraulic fracturing) has become an increasingly important tool for hazard identification and avoidance. The information obtained from this data is often limited to seismic event properties (e.g., location, approximate time, moment tensor), the accuracy of which greatly depends on the estimated elastic velocity models. However, creating accurate velocity models from passive array data remains a challenging problem. Common techniques rely on picking arrivals or matching waveforms requiring high signal-to-noise data that is often not available for the magnitude earthquakes observed over injection sites. We present a new method for obtaining elastic velocity information from earthquakes though full-wavefield wave-equation imaging and adjoint-state tomography. The technique exploits the fact that the P- and S-wave arrivals originate at the same time and location in the subsurface. We generate image volumes by back-propagating P- and S-wave data through initial Earth models and then applying a correlation-based extended-imaging condition. Energy focusing away from zero lag in the extended image volume is used as a (penalized) residual in an adjoint-state tomography scheme to update the P- and S-wave velocity models. We use an acousto-elastic approximation to greatly reduce the computational cost. Because the method requires neither an initial source location or origin time estimate nor picking of arrivals, it is suitable for low signal-to-noise datasets, such as microseismic data. Synthetic results show that with a realistic distribution of microseismic sources, P- and S-velocity perturbations can be recovered. Although demonstrated at an oil and gas reservoir scale, the technique can be applied to problems of all scales from geologic core samples to global seismology.

Comparison of the Modified Biot-Gassmann Theory and the Kuster-Toksoz Theory in Predicting Elastic Velocities of Sediments

USGS Publications Warehouse

Lee, Myung W.

2008-01-01

Elastic velocities of water-saturated sandstones depend primarily on porosity, effective pressure, and the degree of consolidation. If the dry-frame moduli are known, from either measurements or theoretical calculations, the effect of pore water on velocities can be modeled using the Gassmann theory. Kuster and Toksoz developed a theory based on wave-scattering theory for a variety of inclusion shapes, which provides a means for calculating dry- or wet-frame moduli. In the Kuster-Toksoz theory, elastic wave velocities through different sediments can be predicted by using different aspect ratios of the sediment's pore space. Elastic velocities increase as the pore aspect ratio increases (larger pore aspect ratio describes a more spherical pore). On the basis of the velocity ratio, which is assumed to be a function of (1-0)n, and the Biot-Gassmann theory, Lee developed a semi-empirical equation for predicting elastic velocities, which is referred to as the modified Biot-Gassmann theory of Lee. In this formulation, the exponent n, which depends on the effective pressure and the degree of consolidation, controls elastic velocities; as n increases, elastic velocities decrease. Computationally, the role of exponent n in the modified Biot-Gassmann theory by Lee is similar to the role of pore aspect ratios in the Kuster-Toksoz theory. For consolidated sediments, either theory predicts accurate velocities. However, for unconsolidated sediments, the modified Biot-Gassmann theory by Lee performs better than the Kuster-Toksoz theory, particularly in predicting S-wave velocities.

Long-wave dynamics of an elastic sheet lubricated by a thin liquid film on a wetting substrate

NASA Astrophysics Data System (ADS)

Young, Y.-N.; Stone, H. A.

2017-06-01

The dynamics of an elastic sheet lubricated by a thin liquid film on a wetting solid substrate is examined using both numerical simulations of a long-wave lubrication equation and a quasistatic model. Interactions between the liquid and the wetting substrate are modeled by a disjoining pressure that gives rise to an ultrathin (precursor) film. For a fluid interface without elastic bending stiffness, a flat precursor film may be linearly unstable and evolve towards an equilibrium of a single "drop" connected to a flat ultrathin film. Similar behavior is found when the thin film is covered by an elastic sheet: The sheet deforms, rearranging the thin liquid film, and contributes regulating surface forces such as a bending resistance and/or a tensile force, which may arise from interactions between the sheet and liquid or inextensibility of the sheet. Glasner's quasistatic model [Phys. Fluids 15, 1837 (2003), 10.1063/1.1578076], developed for a liquid film, is adopted to investigate the combined effects of elastic and tensile forces in the sheet on the thin film dynamics. The equilibrium height of the drop is found to vary inversely with the bending rigidity. When the elastic sheet is inextensible (such as a lipid bilayer membrane), a compressive tensile force may occur and the equilibrium film height is dependent less on the bending rigidity and more on the excess area of the membrane. Analyses of the lubrication equation also show that the precursor film transitions monotonically to the core film for tension-dominated dynamics. In contrast, for elasticity-dominated dynamics, a spatial oscillation of film height in the contact line region is found. In addition, elasticity in the sheet causes a sliding motion of the thin film: the contact angle is rendered zero by elasticity, and the contact line moves at a finite speed.

Analysis of a monolithic crystal plate acoustic wave filter.

PubMed

He, Huijing; Liu, Jinxi; Yang, Jiashi

2011-12-01

We study thickness-shear and thickness-twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c(56). An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined. Copyright © 2011 Elsevier B.V. All rights reserved.

Elastic Properties of Synthetic Pyrope (Mg3Al2Si3O12) to 9 GPa and 1000°C

NASA Astrophysics Data System (ADS)

Gwanmesia, G. D.; Zhang, J.; Li, B.; Darling, K.; Kung, J.; Neuville, D.; Raterron, P.; Sullivan, S.; Liebermann, R. C.

2003-04-01

We have measured the elastic wave velocities of polycrystalline pyrope (Mg_3Al_2Si_3O12) to 9 GPa and 1000^oC by ultrasonic interferometry, combined with in-situ synchrotron x-ray diffraction and imaging techniques. Fine-grained polycrystalline specimens (99.5% of theoretical density) were hot-pressed from a homogeneous glass starting material in the USSA-2000 apparatus at Stony Brook; the physical properties of the recovered specimens were characterized with density measurements, x-ray diffraction and transmission electron microscopy. Bench-top elastic wave velocities were in excellent agreement with the isotropic averages calculated from single-crystal elastic moduli of Leitner et al. (1980) by the Hashin-Shtrikman method. Travel times of acoustic compressional (P) and shear (S) waves, specimen lengths and PVT equations of state for the specimen and a NaCl standard were measured to 9 GPa and 1000^oC in a DIA-type high pressure apparatus (SAM-85), installed on the superconducting wiggler beamline (X17B) at the National Synchrotron Light Source of the Brookhaven National Laboratory. These data enabled us to determine the pressure and temperature derivatives of the elastic wave velocities and moduli for isotropic pyrope. We compare our new values with those of previous investigators and discuss the implications of these data for interpreting the seismic velocity gradients in the transition zone of the Earth's mantle.

Wave propagation in embedded inhomogeneous nanoscale plates incorporating thermal effects

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Barati, Mohammad Reza; Dabbagh, Ali

2018-04-01

In this article, an analytical approach is developed to study the effects of thermal loading on the wave propagation characteristics of an embedded functionally graded (FG) nanoplate based on refined four-variable plate theory. The heat conduction equation is solved to derive the nonlinear temperature distribution across the thickness. Temperature-dependent material properties of nanoplate are graded using Mori-Tanaka model. The nonlocal elasticity theory of Eringen is introduced to consider small-scale effects. The governing equations are derived by the means of Hamilton's principle. Obtained frequencies are validated with those of previously published works. Effects of different parameters such as temperature distribution, foundation parameters, nonlocal parameter, and gradient index on the wave propagation response of size-dependent FG nanoplates have been investigated.

Wave Propagation Analysis of Edge Cracked Circular Beams under Impact Force

PubMed Central

Akbaş, Şeref Doğuşcan

2014-01-01

This paper presents responses of an edge circular cantilever beam under the effect of an impact force. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin–Voigt model for the material of the beam is used. The cracked beam is modelled as an assembly of two sub-beams connected through a massless elastic rotational spring. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the effects of the location of crack, the depth of the crack, on the characteristics of the reflected waves are investigated in detail. Also, the positions of the cracks are calculated by using reflected waves. PMID:24972050

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.

Discretizing singular point sources in hyperbolic wave propagation problems

DOE PAGES

Petersson, N. Anders; O'Reilly, Ossian; Sjogreen, Bjorn; ...

2016-06-01

Here, we develop high order accurate source discretizations for hyperbolic wave propagation problems in first order formulation that are discretized by finite difference schemes. By studying the Fourier series expansions of the source discretization and the finite difference operator, we derive sufficient conditions for achieving design accuracy in the numerical solution. Only half of the conditions in Fourier space can be satisfied through moment conditions on the source discretization, and we develop smoothness conditions for satisfying the remaining accuracy conditions. The resulting source discretization has compact support in physical space, and is spread over as many grid points as themore » number of moment and smoothness conditions. In numerical experiments we demonstrate high order of accuracy in the numerical solution of the 1-D advection equation (both in the interior and near a boundary), the 3-D elastic wave equation, and the 3-D linearized Euler equations.« less

Analysis of fluid-structure interaction in a frame pipe undergoing plastic deformations

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

Khamlichi, A.; Jezequel, L.; Jacques, Y.

1995-11-01

Water hammer pressure waves of sufficiently large magnitude can cause plastic flexural deformations in a frame pipe. In this study, the authors propose a modelization of this problem based on plane wave approximation for the fluid equations and approximation of the structure motion by a single-degree-of-freedom elastic-plastic oscillator. Direct analytical integration of elastic-plastic equations through pipe sections, then over the pipe length is performed in order to identify the oscillator parameters. Comparison of the global load-displacement relationship obtained with the finite element solution was considered and has shown good agreement. Fluid-structure coupling is achieved by assuming elbows to act likemore » plane monopole sources, where localized jumps of fluid velocity occur and where net pressure forces are exerted on the structure. The authors have applied this method to analyze the fluid-structure interaction in this range of deformations. Energy exchange between the fluid and the structure and energy dissipation are quantified.« less

Simulation of elastic wave propagation using cellular automata and peridynamics, and comparison with experiments

DOE PAGES

Nishawala, Vinesh V.; Ostoja-Starzewski, Martin; Leamy, Michael J.; ...

2015-09-10

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’smore » Problem. The results are compared with theoretical solution from classical elasticity and experimental results. Furthermore, this paper is used to validate our implementation of these methods.« less

Impact buckling of thin bars in the elastic range for any end condition

NASA Technical Reports Server (NTRS)

Taub, Josef

1934-01-01

Following a qualitative discussion of the complicated process involved in a short-period, longitudinal force applied to an originally not quite straight bar, the actual process is substituted by an idealized process for the purpose of analytical treatment. The simplifications are: the assumption of an infinitely high rate of propagation of the elastic longitudinal waves in the bar, limitation to slender bars, disregard of material damping and of rotatory inertia, the assumption of consistently small elastic deformations, the assumption of cross-sectional dimensions constant along the bar axis, the assumption of a shock-load constant in time, and the assumption of eccentricities on one plane. Then follow the mathematical principles for resolving the differential equation of the simplified problem, particularly the developability of arbitrary functions with steady first and second and intermittently steady third and fourth derivatives into one convergent series, according to the natural functions of the homogeneous differential equation.

Elasticity of methane hydrate phases at high pressure.

PubMed

Beam, Jennifer; Yang, Jing; Liu, Jin; Liu, Chujie; Lin, Jung-Fu

2016-04-21

Determination of the full elastic constants (cij) of methane hydrates (MHs) at extreme pressure-temperature environments is essential to our understanding of the elastic, thermodynamic, and mechanical properties of methane in MH reservoirs on Earth and icy satellites in the solar system. Here, we have investigated the elastic properties of singe-crystal cubic MH-sI, hexagonal MH-II, and orthorhombic MH-III phases at high pressures in a diamond anvil cell. Brillouin light scattering measurements, together with complimentary equation of state (pressure-density) results from X-ray diffraction and methane site occupancies in MH from Raman spectroscopy, were used to derive elastic constants of MH-sI, MH-II, and MH-III phases at high pressures. Analysis of the elastic constants for MH-sI and MH-II showed intriguing similarities and differences between the phases' compressional wave velocity anisotropy and shear wave velocity anisotropy. Our results show that these high-pressure MH phases can exhibit distinct elastic, thermodynamic, and mechanical properties at relevant environments of their respective natural reservoirs. These results provide new insight into the determination of how much methane exists in MH reservoirs on Earth and on icy satellites elsewhere in the solar system and put constraints on the pressure and temperature conditions of their environment.

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.

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai; Fu, Shubin; Gibson, Richard L.

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai, E-mail: kaigao87@gmail.com; Fu, Shubin, E-mail: shubinfu89@gmail.com; Gibson, Richard L., E-mail: gibson@tamu.edu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE PAGES

Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Laplace-domain waveform modeling and inversion for the 3D acoustic-elastic coupled media

NASA Astrophysics Data System (ADS)

Shin, Jungkyun; Shin, Changsoo; Calandra, Henri

2016-06-01

Laplace-domain waveform inversion reconstructs long-wavelength subsurface models by using the zero-frequency component of damped seismic signals. Despite the computational advantages of Laplace-domain waveform inversion over conventional frequency-domain waveform inversion, an acoustic assumption and an iterative matrix solver have been used to invert 3D marine datasets to mitigate the intensive computing cost. In this study, we develop a Laplace-domain waveform modeling and inversion algorithm for 3D acoustic-elastic coupled media by using a parallel sparse direct solver library (MUltifrontal Massively Parallel Solver, MUMPS). We precisely simulate a real marine environment by coupling the 3D acoustic and elastic wave equations with the proper boundary condition at the fluid-solid interface. In addition, we can extract the elastic properties of the Earth below the sea bottom from the recorded acoustic pressure datasets. As a matrix solver, the parallel sparse direct solver is used to factorize the non-symmetric impedance matrix in a distributed memory architecture and rapidly solve the wave field for a number of shots by using the lower and upper matrix factors. Using both synthetic datasets and real datasets obtained by a 3D wide azimuth survey, the long-wavelength component of the P-wave and S-wave velocity models is reconstructed and the proposed modeling and inversion algorithm are verified. A cluster of 80 CPU cores is used for this study.

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.

Acceleration of stable TTI P-wave reverse-time migration with GPUs

NASA Astrophysics Data System (ADS)

Kim, Youngseo; Cho, Yongchae; Jang, Ugeun; Shin, Changsoo

2013-03-01

When a pseudo-acoustic TTI (tilted transversely isotropic) coupled wave equation is used to implement reverse-time migration (RTM), shear wave energy is significantly included in the migration image. Because anisotropy has intrinsic elastic characteristics, coupling P-wave and S-wave modes in the pseudo-acoustic wave equation is inevitable. In RTM with only primary energy or the P-wave mode in seismic data, the S-wave energy is regarded as noise for the migration image. To solve this problem, we derive a pure P-wave equation for TTI media that excludes the S-wave energy. Additionally, we apply the rapid expansion method (REM) based on a Chebyshev expansion and a pseudo-spectral method (PSM) to calculate spatial derivatives in the wave equation. When REM is incorporated with the PSM for the spatial derivatives, wavefields with high numerical accuracy can be obtained without grid dispersion when performing numerical wave modeling. Another problem in the implementation of TTI RTM is that wavefields in an area with high gradients of dip or azimuth angles can be blown up in the progression of the forward and backward algorithms of the RTM. We stabilize the wavefields by applying a spatial-frequency domain high-cut filter when calculating the spatial derivatives using the PSM. In addition, to increase performance speed, the graphic processing unit (GPU) architecture is used instead of traditional CPU architecture. To confirm the degree of acceleration compared to the CPU version on our RTM, we then analyze the performance measurements according to the number of GPUs employed.

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion

PubMed Central

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-01-01

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g., Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with Shearwave Dispersion Ultrasound Vibrometry (SDUV) is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements. PMID:22345425

Loss tangent and complex modulus estimated by acoustic radiation force creep and shear wave dispersion.

PubMed

Amador, Carolina; Urban, Matthew W; Chen, Shigao; Greenleaf, James F

2012-03-07

Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. In current shear wave elasticity imaging methods typically only shear wave speed is measured and rheological models, e.g. Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for tissue mechanical properties such as the shear viscoelastic complex modulus. This paper presents a method to quantify viscoelastic material properties in a model-independent way by estimating the complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. This radiation force induced creep method uses a conversion formula that is the analytic solution of a constitutive equation. The proposed method in combination with shearwave dispersion ultrasound vibrometry is used to measure the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. The conversion formula is shown to be sensitive to sampling frequency and the first reliable measure in time according to numerical simulations using the Kelvin-Voigt model creep strain and compliance. Representative model-free shear complex moduli from homogeneous tissue mimicking phantoms and one excised swine kidney were obtained. This work proposes a novel model-free ultrasound-based elasticity method that does not require a rheological model with associated fitting requirements.

The Green's matrix and the boundary integral equations for analysis of time-harmonic dynamics of elastic helical springs.

PubMed

Sorokin, Sergey V

2011-03-01

Helical springs serve as vibration isolators in virtually any suspension system. Various exact and approximate methods may be employed to determine the eigenfrequencies of vibrations of these structural elements and their dynamic transfer functions. The method of boundary integral equations is a meaningful alternative to obtain exact solutions of problems of the time-harmonic dynamics of elastic springs in the framework of Bernoulli-Euler beam theory. In this paper, the derivations of the Green's matrix, of the Somigliana's identities, and of the boundary integral equations are presented. The vibrational power transmission in an infinitely long spring is analyzed by means of the Green's matrix. The eigenfrequencies and the dynamic transfer functions are found by solving the boundary integral equations. In the course of analysis, the essential features and advantages of the method of boundary integral equations are highlighted. The reported analytical results may be used to study the time-harmonic motion in any wave guide governed by a system of linear differential equations in a single spatial coordinate along its axis. © 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.

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).

Modeling elastic wave propagation in kidney stones with application to shock wave lithotripsy.

PubMed

Cleveland, Robin O; Sapozhnikov, Oleg A

2005-10-01

A time-domain finite-difference solution to the equations of linear elasticity was used to model the propagation of lithotripsy waves in kidney stones. The model was used to determine the loading on the stone (principal stresses and strains and maximum shear stresses and strains) due to the impact of lithotripsy shock waves. The simulations show that the peak loading induced in kidney stones is generated by constructive interference from shear waves launched from the outer edge of the stone with other waves in the stone. Notably the shear wave induced loads were significantly larger than the loads generated by the classic Hopkinson or spall effect. For simulations where the diameter of the focal spot of the lithotripter was smaller than that of the stone the loading decreased by more than 50%. The constructive interference was also sensitive to shock rise time and it was found that the peak tensile stress reduced by 30% as rise time increased from 25 to 150 ns. These results demonstrate that shear waves likely play a critical role in stone comminution and that lithotripters with large focal widths and short rise times should be effective at generating high stresses inside kidney stones.

A mixed finite-element method for solving the poroelastic Biot equations with electrokinetic coupling

NASA Astrophysics Data System (ADS)

Pain, C. C.; Saunders, J. H.; Worthington, M. H.; Singer, J. M.; Stuart-Bruges, W.; Mason, G.; Goddard, A.

2005-02-01

In this paper, a numerical method for solving the Biot poroelastic equations is developed. These equations comprise acoustic (typically water) and elastic (porous medium frame) equations, which are coupled mainly through fluid/solid drag terms. This wave solution is coupled to a simplified form of Maxwell's equations, which is solved for the streaming potential resulting from electrokinesis. The ultimate aim is to use the generated electrical signals to provide porosity, permeability and other information about the formation surrounding a borehole. The electrical signals are generated through electrokinesis by seismic waves causing movement of the fluid through pores or fractures of a porous medium. The focus of this paper is the numerical solution of the Biot equations in displacement form, which is achieved using a mixed finite-element formulation with a different finite-element representation for displacements and stresses. The mixed formulation is used in order to reduce spurious displacement modes and fluid shear waves in the numerical solutions. These equations are solved in the time domain using an implicit unconditionally stable time-stepping method using iterative solution methods amenable to solving large systems of equations. The resulting model is embodied in the MODELLING OF ACOUSTICS, POROELASTICS AND ELECTROKINETICS (MAPEK) computer model for electroseismic analysis.

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.

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.

Thermo-magnetic field effects on the wave propagation behavior of smart magnetostrictive sandwich nanoplates

NASA Astrophysics Data System (ADS)

Ebrahimi, Farzad; Dabbagh, Ali

2018-03-01

In this paper, a three-variable plate model is utilized to explore the wave propagation problem of smart sandwich nanoplates made of a magnetostrictive core and ceramic face sheets while subjected to thermo-magnetic loading. Herein, the magnetostriction effect is considered and controlled via a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak elastic substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small-scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations are derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of the propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of the presented model are verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

Plane waves in magneto-thermoelastic anisotropic medium based on (L-S) theory under the effect of Coriolis and centrifugal forces

NASA Astrophysics Data System (ADS)

Alesemi, Meshari

2018-04-01

The objective of this research is to illustrate the effectiveness of the thermal relaxation time based on the theory of Lord-Shulman (L-S), Coriolis and Centrifugal Forces on the reflection coefficients of plane waves in an anisotropic magneto-thermoelastic medium. Assuming the elastic medium is rotating with stable angular velocity and the imposed magnetic field is parallel to the boundary of the half-space. The basic equations of a transversely isotropic rotating magneto-thermoelastic medium are formulated according to thermoelasticity theory of Lord-Shulman (L-S). Next to that, getting the velocity equation which is illustrated to show existence of three quasi-plane waves propagating in the medium. The amplitude ratios coefficients of these plane waves have been given and then computed numerically and plotted graphically to demonstrate the influences of the rotation on the Zinc material.

Dynamic properties of ceramic materials

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

Grady, D.E.

1995-02-01

The present study offers new data and analysis on the transient shock strength and equation-of-state properties of ceramics. Various dynamic data on nine high strength ceramics are provided with wave profile measurements, through velocity interferometry techniques, the principal observable. Compressive failure in the shock wave front, with emphasis on brittle versus ductile mechanisms of deformation, is examined in some detail. Extensive spall strength data are provided and related to the theoretical spall strength, and to energy-based theories of the spall process. Failure waves, as a mechanism of deformation in the transient shock process, are examined. Strength and equation-of-state analysis ofmore » shock data on silicon carbide, boron carbide, tungsten carbide, silicon dioxide and aluminum nitride is presented with particular emphasis on phase transition properties for the latter two. Wave profile measurements on selected ceramics are investigated for evidence of rate sensitive elastic precursor decay in the shock front failure process.« less

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.

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.

Methods of Investigation of Equations that Describe Waves in Tubes with Elastic Walls and Application of the Theory of Reversible and Weak Dissipative Shocks

NASA Astrophysics Data System (ADS)

Bakholdin, Igor

2018-02-01

Various models of a tube with elastic walls are investigated: with controlled pressure, filled with incompressible fluid, filled with compressible gas. The non-linear theory of hyperelasticity is applied. The walls of a tube are described with complete membrane model. It is proposed to use linear model of plate in order to take the bending resistance of walls into account. The walls of the tube were treated previously as inviscid and incompressible. Compressibility of material of walls and viscosity of material, either gas or liquid are considered. Equations are solved numerically. Three-layer time and space centered reversible numerical scheme and similar two-layer space reversible numerical scheme with approximation of time derivatives by Runge-Kutta method are used. A method of correction of numerical schemes by inclusion of terms with highorder derivatives is developed. Simplified hyperbolic equations are derived.

Dynamics and elastic interactions of the discrete multi-dark soliton solutions for the Kaup-Newell lattice equation

NASA Astrophysics Data System (ADS)

Liu, Nan; Wen, Xiao-Yong

2018-03-01

Under consideration in this paper is the Kaup-Newell (KN) lattice equation which is an integrable discretization of the KN equation. Infinitely, many conservation laws and discrete N-fold Darboux transformation (DT) for this system are constructed and established based on its Lax representation. Via the resulting N-fold DT, the discrete multi-dark soliton solutions in terms of determinants are derived from non-vanishing background. Propagation and elastic interaction structures of such solitons are shown graphically. Overtaking interaction phenomena between/among the two, three and four solitons are discussed. Numerical simulations are used to explore their dynamical behaviors of such multi-dark solitons. Numerical results show that their evolutions are stable against a small noise. Results in this paper might be helpful for understanding the propagation of nonlinear Alfvén waves in plasmas.

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.

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.

Petrophysical approach for S-wave velocity prediction based on brittleness index and total organic carbon of shale gas reservoir: A case study from Horn River Basin, Canada

NASA Astrophysics Data System (ADS)

Kim, Taeyoun; Hwang, Seho; Jang, Seonghyung

2017-01-01

When finding the "sweet spot" of a shale gas reservoir, it is essential to estimate the brittleness index (BI) and total organic carbon (TOC) of the formation. Particularly, the BI is one of the key factors in determining the crack propagation and crushing efficiency for hydraulic fracturing. There are several methods for estimating the BI of a formation, but most of them are empirical equations that are specific to particular rock types. We estimated the mineralogical BI based on elemental capture spectroscopy (ECS) log and elastic BI based on well log data, and we propose a new method for predicting S-wave velocity (VS) using mineralogical BI and elastic BI. The TOC is related to the gas content of shale gas reservoirs. Since it is difficult to perform core analysis for all intervals of shale gas reservoirs, we make empirical equations for the Horn River Basin, Canada, as well as TOC log using a linear relation between core-tested TOC and well log data. In addition, two empirical equations have been suggested for VS prediction based on density and gamma ray log used for TOC analysis. By applying the empirical equations proposed from the perspective of BI and TOC to another well log data and then comparing predicted VS log with real VS log, the validity of empirical equations suggested in this paper has been tested.

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.

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.

Wave Propagation in Bimodular Geomaterials

NASA Astrophysics Data System (ADS)

Kuznetsova, Maria; Pasternak, Elena; Dyskin, Arcady; Pelinovsky, Efim

2016-04-01

Observations and laboratory experiments show that fragmented or layered geomaterials have the mechanical response dependent on the sign of the load. The most adequate model accounting for this effect is the theory of bimodular (bilinear) elasticity - a hyperelastic model with different elastic moduli for tension and compression. For most of geo- and structural materials (cohesionless soils, rocks, concrete, etc.) the difference between elastic moduli is such that their modulus in compression is considerably higher than that in tension. This feature has a profound effect on oscillations [1]; however, its effect on wave propagation has not been comprehensively investigated. It is believed that incorporation of bilinear elastic constitutive equations within theory of wave dynamics will bring a deeper insight to the study of mechanical behaviour of many geomaterials. The aim of this paper is to construct a mathematical model and develop analytical methods and numerical algorithms for analysing wave propagation in bimodular materials. Geophysical and exploration applications and applications in structural engineering are envisaged. The FEM modelling of wave propagation in a 1D semi-infinite bimodular material has been performed with the use of Marlow potential [2]. In the case of the initial load expressed by a harmonic pulse loading strong dependence on the pulse sign is observed: when tension is applied before compression, the phenomenon of disappearance of negative (compressive) strains takes place. References 1. Dyskin, A., Pasternak, E., & Pelinovsky, E. (2012). Periodic motions and resonances of impact oscillators. Journal of Sound and Vibration, 331(12), 2856-2873. 2. Marlow, R. S. (2008). A Second-Invariant Extension of the Marlow Model: Representing Tension and Compression Data Exactly. In ABAQUS Users' Conference.

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.

Seismic wavefield propagation in 2D anisotropic media: Ray theory versus wave-equation simulation

NASA Astrophysics Data System (ADS)

Bai, Chao-ying; Hu, Guang-yi; Zhang, Yan-teng; Li, Zhong-sheng

2014-05-01

Despite the ray theory that is based on the high frequency assumption of the elastic wave-equation, the ray theory and the wave-equation simulation methods should be mutually proof of each other and hence jointly developed, but in fact parallel independent progressively. For this reason, in this paper we try an alternative way to mutually verify and test the computational accuracy and the solution correctness of both the ray theory (the multistage irregular shortest-path method) and the wave-equation simulation method (both the staggered finite difference method and the pseudo-spectral method) in anisotropic VTI and TTI media. Through the analysis and comparison of wavefield snapshot, common source gather profile and synthetic seismogram, it is able not only to verify the accuracy and correctness of each of the methods at least for kinematic features, but also to thoroughly understand the kinematic and dynamic features of the wave propagation in anisotropic media. The results show that both the staggered finite difference method and the pseudo-spectral method are able to yield the same results even for complex anisotropic media (such as a fault model); the multistage irregular shortest-path method is capable of predicting similar kinematic features as the wave-equation simulation method does, which can be used to mutually test each other for methodology accuracy and solution correctness. In addition, with the aid of the ray tracing results, it is easy to identify the multi-phases (or multiples) in the wavefield snapshot, common source point gather seismic section and synthetic seismogram predicted by the wave-equation simulation method, which is a key issue for later seismic application.

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.

Love-type waves in functionally graded piezoelectric material (FGPM) sandwiched between initially stressed layer and elastic substrate

NASA Astrophysics Data System (ADS)

Saroj, Pradeep K.; Sahu, S. A.; Chaudhary, S.; Chattopadhyay, A.

2015-10-01

This paper investigates the propagation behavior of Love-type surface waves in three-layered composite structure with initial stress. The composite structure has been taken in such a way that a functionally graded piezoelectric material (FGPM) layer is bonded between initially stressed piezoelectric upper layer and an elastic substrate. Using the method of separation of variables, frequency equation for the considered wave has been established in the form of determinant for electrical open and short cases on free surface. The bisection method iteration technique has been used to find the roots of the dispersion relations which give the modes for electrical open and short cases. The effects of gradient variation of material constant and initial stress on the phase velocity of surface waves are discussed. Dependence of thickness on each parameter of the study has been shown explicitly. Study has been also done to show the existence of cut-off frequency. Graphical representation has been done to exhibit the findings. The obtained results are significant for the investigation and characterization of Love-type waves in FGPM-layered media.

Elasticity of Pargasite Amphibole: A Hydrous Phase at Mid Lithospheric Discontinuity

NASA Astrophysics Data System (ADS)

Peng, Y.; Mookherjee, M.

2017-12-01

Mid Lithospheric Discontinuity (MLD) is characterized by a low shear wave velocity ( 3 to 10 %). In cratons, the depth of MLD varies between 80 and 100 km. The reduction of the shear wave velocity at MLD is similar to what is observed in the lithosphere-asthenosphere boundary (LAB). Such low velocity at MLD could be caused by partial melting, temperature induced grain boundary sliding, changes in the elastic anisotropy, and/or metasomatism which may lead to the formation of hydrous phases including mica and amphibole. Thus, it is clear that in order to assess the role of metasomatism at MLD, we need better constraints on the elasticity of hydrous phases. However, such elasticity data are scarce. In this study, we explore elasticity of pargasite amphibole [NaCa2(Mg4Al)(Si6Al2)O22(OH)2] using density functional theory (DFT) with local density approximation (LDA) and generalized gradient approximation (GGA). We find that the pressure-volume results can be adequately described by a finite strain equation with the bulk modulus, K0 being 102 and 85 GPa for LDA and GGA respectively. We also determined the full elastic constant tensor (Cij) using the finite difference method. The bulk modulus, K0 determined from the full elastic constant tensor is 104 GPa for LDA and 87 GPa for GGA. The shear modulus, G0 determined from the full elastic constant tensor is 64 GPa for LDA and 58 GPa for GGA. The bulk and shear moduli predicted with LDA are 5 and 1 % stiffer than the recent results [1]. In contrast, the bulk and shear moduli predicted with GGA are 12 and 10 % softer compared to the recent results [1]. The full elastic constant tensor for pargasite shows significant anisotropy. For instance, LDA predicts compressional (AVP) and shear (AVS) wave anisotropy of 22 and 20 % respectively. At higher pressure, elastic moduli stiffen. However, temperature is likely to have an opposite effect on the elasticity and this remains largely unknown for pargasite. Compared to the major mantle minerals, pargasite has softer elastic constants and significant anisotropy and may explain the reduction in shear wave velocity at MLD. Reference: [1] Brown, J. M., Abramson, E. H.,2016, Phys. Earth Planet. Int., 261, 161-171. Acknowledgement: This work is supported by US NSF award EAR 1639552.

Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

NASA Technical Reports Server (NTRS)

Fu, L. S.; Mura, T.

1983-01-01

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

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.

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.

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

NASA Astrophysics Data System (ADS)

Kumari, Nirmala; Chattopadhyay, Amares; Singh, Abhishek K.; Sahu, Sanjeev A.

2017-03-01

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker's asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot's gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.

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.

Acoustic and elastic multiple scattering and radiation from cylindrical structures

NASA Astrophysics Data System (ADS)

Amirkulova, Feruza Abdukadirovna

Multiple scattering (MS) and radiation of waves by a system of scatterers is of great theoretical and practical importance and is required in a wide variety of physical contexts such as the implementation of "invisibility" cloaks, the effective parameter characterization, and the fabrication of dynamically tunable structures, etc. The dissertation develops fast, rapidly convergent iterative techniques to expedite the solution of MS problems. The formulation of MS problems reduces to a system of linear algebraic equations using Graf's theorem and separation of variables. The iterative techniques are developed using Neumann expansion and Block Toeplitz structure of the linear system; they are very general, and suitable for parallel computations and a large number of MS problems, i.e. acoustic, elastic, electromagnetic, etc., and used for the first time to solve MS problems. The theory is implemented in Matlab and FORTRAN, and the theoretical predictions are compared to computations obtained by COMSOL. To formulate the MS problem, the transition matrix is obtained by analyzing an acoustic and an elastic single scattering of incident waves by elastic isotropic and anisotropic solids. The mathematical model of wave scattering from multilayered cylindrical and spherical structures is developed by means of an exact solution of dynamic 3D elasticity theory. The recursive impedance matrix algorithm is derived for radially heterogeneous anisotropic solids. An explicit method for finding the impedance in piecewise uniform, transverse-isotropic material is proposed; the solution is compared to elasticity theory solutions involving Buchwald potentials. Furthermore, active exterior cloaking devices are modeled for acoustic and elastic media using multipole sources. A cloaking device can render an object invisible to some incident waves as seen by some external observer. The active cloak is generated by a discrete set of multipole sources that destructively interfere with an incident wave to produce zero total field over a finite spatial region. The approach precisely determines the necessary source amplitudes and enables a cloaked region to be determined using Graf's theorem. To apply the approach, the infinite series of multipole expansions are truncated, and the accuracy of cloaking is studied by modifying the truncation parameter.

Fast 3D elastic micro-seismic source location using new GPU features

NASA Astrophysics Data System (ADS)

Xue, Qingfeng; Wang, Yibo; Chang, Xu

2016-12-01

In this paper, we describe new GPU features and their applications in passive seismic - micro-seismic location. Locating micro-seismic events is quite important in seismic exploration, especially when searching for unconventional oil and gas resources. Different from the traditional ray-based methods, the wave equation method, such as the method we use in our paper, has a remarkable advantage in adapting to low signal-to-noise ratio conditions and does not need a person to select the data. However, because it has a conspicuous deficiency due to its computation cost, these methods are not widely used in industrial fields. To make the method useful, we implement imaging-like wave equation micro-seismic location in a 3D elastic media and use GPU to accelerate our algorithm. We also introduce some new GPU features into the implementation to solve the data transfer and GPU utilization problems. Numerical and field data experiments show that our method can achieve a more than 30% performance improvement in GPU implementation just by using these new features.

3D Orthorhombic Elastic Wave Propagation Pre-Test Simulation of SPE DAG-1 Test

NASA Astrophysics Data System (ADS)

Jensen, R. P.; Preston, L. A.

2017-12-01

A more realistic representation of many geologic media can be characterized as a dense system of vertically-aligned microfractures superimposed on a finely-layered horizontal geology found in shallow crustal rocks. This seismic anisotropy representation lends itself to being modeled as an orthorhombic elastic medium comprising three mutually orthogonal symmetry planes containing nine independent moduli. These moduli can be determined by observing (or prescribing) nine independent P-wave and S-wave phase speeds along different propagation directions. We have developed an explicit time-domain finite-difference (FD) algorithm for simulating 3D elastic wave propagation in a heterogeneous orthorhombic medium. The components of the particle velocity vector and the stress tensor are governed by a set of nine, coupled, first-order, linear, partial differential equations (PDEs) called the velocity-stress system. All time and space derivatives are discretized with centered and staggered FD operators possessing second- and fourth-order numerical accuracy, respectively. Additionally, we have implemented novel perfectly matched layer (PML) absorbing boundary conditions, specifically designed for orthorhombic media, to effectively suppress grid boundary reflections. In support of the Source Physics Experiment (SPE) Phase II, a series of underground chemical explosions at the Nevada National Security Site, the code has been used to perform pre-test estimates of the Dry Alluvium Geology - Experiment 1 (DAG-1). Based on literature searches, realistic geologic structure and values for orthorhombic P-wave and S-wave speeds have been estimated. Results and predictions from the simulations are presented.

Special discontinuities in nonlinearly elastic media

NASA Astrophysics Data System (ADS)

Chugainova, A. P.

2017-06-01

Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

Wave transmission approach based on modal analysis for embedded mechanical systems

NASA Astrophysics Data System (ADS)

Cretu, Nicolae; Nita, Gelu; Ioan Pop, Mihail

2013-09-01

An experimental method for determining the phase velocity in small solid samples is proposed. The method is based on measuring the resonant frequencies of a binary or ternary solid elastic system comprising the small sample of interest and a gauge material of manageable size. The wave transmission matrix of the combined system is derived and the theoretical values of its eigenvalues are used to determine the expected eigenfrequencies that, equated with the measured values, allow for the numerical estimation of the phase velocities in both materials. The known phase velocity of the gauge material is then used to asses the accuracy of the method. Using computer simulation and the experimental values for phase velocities, the theoretical values for the eigenfrequencies of the eigenmodes of the embedded elastic system are obtained, to validate the method. We conclude that the proposed experimental method may be reliably used to determine the elastic properties of small solid samples whose geometries do not allow a direct measurement of their resonant frequencies.

Refined boundary conditions on the free surface of an elastic half-space taking into account non-local effects.

PubMed

Chebakov, R; Kaplunov, J; Rogerson, G A

2016-02-01

The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is shown to coincide formally with the 'local' problem for a half-space with a vertical inhomogeneity localized near the surface. Subsequent asymptotic analysis of the inhomogeneity results in an explicit correction to the classical boundary conditions on the surface. The order of the correction is greater than the order of the better-known correction to the governing differential equations. The refined boundary conditions enable us to evaluate the interior solution outside a narrow boundary layer localized near the surface. As an illustration, the effect of non-local elastic phenomena on the Rayleigh wave speed is investigated.

Scattering of Lamb waves in a composite plate

NASA Technical Reports Server (NTRS)

Bratton, Robert; Datta, Subhendu; Shah, Arvind

1991-01-01

A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.

Shear wave speed recovery in transient elastography and supersonic imaging using propagating fronts

NASA Astrophysics Data System (ADS)

McLaughlin, Joyce; Renzi, Daniel

2006-04-01

Transient elastography and supersonic imaging are promising new techniques for characterizing the elasticity of soft tissues. Using this method, an 'ultrafast imaging' system (up to 10 000 frames s-1) follows in real time the propagation of a low frequency shear wave. The displacement of the propagating shear wave is measured as a function of time and space. The objective of this paper is to develop and test algorithms whose ultimate product is images of the shear wave speed of tissue mimicking phantoms. The data used in the algorithms are the front of the propagating shear wave. Here, we first develop techniques to find the arrival time surface given the displacement data from a transient elastography experiment. The arrival time surface satisfies the Eikonal equation. We then propose a family of methods, called distance methods, to solve the inverse Eikonal equation: given the arrival times of a propagating wave, find the wave speed. Lastly, we explain why simple inversion schemes for the inverse Eikonal equation lead to large outliers in the wave speed and numerically demonstrate that the new scheme presented here does not have any large outliers. We exhibit two recoveries using these methods: one is with synthetic data; the other is with laboratory data obtained by Mathias Fink's group (the Laboratoire Ondes et Acoustique, ESPCI, Université Paris VII).

Analysis of Transient Shear Wave in Lossy Media.

PubMed

Parker, Kevin J; Ormachea, Juvenal; Will, Scott; Hah, Zaegyoo

2018-07-01

The propagation of shear waves from impulsive forces is an important topic in elastography. Observations of shear wave propagation can be obtained with numerous clinical imaging systems. Parameter estimations of the shear wave speed in tissues, and more generally the viscoelastic parameters of tissues, are based on some underlying models of shear wave propagation. The models typically include specific choices of the spatial and temporal shape of the impulsive force and the elastic or viscoelastic properties of the medium. In this work, we extend the analytical treatment of 2-D shear wave propagation in a biomaterial. The approach applies integral theorems relevant to the solution of the generalized Helmholtz equation, and does not depend on a specific rheological model of the tissue's viscoelastic properties. Estimators of attenuation and shear wave speed are derived from the analytical solutions, and these are applied to an elastic phantom, a viscoelastic phantom and in vivo liver using a clinical ultrasound scanner. In these samples, estimated shear wave group velocities ranged from 1.7 m/s in the liver to 2.5 m/s in the viscoelastic phantom, and these are lower-bounded by independent measurements of phase velocity. Copyright © 2018 World Federation for Ultrasound in Medicine and Biology. Published by Elsevier Inc. All rights reserved.

Anomalous density and elastic properties of basalt at high pressure: Reevaluating of the effect of melt fraction on seismic velocity in the Earth's crust and upper mantle

NASA Astrophysics Data System (ADS)

Clark, Alisha N.; Lesher, Charles E.; Jacobsen, Steven D.; Wang, Yanbin

2016-06-01

Independent measurements of the volumetric and elastic properties of Columbia River basalt glass were made up to 5.5 GPa by high-pressure X-ray microtomography and GHz-ultrasonic interferometry, respectively. The Columbia River basalt displays P and S wave velocity minima at 4.5 and 5 GPa, respectively, violating Birch's law. These data constrain the pressure dependence of the density and elastic moduli at high pressure, which cannot be modeled through usual equations of state nor determined by stepwise integrating the bulk sound velocity as is common practice. We propose a systematic variation in compression behavior of silicate glasses that is dependent on the degree of polymerization and arises from the flexibility of the aluminosilicate network. This behavior likely persists into the liquid state for basaltic melts resulting in weak pressure dependence for P wave velocities perhaps to depths of the transition zone. Modeling the effect of partial melt on P wave velocity reductions suggests that melt fraction determined by seismic velocity variations may be significantly overestimated in the crust and upper mantle.

Anomalous density and elastic properties of basalt at high pressure: Reevaluating of the effect of melt fraction on seismic velocity in the Earth's crust and upper mantle

DOE PAGES

Clark, Alisha N.; Lesher, Charles E.; Jacobsen, Steven D.; ...

2016-06-27

Independent measurements of the volumetric and elastic properties of Columbia River basalt glass were made up to 5.5 GPa by high-pressure X-ray microtomography and GHz-ultrasonic interferometry, respectively. The Columbia River basalt displays P and S wave velocity minima at 4.5 and 5 GPa, respectively, violating Birch’s law. These data constrain the pressure dependence of the density and elastic moduli at high pressure, which cannot be modeled through usual equations of state nor determined by stepwise integrating the bulk sound velocity as is common practice. We propose a systematic variation in compression behavior of silicate glasses that is dependent on themore » degree of polymerization and arises from the flexibility of the aluminosilicate network. Likewise, this behavior likely persists into the liquid state for basaltic melts resulting in weak pressure dependence for P wave velocities perhaps to depths of the transition zone. By modeling the effect of partial melt on P wave velocity reductions it is suggested that melt fraction determined by seismic velocity variations may be significantly overestimated in the crust and upper mantle.« less

QUANTITATIVE NON-DESTRUCTIVE EVALUATION (QNDE) OF THE ELASTIC MODULI OF POROUS TIAL ALLOYS

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

Yeheskel, O.

2008-02-28

The elastic moduli of {gamma}-TiA1 were studied in porous samples consolidated by various techniques e.g. cold isostatic pressing (CIP), pressure-less sintering, or hot isostatic pressing (HIP). Porosity linearly affects the dynamic elastic moduli of samples. The results indicate that the sound wave velocities and the elastic moduli affected by the processing route and depend not only on the attained density but also on the consolidation temperature. In this paper we show that there is linear correlation between the shear and the longitudinal sound velocities in porous TiA1. This opens the way to use a single sound velocity as a toolmore » for quantitative non-destructive evaluation (QNDE) of porous TiA1 alloys. Here we demonstrate the applicability of an equation derived from the elastic theory and used previously for porous cubic metals.« less

Atmospheric gravity waves with small vertical-to-horizotal wavelength ratios

NASA Astrophysics Data System (ADS)

Song, I. S.; Jee, G.; Kim, Y. H.; Chun, H. Y.

2017-12-01

Gravity wave modes with small vertical-to-horizontal wavelength ratios of an order of 10-3 are investigated through the systematic scale analysis of governing equations for gravity wave perturbations embedded in the quasi-geostrophic large-scale flow. These waves can be categorized as acoustic gravity wave modes because their total energy is given by the sum of kinetic, potential, and elastic parts. It is found that these waves can be forced by density fluctuations multiplied by the horizontal gradients of the large-scale pressure (geopotential) fields. These theoretical findings are evaluated using the results of a high-resolution global model (Specified Chemistry WACCM with horizontal resolution of 25 km and vertical resolution of 600 m) by computing the density-related gravity-wave forcing terms from the modeling results.

Temporal variations in magnetic signals generated by the piezomagnetic effect for dislocation sources in a uniform medium

NASA Astrophysics Data System (ADS)

Yamazaki, Ken'ichi

2016-07-01

Fault ruptures in the Earth's crust generate both elastic and electromagnetic (EM) waves. If the corresponding EM signals can be observed, then earthquakes could be detected before the first seismic waves arrive. In this study, I consider the piezomagnetic effect as a mechanism that converts elastic waves to EM energy, and I derive analytical formulas for the conversion process. The situation considered in this study is a whole-space model, in which elastic and EM properties are uniform and isotropic. In this situation, the governing equations of the elastic and EM fields, combined with the piezomagnetic constitutive law, can be solved analytically in the time domain by ignoring the displacement current term. Using the derived formulas, numerical examples are investigated, and the corresponding characteristics of the expected magnetic signals are resolved. I show that temporal variations in the magnetic field depend strongly on the electrical conductivity of the medium, meaning that precise detection of signals generated by the piezomagnetic effect is generally difficult. Expected amplitudes of piezomagnetic signals are estimated to be no larger than 0.3 nT for earthquakes with a moment magnitude of ≥7.0 at a source distance of 25 km; however, this conclusion may not extend to the detection of real earthquakes, because piezomagnetic stress sensitivity is currently poorly constrained.

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.

A feasibility study of the use of bounded beams resembling the shape of evanescent and inhomogeneous waves.

PubMed

Declercq, Nico F; Leroy, Oswald

2011-08-01

Plane waves are solutions of the visco-elastic wave equation. Their wave vector can be real for homogeneous plane waves or complex for inhomogeneous and evanescent plane waves. Although interesting from a theoretical point of view, complex wave vectors normally only emerge naturally when propagation or scattering is studied of sound under the appearance of damping effects. Because of the particular behavior of inhomogeneous and evanescent waves and their estimated efficiency for surface wave generation, bounded beams, experimentally mimicking their infinite counterparts similar to (wide) Gaussian beams imitating infinite harmonic plane waves, are of special interest in this report. The study describes the behavior of bounded inhomogeneous and bounded evanescent waves in terms of amplitude and phase distribution as well as energy flow direction. The outcome is of importance to the applicability of bounded inhomogeneous ultrasonic waves for nondestructive testing. Copyright © 2011. Published by Elsevier B.V.

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

NASA Technical Reports Server (NTRS)

Goldman, Benjamin D.; Dowell, Earl H.; Scott, Robert C.

2014-01-01

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Exact result in strong wave turbulence of thin elastic plates

NASA Astrophysics Data System (ADS)

Düring, Gustavo; Krstulovic, Giorgio

2018-02-01

An exact result concerning the energy transfers between nonlinear waves of a thin elastic plate is derived. Following Kolmogorov's original ideas in hydrodynamical turbulence, but applied to the Föppl-von Kármán equation for thin plates, the corresponding Kármán-Howarth-Monin relation and an equivalent of the 4/5 -Kolmogorov's law is derived. A third-order structure function involving increments of the amplitude, velocity, and the Airy stress function of a plate, is proven to be equal to -ɛ ℓ , where ℓ is a length scale in the inertial range at which the increments are evaluated and ɛ the energy dissipation rate. Numerical data confirm this law. In addition, a useful definition of the energy fluxes in Fourier space is introduced and proven numerically to be flat in the inertial range. The exact results derived in this Rapid Communication are valid for both weak and strong wave turbulence. They could be used as a theoretical benchmark of new wave-turbulence theories and to develop further analogies with hydrodynamical turbulence.

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.

Hydroelastic analysis of ice shelves under long wave excitation

NASA Astrophysics Data System (ADS)

Papathanasiou, T. K.; Karperaki, A. E.; Theotokoglou, E. E.; Belibassakis, K. A.

2015-05-01

The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length.

Hydroelastic analysis of ice shelves under long wave excitation

NASA Astrophysics Data System (ADS)

Papathanasiou, T. K.; Karperaki, A. E.; Theotokoglou, E. E.; Belibassakis, K. A.

2015-08-01

The transient hydroelastic response of an ice shelf under long wave excitation is analysed by means of the finite element method. The simple model, presented in this work, is used for the simulation of the generated kinematic and stress fields in an ice shelf, when the latter interacts with a tsunami wave. The ice shelf, being of large length compared to its thickness, is modelled as an elastic Euler-Bernoulli beam, constrained at the grounding line. The hydrodynamic field is represented by the linearised shallow water equations. The numerical solution is based on the development of a special hydroelastic finite element for the system of governing of equations. Motivated by the 2011 Sulzberger Ice Shelf (SIS) calving event and its correlation with the Honshu Tsunami, the SIS stable configuration is studied. The extreme values of the bending moment distribution in both space and time are examined. Finally, the location of these extrema is investigated for different values of ice shelf thickness and tsunami wave length.

Wave energy focusing to subsurface poroelastic formations to promote oil mobilization

NASA Astrophysics Data System (ADS)

Karve, Pranav M.; Kallivokas, Loukas F.

2015-07-01

We discuss an inverse source formulation aimed at focusing wave energy produced by ground surface sources to target subsurface poroelastic formations. The intent of the focusing is to facilitate or enhance the mobility of oil entrapped within the target formation. The underlying forward wave propagation problem is cast in two spatial dimensions for a heterogeneous poroelastic target embedded within a heterogeneous elastic semi-infinite host. The semi-infiniteness of the elastic host is simulated by augmenting the (finite) computational domain with a buffer of perfectly matched layers. The inverse source algorithm is based on a systematic framework of partial-differential-equation-constrained optimization. It is demonstrated, via numerical experiments, that the algorithm is capable of converging to the spatial and temporal characteristics of surface loads that maximize energy delivery to the target formation. Consequently, the methodology is well-suited for designing field implementations that could meet a desired oil mobility threshold. Even though the methodology, and the results presented herein are in two dimensions, extensions to three dimensions are straightforward.

Fully nonlocal inelastic scattering computations for spectroscopical transmission electron microscopy methods

NASA Astrophysics Data System (ADS)

Rusz, Ján; Lubk, Axel; Spiegelberg, Jakob; Tyutyunnikov, Dmitry

2017-12-01

The complex interplay of elastic and inelastic scattering amenable to different levels of approximation constitutes the major challenge for the computation and hence interpretation of TEM-based spectroscopical methods. The two major approaches to calculate inelastic scattering cross sections of fast electrons on crystals—Yoshioka-equations-based forward propagation and the reciprocal wave method—are founded in two conceptually differing schemes—a numerical forward integration of each inelastically scattered wave function, yielding the exit density matrix, and a computation of inelastic scattering matrix elements using elastically scattered initial and final states (double channeling). Here, we compare both approaches and show that the latter is computationally competitive to the former by exploiting analytical integration schemes over multiple excited states. Moreover, we show how to include full nonlocality of the inelastic scattering event, neglected in the forward propagation approaches, at no additional computing costs in the reciprocal wave method. Detailed simulations show in some cases significant errors due to the z -locality approximation and hence pitfalls in the interpretation of spectroscopical TEM results.

Dynamic interaction of twin vertically overlapping lined tunnels in an elastic half space subjected to incident plane waves

NASA Astrophysics Data System (ADS)

Liu, Zhongxian; Wang, Yirui; Liang, Jianwen

2016-06-01

The scattering of plane harmonic P and SV waves by a pair of vertically overlapping lined tunnels buried in an elastic half space is solved using a semi-analytic indirect boundary integration equation method. Then the effect of the distance between the two tunnels, the stiffness and density of the lining material, and the incident frequency on the seismic response of the tunnels is investigated. Numerical results demonstrate that the dynamic interaction between the twin tunnels cannot be ignored and the lower tunnel has a significant shielding effect on the upper tunnel for high-frequency incident waves, resulting in great decrease of the dynamic hoop stress in the upper tunnel; for the low-frequency incident waves, in contrast, the lower tunnel can lead to amplification effect on the upper tunnel. It also reveals that the frequency-spectrum characteristics of dynamic stress of the lower tunnel are significantly different from those of the upper tunnel. In addition, for incident P waves in low-frequency region, the soft lining tunnels have significant amplification effect on the surface displacement amplitude, which is slightly larger than that of the corresponding single tunnel.

Shear waves in inhomogeneous, compressible fluids in a gravity field.

PubMed

Godin, Oleg A

2014-03-01

While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

On the propagation of elasto-thermodiffusive surface waves in heat-conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.; Sharma, Y. D.; Sharma, P. K.

2008-09-01

The present paper deals with the study of the propagation of Rayleigh surface waves in homogeneous isotropic, thermodiffusive elastic half-space. After developing the formal solution of the model, the secular equations for stress free, thermally insulated or isothermal, and isoconcentrated boundary conditions of the half-space have been obtained. The secular equations have been solved by using irreducible Cardano's method with the help of DeMoivre's theorem in order to obtain phase velocity and attenuation coefficient of waves under consideration. The motion of the surface particles during the Rayleigh surface wave propagation is also discussed and found to be elliptical in general. The inclinations of wave normal with the major axis of the elliptical path of a typical particle have also been computed. Finally, the numerically simulated results regarding phase velocity, attenuation coefficient, specific loss and thermo-mechanical coupling factors of thermoelastic diffusive waves have been obtained and presented graphically. Some very interesting and useful characteristics of surface acoustic waves have been obtained, which may help in improving the fabrication quality of optical and electronic devices in addition to construction and design of materials such as semiconductors and composite structures. Therefore, this work finds applications in the geophysics and electronics industry.

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.

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.

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.

Frequency domain, waveform inversion of laboratory crosswell radar data

USGS Publications Warehouse

Ellefsen, Karl J.; Mazzella, Aldo T.; Horton, Robert J.; McKenna, Jason R.

2010-01-01

A new waveform inversion for crosswell radar is formulated in the frequency-domain for a 2.5D model. The inversion simulates radar waves using the vector Helmholtz equation for electromagnetic waves. The objective function is minimized using a backpropagation method suitable for a 2.5D model. The inversion is tested by processing crosswell radar data collected in a laboratory tank. The estimated model is consistent with the known electromagnetic properties of the tank. The formulation for the 2.5D model can be extended to inversions of acoustic and elastic data.

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

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

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

Elastic-wave-mode separation in TTI media with inverse-distance weighted interpolation involving position shading

NASA Astrophysics Data System (ADS)

Wang, Jian; Meng, Xiaohong; Zheng, Wanqiu

2017-10-01

The elastic-wave reverse-time migration of inhomogeneous anisotropic media is becoming the hotspot of research today. In order to ensure the accuracy of the migration, it is necessary to separate the wave mode into P-wave and S-wave before migration. For inhomogeneous media, the Kelvin-Christoffel equation can be solved in the wave-number domain by using the anisotropic parameters of the mesh nodes, and the polarization vector of the P-wave and S-wave at each node can be calculated and transformed into the space domain to obtain the quasi-differential operators. However, this method is computationally expensive, especially for the process of quasi-differential operators. In order to reduce the computational complexity, the wave-mode separation of mixed domain can be realized on the basis of a reference model in the wave-number domain. But conventional interpolation methods and reference model selection methods reduce the separation accuracy. In order to further improve the separation effect, this paper introduces an inverse-distance interpolation method involving position shading and uses the reference model selection method of random points scheme. This method adds the spatial weight coefficient K, which reflects the orientation of the reference point on the conventional IDW algorithm, and the interpolation process takes into account the combined effects of the distance and azimuth of the reference points. Numerical simulation shows that the proposed method can separate the wave mode more accurately using fewer reference models and has better practical value.

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.

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

Simulation of Richtmyer-Meshkov flows for elastic-plastic solids in planar and converging geometries using an Eulerian framework

NASA Astrophysics Data System (ADS)

Lopez Ortega, Alejandro

This thesis presents a numerical and analytical study of two problems of interest involving shock waves propagating through elastic-plastic media: the motion of converging (imploding) shocks and the Richtmyer-Meshkov (RM) instability. Since the stress conditions encountered in these cases normally produce large deformations in the materials, an Eulerian description, in which the spatial coordinates are fixed, is employed. This formulation enables a direct comparison of similarities and differences between the present study of phenomena driven by shock-loading in elastic-plastic solids, and in fluids, where they have been studied extensively. In the first application, Whitham's shock dynamics (WSD) theory is employed for obtaining an approximate description of the motion of an elastic-plastic material processed by a cylindrically/spherically converging shock. Comparison with numerical simulations of the full set of equations of motion reveal that WSD is an accurate tool for characterizing the evolution of converging shocks at all stages. The study of the Richtmyer-Meshkov flow (i.e., interaction between the interface separating two materials of different density and a shock wave incoming at an angle) in solids is performed by means of analytical models for purely elastic solids and numerical simulations when plasticity is included in the material model. To this effect, an updated version of a previously developed multi-material, level-set-based, Eulerian framework for solid mechanics is employed. The revised code includes the use of a multi-material HLLD Riemann problem for imposing material boundary conditions, and a new formulation of the equations of motion that makes use of the stretch tensor while avoiding the degeneracy of the stress tensor under rotation. Results reveal that the interface separating two elastic solids always behaves in a stable oscillatory or decaying oscillatory manner due to the existence of shear waves, which are able to transport the initial vorticity away from the interface. In the case of elastic-plastic materials, the interface behaves at first in an unstable manner similar to a fluid. Ejecta formation is appreciated under certain initial conditions while in other conditions, after an initial period of growth, the interface displays a quasi-stationary long-term behavior due to stress relaxation. The effect of secondary shock-interface interactions (re-shocks) in converging geometries is also studied. A turbulent mixing zone, similar to what is observed in gas--gas interfaces, is created, especially when materials with low strength driven by moderate to strong shocks are considered.

Crystal structure, equation of state, and elasticity of phase H (MgSiO4H2) at Earth's lower mantle pressures.

PubMed

Tsuchiya, Jun; Mookherjee, Mainak

2015-10-23

Dense hydrous magnesium silicate (DHMS) phases play a crucial role in transporting water in to the Earth's interior. A newly discovered DHMS, phase H (MgSiO4H2), is stable at Earth's lower mantle, i.e., at pressures greater than 30 GPa. Here we report the crystal structure and elasticity of phase H and its evolution upon compression. Using first principles simulations, we have explored the relative energetics of the candidate crystal structures with ordered and disordered configurations of magnesium and silicon atoms in the octahedral sites. At conditions relevant to Earth's lower mantle, it is likely that phase H is able to incorporate a significant amount of aluminum, which may enhance the thermodynamic stability of phase H. The sound wave velocities of phase H are ~2-4% smaller than those of isostructural δ-AlOOH. The shear wave impedance contrast due to the transformation of phase D to a mixture of phase H and stishovite at pressures relevant to the upper part of the lower mantle could partly explain the geophysical observations. The calculated elastic wave velocities and anisotropies indicate that phase H can be a source of significant seismic anisotropy in the lower mantle.

Light scattering from an atomic gas under conditions of quantum degeneracy

NASA Astrophysics Data System (ADS)

Porozova, V. M.; Gerasimov, L. V.; Havey, M. D.; Kupriyanov, D. V.

2018-05-01

Elastic light scattering from a macroscopic atomic sample existing in the Bose-Einstein condensate phase reveals a unique physical configuration of interacting light and matter waves. However, the joint coherent dynamics of the optical excitation induced by an incident photon is influenced by the presence of incoherent scattering channels. For a sample of sufficient length the excitation transports as a polariton wave and the propagation Green's function obeys the scattering equation which we derive. The polariton dynamics could be tracked in the outgoing channel of the scattered photon as we show via numerical solution of the scattering equation for one-dimensional geometry. The results are analyzed and compared with predictions of the conventional macroscopic Maxwell theory for light scattering from a nondegenerate atomic sample of the same density and size.

Hydrodynamics of Turning Flocks.

PubMed

Yang, Xingbo; Marchetti, M Cristina

2015-12-18

We present a hydrodynamic model of flocking that generalizes the familiar Toner-Tu equations to incorporate turning inertia of well-polarized flocks. The continuum equations controlled by only two dimensionless parameters, orientational inertia and alignment strength, are derived by coarse-graining the inertial spin model recently proposed by Cavagna et al. The interplay between orientational inertia and bend elasticity of the flock yields anisotropic spin waves that mediate the propagation of turning information throughout the flock. The coupling between spin-current density to the local vorticity field through a nonlinear friction gives rise to a hydrodynamic mode with angular-dependent propagation speed at long wavelengths. This mode becomes unstable as a result of the growth of bend and splay deformations augmented by the spin wave, signaling the transition to complex spatiotemporal patterns of continuously turning and swirling flocks.

Stabilizing effect of elasticity on the inertial instability of submerged viscoelastic liquid jets

NASA Astrophysics Data System (ADS)

Keshavarz, Bavand; McKinley, Gareth

2017-11-01

The stability of submerged Newtonian and viscoelastic liquid jets is studied experimentally using flow visualization. Precise control of the amplitude and frequency of the imposed linear perturbations is achieved through a piezoelectric actuator attached to the nozzle. By illuminating the jet with a strobe light driven at a frequency slightly less than the frequency of the perturbation we slow down the apparent motion by large factors ( 100 , 000) and capture the phenomena with high temporal and spatial resolution. Newtonian liquid jets become unstable at moderate Reynolds numbers (Rej 150) and sinuous or varicose patterns emerge and grow in amplitude. As the jet moves downstream, the varicose waves gradually pile up in the sinuous ones due to the difference in their corresponding wave speeds, leading to a unique chevron-like morphology. Experiments with model viscoelastic polymer solutions show that this inertial instability is fully stabilized sufficiently large levels of elasticity. We compare our experimental results with the theoretical predictions of an elastic Rayleigh equation for an axisymmetric jet and show that the presence of streamline tension is indeed the stabilizing effect for inertioelastic jets.

Topology preserving non-rigid image registration using time-varying elasticity model for MRI brain volumes.

PubMed

Ahmad, Sahar; Khan, Muhammad Faisal

2015-12-01

In this paper, we present a new non-rigid image registration method that imposes a topology preservation constraint on the deformation. We propose to incorporate the time varying elasticity model into the deformable image matching procedure and constrain the Jacobian determinant of the transformation over the entire image domain. The motion of elastic bodies is governed by a hyperbolic partial differential equation, generally termed as elastodynamics wave equation, which we propose to use as a deformation model. We carried out clinical image registration experiments on 3D magnetic resonance brain scans from IBSR database. The results of the proposed registration approach in terms of Kappa index and relative overlap computed over the subcortical structures were compared against the existing topology preserving non-rigid image registration methods and non topology preserving variant of our proposed registration scheme. The Jacobian determinant maps obtained with our proposed registration method were qualitatively and quantitatively analyzed. The results demonstrated that the proposed scheme provides good registration accuracy with smooth transformations, thereby guaranteeing the preservation of topology. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

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 staggered-grid convolutional differentiator for elastic wave modelling

NASA Astrophysics Data System (ADS)

Sun, Weijia; Zhou, Binzhong; Fu, Li-Yun

2015-11-01

The computation of derivatives in governing partial differential equations is one of the most investigated subjects in the numerical simulation of physical wave propagation. An analytical staggered-grid convolutional differentiator (CD) for first-order velocity-stress elastic wave equations is derived in this paper by inverse Fourier transformation of the band-limited spectrum of a first derivative operator. A taper window function is used to truncate the infinite staggered-grid CD stencil. The truncated CD operator is almost as accurate as the analytical solution, and as efficient as the finite-difference (FD) method. The selection of window functions will influence the accuracy of the CD operator in wave simulation. We search for the optimal Gaussian windows for different order CDs by minimizing the spectral error of the derivative and comparing the windows with the normal Hanning window function for tapering the CD operators. It is found that the optimal Gaussian window appears to be similar to the Hanning window function for tapering the same CD operator. We investigate the accuracy of the windowed CD operator and the staggered-grid FD method with different orders. Compared to the conventional staggered-grid FD method, a short staggered-grid CD operator achieves an accuracy equivalent to that of a long FD operator, with lower computational costs. For example, an 8th order staggered-grid CD operator can achieve the same accuracy of a 16th order staggered-grid FD algorithm but with half of the computational resources and time required. Numerical examples from a homogeneous model and a crustal waveguide model are used to illustrate the superiority of the CD operators over the conventional staggered-grid FD operators for the simulation of wave propagations.

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.

Loss-less propagation, elastic and inelastic interaction of electromagnetic soliton in an anisotropic ferromagnetic nanowire

NASA Astrophysics Data System (ADS)

Senthil Kumar, V.; Kavitha, L.; Boopathy, C.; Gopi, D.

2017-10-01

Nonlinear interaction of electromagnetic solitons leads to a plethora of interesting physical phenomena in the diverse area of science that include magneto-optics based data storage industry. We investigate the nonlinear magnetization dynamics of a one-dimensional anisotropic ferromagnetic nanowire. The famous Landau-Lifshitz-Gilbert equation (LLG) describes the magnetization dynamics of the ferromagnetic nanowire and the Maxwell's equations govern the propagation dynamics of electromagnetic wave passing through the axis of the nanowire. We perform a uniform expansion of magnetization and magnetic field along the direction of propagation of electromagnetic wave in the framework of reductive perturbation method. The excitation of magnetization of the nanowire is restricted to the normal plane at the lowest order of perturbation and goes out of plane for higher orders. The dynamics of the ferromagnetic nanowire is governed by the modified Korteweg-de Vries (mKdV) equation and the perturbed modified Korteweg-de Vries (pmKdV) equation for the lower and higher values of damping respectively. We invoke the Hirota bilinearization procedure to mKdV and pmKdV equation to construct the multi-soliton solutions, and explicitly analyze the nature of collision phenomena of the co-propagating EM solitons for the above mentioned lower and higher values of Gilbert-damping due to the precessional motion of the ferromagnetic spin. The EM solitons appearing in the higher damping regime exhibit elastic collision thus yielding the fascinating state restoration property, whereas those of lower damping regime exhibit inelastic collision yielding the solitons of suppressed intensity profiles. The propagation of EM soliton in the nanoscale magnetic wire has potential technological applications in optimizing the magnetic storage devices and magneto-electronics.

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.

Dynamics of an elastic sphere containing a thin creeping region and immersed in an acoustic region for similar viscous-elastic and acoustic time- and length-scales

NASA Astrophysics Data System (ADS)

Gat, Amir; Friedman, Yonathan

2017-11-01

The characteristic time of low-Reynolds number fluid-structure interaction scales linearly with the ratio of fluid viscosity to solid Young's modulus. For sufficiently large values of Young's modulus, both time- and length-scales of the viscous-elastic dynamics may be similar to acoustic time- and length-scales. However, the requirement of dominant viscous effects limits the validity of such regimes to micro-configurations. We here study the dynamics of an acoustic plane wave impinging on the surface of a layered sphere, immersed within an inviscid fluid, and composed of an inner elastic sphere, a creeping fluid layer and an external elastic shell. We focus on configurations with similar viscous-elastic and acoustic time- and length-scales, where the viscous-elastic speed of interaction between the creeping layer and the elastic regions is similar to the speed of sound. By expanding the linearized spherical Reynolds equation into the relevant spectral series solution for the hyperbolic elastic regions, a global stiffness matrix of the layered elastic sphere was obtained. This work relates viscous-elastic dynamics to acoustic scattering and may pave the way to the design of novel meta-materials with unique acoustic properties. ISF 818/13.

The velocity of the arterial pulse wave: a viscous-fluid shock wave in an elastic tube.

PubMed

Painter, Page R

2008-07-29

The arterial pulse is a viscous-fluid shock wave that is initiated by blood ejected from the heart. This wave travels away from the heart at a speed termed the pulse wave velocity (PWV). The PWV increases during the course of a number of diseases, and this increase is often attributed to arterial stiffness. As the pulse wave approaches a point in an artery, the pressure rises as does the pressure gradient. This pressure gradient increases the rate of blood flow ahead of the wave. The rate of blood flow ahead of the wave decreases with distance because the pressure gradient also decreases with distance ahead of the wave. Consequently, the amount of blood per unit length in a segment of an artery increases ahead of the wave, and this increase stretches the wall of the artery. As a result, the tension in the wall increases, and this results in an increase in the pressure of blood in the artery. An expression for the PWV is derived from an equation describing the flow-pressure coupling (FPC) for a pulse wave in an incompressible, viscous fluid in an elastic tube. The initial increase in force of the fluid in the tube is described by an increasing exponential function of time. The relationship between force gradient and fluid flow is approximated by an expression known to hold for a rigid tube. For large arteries, the PWV derived by this method agrees with the Korteweg-Moens equation for the PWV in a non-viscous fluid. For small arteries, the PWV is approximately proportional to the Korteweg-Moens velocity divided by the radius of the artery. The PWV in small arteries is also predicted to increase when the specific rate of increase in pressure as a function of time decreases. This rate decreases with increasing myocardial ischemia, suggesting an explanation for the observation that an increase in the PWV is a predictor of future myocardial infarction. The derivation of the equation for the PWV that has been used for more than fifty years is analyzed and shown to yield predictions that do not appear to be correct. Contrary to the theory used for more than fifty years to predict the PWV, it speeds up as arteries become smaller and smaller. Furthermore, an increase in the PWV in some cases may be due to decreasing force of myocardial contraction rather than arterial stiffness.

Simulating Seismic Wave Propagation in Viscoelastic Media with an Irregular Free Surface

NASA Astrophysics Data System (ADS)

Liu, Xiaobo; Chen, Jingyi; Zhao, Zhencong; Lan, Haiqiang; Liu, Fuping

2018-05-01

In seismic numerical simulations of wave propagation, it is very important for us to consider surface topography and attenuation, which both have large effects (e.g., wave diffractions, conversion, amplitude/phase change) on seismic imaging and inversion. An irregular free surface provides significant information for interpreting the characteristics of seismic wave propagation in areas with rugged or rapidly varying topography, and viscoelastic media are a better representation of the earth's properties than acoustic/elastic media. In this study, we develop an approach for seismic wavefield simulation in 2D viscoelastic isotropic media with an irregular free surface. Based on the boundary-conforming grid method, the 2D time-domain second-order viscoelastic isotropic equations and irregular free surface boundary conditions are transferred from a Cartesian coordinate system to a curvilinear coordinate system. Finite difference operators with second-order accuracy are applied to discretize the viscoelastic wave equations and the irregular free surface in the curvilinear coordinate system. In addition, we select the convolutional perfectly matched layer boundary condition in order to effectively suppress artificial reflections from the edges of the model. The snapshot and seismogram results from numerical tests show that our algorithm successfully simulates seismic wavefields (e.g., P-wave, Rayleigh wave and converted waves) in viscoelastic isotropic media with an irregular free surface.

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.

Unveiling Extreme Anisotropy in Elastic Structured Media

NASA Astrophysics Data System (ADS)

Lefebvre, G.; Antonakakis, T.; Achaoui, Y.; Craster, R. V.; Guenneau, S.; Sebbah, P.

2017-06-01

Periodic structures can be engineered to exhibit unique properties observed at symmetry points, such as zero group velocity, Dirac cones, and saddle points; identifying these and the nature of the associated modes from a direct reading of the dispersion surfaces is not straightforward, especially in three dimensions or at high frequencies when several dispersion surfaces fold back in the Brillouin zone. A recently proposed asymptotic high-frequency homogenization theory is applied to a challenging time-domain experiment with elastic waves in a pinned metallic plate. The prediction of a narrow high-frequency spectral region where the effective medium tensor dramatically switches from positive definite to indefinite is confirmed experimentally; a small frequency shift of the pulse carrier results in two distinct types of highly anisotropic modes. The underlying effective equation mirrors this behavior with a change in form from elliptic to hyperbolic exemplifying the high degree of wave control available and the importance of a simple and effective predictive model.

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

Non-periodic homogenization of 3-D elastic media for the seismic wave equation

NASA Astrophysics Data System (ADS)

Cupillard, Paul; Capdeville, Yann

2018-05-01

Because seismic waves have a limited frequency spectrum, the velocity structure of the Earth that can be extracted from seismic records has a limited resolution. As a consequence, one obtains smooth images from waveform inversion, although the Earth holds discontinuities and small scales of various natures. Within the last decade, the non-periodic homogenization method shed light on how seismic waves interact with small geological heterogeneities and `see' upscaled properties. This theory enables us to compute long-wave equivalent density and elastic coefficients of any media, with no constraint on the size, the shape and the contrast of the heterogeneities. In particular, the homogenization leads to the apparent, structure-induced anisotropy. In this paper, we implement this method in 3-D and show 3-D tests for the very first time. The non-periodic homogenization relies on an asymptotic expansion of the displacement and the stress involved in the elastic wave equation. Limiting ourselves to the order 0, we show that the practical computation of an upscaled elastic tensor basically requires (i) to solve an elastostatic problem and (ii) to low-pass filter the strain and the stress associated with the obtained solution. The elastostatic problem consists in finding the displacements due to local unit strains acting in all directions within the medium to upscale. This is solved using a parallel, highly optimized finite-element code. As for the filtering, we rely on the finite-element quadrature to perform the convolution in the space domain. We end up with an efficient numerical tool that we apply on various 3-D models to test the accuracy and the benefit of the homogenization. In the case of a finely layered model, our method agrees with results derived from Backus. In a more challenging model composed by a million of small cubes, waveforms computed in the homogenized medium fit reference waveforms very well. Both direct phases and complex diffracted waves are accurately retrieved in the upscaled model, although it is smooth. Finally, our upscaling method is applied to a realistic geological model. The obtained homogenized medium holds structure-induced anisotropy. Moreover, full seismic wavefields in this medium can be simulated with a coarse mesh (no matter what the numerical solver is), which significantly reduces computation costs usually associated with discontinuities and small heterogeneities. These three tests show that the non-periodic homogenization is both accurate and tractable in large 3-D cases, which opens the path to the correct account of the effect of small-scale features on seismic wave propagation for various applications and to a deeper understanding of the apparent anisotropy.

Working towards a numerical solver for seismic wave propagation in unsaturated porous media

NASA Astrophysics Data System (ADS)

Boxberg, Marc S.; Friederich, Wolfgang

2017-04-01

Modeling the propagation of seismic waves in porous media gets more and more popular in the seismological community. However, it is still a challenging task in the field of computational seismology. Nevertheless, it is important to account for the fluid content of, e.g., reservoir rocks or soils, and the interaction between the fluid and the rock or between different immiscible fluids to accurately describe seismic wave propagation through such porous media. Often, numerical models are based on the elastic wave equation and some might include artificially introduced attenuation. This simplifies the computation, because it only approximates the physics behind that problem. However, the results are also simplified and could miss phenomena and lack accuracy in some applications. We present a numerical solver for wave propagation in porous media saturated by two immiscible fluids. It is based on Biot's theory of poroelasticity and accounts for macroscopic flow that occurs on the same scale as the wavelength of the seismic waves. Fluid flow is described by a Darcy type flow law and interactions between the fluids by means of capillary pressure curve models. In addition, consistent boundary conditions on interfaces between poroelastic media and elastic or acoustic media are derived from this poroelastic theory itself. The poroelastic solver is integrated into the larger software package NEXD that uses the nodal discontinuous Galerkin method to solve wave equations in 1D, 2D, and 3D on a mesh of linear (1D), triangular (2D), or tetrahedral (3D) elements. Triangular and tetrahedral elements have great advantages as soon as the model has a complex structure, like it is often the case for geologic models. We illustrate the capabilities of the codes by numerical examples. This work can be applied to various scientific questions in, e.g., exploration and monitoring of hydrocarbon or geothermal reservoirs as well as CO2 storage sites.

The exact solution of a four-body Coulomb problem

NASA Astrophysics Data System (ADS)

Ray, Hasi

2018-03-01

The elastic collision between two H-like atoms utilizing an ab initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly, is studied thoroughly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. The new SEM code [Ray, Pramana 83, 907 (2014)] in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude using partial wave analysis, is utilized to study the s-, p-, d-wave elastic phase shifts and the corresponding partial cross sections. An augmented-Born approximation is used to include the contribution of higher partial waves more accurately to determine the total/integrated elastic cross sections. The effective range theory is used to determine the scattering lengths and effective ranges in the s-wave elastic scattering. The systems studied are Ps-Ps, Ps-Mu, Ps-H, Ps-D, Ps-T, Mu-Mu, Mu-H, Mu-D, Mu-T, H-H, H-D, H-T, D-D, D-T, T-T. The SEM includes the non-adiabatic short-range effects due to exchange. The MSEM code [Ray, Pramana 83, 907 (2014)] is used to study the effect of the long-range van der Waals interaction due to induced dipole polarizabilities of the atoms in H(1s)-H(1s) elastic collision. The dependence of scattering length on the reduced mass of the system and the dependence of scattering length on the strength of long-range van der Waals interaction that varies with the minimum interatomic distance are observed. 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 wave velocities of iron-bearing Ringwoodite (Mg0.8Fe0.2)2SiO2 to 12GPa at room temperature

NASA Astrophysics Data System (ADS)

Higo, Y.; Li, B.; Inoue, T.; Irifune, T.; Libermann, R. C.

2002-12-01

At present, it is widely accepted that olivine is the most important mineral in the Earth's upper mantle. The elastic property changes associated with the phase transformations to its high-pressure polymorphs are very important parameters to constrain the composition of the mantle transition zone. In this study, we measured the elastic wave velocity of iron-bearing Ringwoodite (Mg0.8Fe0.2)2SiO4. The specimen was hot-pressed at 18GPa and 1273K in a 2000-ton Uniaxial Split Sphere Apparatus (ORANGE-2000: GRC at ehime university). The recovered polycrystalline specimen was characterized by x-ray diffraction, EPMA, ultrasonic techniques, and the density was determined by Archimedes' method, and found to be single-phase and fine-grained. Bench top measurements of the compressional and shear wave velocities yielded Vp=9.10 km/s and Vs=5.52 km/s. High-pressure ultrasonic measurement was carried out in a 1000-ton Uniaxial Split-Cylinder Apparatus (USCA-1000: SUNY) at pressures up to 12GPa at room temperature using ZnTe as internal pressure marker. The sample was surrounded by lead to minimize the deviatoric stress. Also in this experiment, the travel times of the Al2O3 buffer rod were used for pressure calculation. The travel times of the buffer rod under the same cell geometry have been calibrated as a function of sample pressure by the thermal equation of state of NaCl using in-situ X-ray diffraction techniques. The results of our high-pressure experiment, including the elastic moduli and their pressure dependence, effect of iron on the elastic moduli, as well as their implication for the mantle transition zone, will be presented.

Elastic Properties of 3D-Printed Rock Models: Dry and Saturated Cracks

NASA Astrophysics Data System (ADS)

Huang, L.; Stewart, R.; Dyaur, N.

2014-12-01

Many regions of subsurface interest are, or will be, fractured. In addition, these zones many be subject to varying saturations and stresses. New 3D printing techniques using different materials and structures, provide opportunities to understand porous or fractured materials and fluid effects on their elastic properties. We use a 3D printer (Stratasys Dimension SST 768) to print two rock models: a solid octahedral prism and a porous cube with thousands of penny-shaped cracks. The printing material is ABS thermal plastic with a density of 1.04 g/cm3. After printing, we measure the elastic properties of the models, both dry and 100% saturated with water. Both models exhibit VTI (Vertical Transverse Isotropic) symmetry due to laying (about 0.25 mm thick) of the printing process. The prism has a density of 0.96 g/cm3 before saturation and 1.00 g/cm3 after saturation. Its effective porosity is calculated to be 4 %. We use ultrasonic transducers (500 kHz) to measure both P- and shear-wave velocities, and the raw material has a P-wave velocity of 1.89 km/s and a shear-wave velocity of 0.91 km/s. P-wave velocity in the un-saturated prism increases from 1.81 km/s to 1.84 km/s after saturation in the direction parallel to layering and from 1.73 km/s to 1.81 km/s in the direction perpendicular to layering. The fast shear-wave velocity decreases from 0.88 km/s to 0.87 km/s and the slow shear-wave velocity decreases from 0.82 km/s to 0.81 km/s. The cube, printed with penny-shaped cracks, gives a density of 0.79 g/cm3 and a porosity of 24 %. We measure its P-wave velocity as 1.78 km/s and 1.68 km/s in the direction parallel and perpendicular to the layering, respectively. Its fast shear-wave velocity is 0.88 km/s and slow shear-wave velocity is 0.70 km/s. The penny-shaped cracks have significant influence on the elastic properties of the 3D-printed rock models. To better understand and explain the fluid effects on the elastic properties of the models, we apply the extended anisotropic Gassmann's equations to predict the effects of saturation changes. We find that the predictions match observations from the experimental data within 1 % difference.

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

Golak, J.; Skibinski, R.; Topolnicki, K.

Here, we solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on A y puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported.

Genetic Algorithm Optimization of Phononic Bandgap Structures

DTIC Science & Technology

2006-09-01

a GA with a computational finite element method for solving the acoustic wave equation, and find optimal designs for both metal-matrix composite...systems consisting of Ti/SiC, and H2O-filled porous ceramic media, by maximizing the relative acoustic bandgap for these media. The term acoustic here...stress minimization, global optimization, phonon bandgap, genetic algorithm, periodic elastic media, inhomogeneity, inclusion, porous media, acoustic

Active tuning of vibration and wave propagation in elastic beams with periodically placed piezoelectric actuator/sensor pairs

NASA Astrophysics Data System (ADS)

Li, Fengming; Zhang, Chuanzeng; Liu, Chunchuan

2017-04-01

A novel strategy is proposed to actively tune the vibration and wave propagation properties in elastic beams. By periodically placing the piezoelectric actuator/sensor pairs along the beam axis, an active periodic beam structure which exhibits special vibration and wave propagation properties such as the frequency pass-bands and stop-bands (or band-gaps) is developed. Hamilton's principle is applied to establish the equations of motion of the sub-beam elements i.e. the unit-cells, bonded by the piezoelectric patches. A negative proportional feedback control strategy is employed to design the controllers which can provide a positive active stiffness to the beam for a positive feedback control gain, which can increase the stability of the structural system. By means of the added positive active stiffness, the periodicity or the band-gap property of the beam with periodically placed piezoelectric patches can be actively tuned. From the investigation, it is shown that better band-gap characteristics can be achieved by using the negative proportional feedback control. The band-gaps can be obviously broadened by properly increasing the control gain, and they can also be greatly enlarged by appropriately designing the structural sizes of the controllers. The control voltages applied on the piezoelectric actuators are in reasonable and controllable ranges, especially, they are very low in the band-gaps. Thus, the vibration and wave propagation behaviors of the elastic beam can be actively controlled by the periodically placed piezoelectric patches.

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.

Negative refraction of elastic waves at the deep-subwavelength scale in a single-phase metamaterial.

PubMed

Zhu, R; Liu, X N; Hu, G K; Sun, C T; Huang, G L

2014-11-24

Negative refraction of elastic waves has been studied and experimentally demonstrated in three- and two-dimensional phononic crystals, but Bragg scattering is impractical for low-frequency wave control because of the need to scale the structures to manageable sizes. Here we present an elastic metamaterial with chiral microstructure made of a single-phase solid material that aims to achieve subwavelength negative refraction of elastic waves. Both negative effective mass density and modulus are observed owing to simultaneous translational and rotational resonances. We experimentally demonstrate negative refraction of the longitudinal elastic wave at the deep-subwavelength scale in the metamaterial fabricated in a stainless steel plate. The experimental measurements are in good agreement with numerical simulations. Moreover, wave mode conversion related with negative refraction is revealed and discussed. The proposed elastic metamaterial may thus be used as a flat lens for elastic wave focusing.

Generalized radially self-accelerating helicon beams.

PubMed

Vetter, Christian; Eichelkraut, Toni; Ornigotti, Marco; Szameit, Alexander

2014-10-31

We report, in theory and experiment, on a new class of optical beams that are radially self-accelerating and nondiffracting. These beams continuously evolve on spiraling trajectories while maintaining their amplitude and phase distribution in their rotating rest frame. We provide a detailed insight into the theoretical origin and characteristics of radial self-acceleration and prove our findings experimentally. As radially self-accelerating beams are nonparaxial and a solution to the full scalar Helmholtz equation, they can be implemented in many linear wave systems beyond optics, from acoustic and elastic waves to surface waves in fluids and soft matter. Our work generalized the study of classical helicon beams to a complete set of solutions for rotating complex fields.

Ultrafast dynamic response of single-crystal β-HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine)

NASA Astrophysics Data System (ADS)

Zaug, Joseph M.; Austin, Ryan A.; Armstrong, Michael R.; Crowhurst, Jonathan C.; Goldman, Nir; Ferranti, Louis; Saw, Cheng K.; Swan, Raymond A.; Gross, Richard; Fried, Laurence E.

2018-05-01

We report experimental and computational studies of shock wave dynamics in single-crystal β-HMX on an ultrafast time scale. Here, a laser-based compression drive (˜1 ns in duration; stresses of up to ˜40 GPa) is used to propagate shock waves normal to the (110) and (010) lattice planes. Ultrafast time-domain interferometry measurements reveal distinct, time-dependent relationships between the shock wave velocity and particle velocity for each crystal orientation, which suggest evolving physical processes on a sub-nanosecond time scale. To help interpret the experimental data, elastic shock wave response was simulated using a finite-strain model of crystal thermoelasticity. At early propagation times (<500 ps), the model is in agreement with the data, which indicates that the mechanical response is dominated by thermoelastic deformation. The model agreement depends on the inclusion of nonlinear elastic effects in both the spherical and deviatoric stress-strain responses. This is achieved by employing an equation-of-state and a pressure-dependent stiffness tensor, which was computed via atomistic simulation. At later times (>500 ps), the crystal samples exhibit signatures of inelastic deformation, structural phase transformation, or chemical reaction, depending on the direction of wave propagation.

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

Bayesian linearized amplitude-versus-frequency inversion for quality factor and its application

NASA Astrophysics Data System (ADS)

Yang, Xinchao; Teng, Long; Li, Jingnan; Cheng, Jiubing

2018-06-01

We propose a straightforward attenuation inversion method by utilizing the amplitude-versus-frequency (AVF) characteristics of seismic data. A new linearized approximation equation of the angle and frequency dependent reflectivity in viscoelastic media is derived. We then use the presented equation to implement the Bayesian linear AVF inversion. The inversion result includes not only P-wave and S-wave velocities, and densities, but also P-wave and S-wave quality factors. Synthetic tests show that the AVF inversion surpasses the AVA inversion for quality factor estimation. However, a higher signal noise ratio (SNR) of data is necessary for the AVF inversion. To show its feasibility, we apply both the new Bayesian AVF inversion and conventional AVA inversion to a tight gas reservoir data in Sichuan Basin in China. Considering the SNR of the field data, a combination of AVF inversion for attenuation parameters and AVA inversion for elastic parameters is recommended. The result reveals that attenuation estimations could serve as a useful complement in combination with the AVA inversion results for the detection of tight gas reservoirs.

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.

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.

Frequency-domain elastic full waveform inversion using encoded simultaneous sources

NASA Astrophysics Data System (ADS)

Jeong, W.; Son, W.; Pyun, S.; Min, D.

2011-12-01

Currently, numerous studies have endeavored to develop robust full waveform inversion and migration algorithms. These processes require enormous computational costs, because of the number of sources in the survey. To avoid this problem, the phase encoding technique for prestack migration was proposed by Romero (2000) and Krebs et al. (2009) proposed the encoded simultaneous-source inversion technique in the time domain. On the other hand, Ben-Hadj-Ali et al. (2011) demonstrated the robustness of the frequency-domain full waveform inversion with simultaneous sources for noisy data changing the source assembling. Although several studies on simultaneous-source inversion tried to estimate P- wave velocity based on the acoustic wave equation, seismic migration and waveform inversion based on the elastic wave equations are required to obtain more reliable subsurface information. In this study, we propose a 2-D frequency-domain elastic full waveform inversion technique using phase encoding methods. In our algorithm, the random phase encoding method is employed to calculate the gradients of the elastic parameters, source signature estimation and the diagonal entries of approximate Hessian matrix. The crosstalk for the estimated source signature and the diagonal entries of approximate Hessian matrix are suppressed with iteration as for the gradients. Our 2-D frequency-domain elastic waveform inversion algorithm is composed using the back-propagation technique and the conjugate-gradient method. Source signature is estimated using the full Newton method. We compare the simultaneous-source inversion with the conventional waveform inversion for synthetic data sets of the Marmousi-2 model. The inverted results obtained by simultaneous sources are comparable to those obtained by individual sources, and source signature is successfully estimated in simultaneous source technique. Comparing the inverted results using the pseudo Hessian matrix with previous inversion results provided by the approximate Hessian matrix, it is noted that the latter are better than the former for deeper parts of the model. This work was financially supported by the Brain Korea 21 project of Energy System Engineering, by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0006155), by the Energy Efficiency & Resources of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No. 2010T100200133).

Fundamental structure of steady plastic shock waves in metals

NASA Astrophysics Data System (ADS)

Molinari, A.; Ravichandran, G.

2004-02-01

The propagation of steady plane shock waves in metallic materials is considered. Following the constitutive framework adopted by R. J. Clifton [Shock Waves and the Mechanical Properties of Solids, edited by J. J. Burke and V. Weiss (Syracuse University Press, Syracuse, N.Y., 1971), p. 73] for analyzing elastic-plastic transient waves, an analytical solution of the steady state propagation of plastic shocks is proposed. The problem is formulated in a Lagrangian setting appropriate for large deformations. The material response is characterized by a quasistatic tensile (compression) test (providing the isothermal strain hardening law). In addition the elastic response is determined up to second order elastic constants by ultrasonic measurements. Based on this simple information, it is shown that the shock kinetics can be quite well described for moderate shocks in aluminum with stress amplitude up to 10 GPa. Under the later assumption, the elastic response is assumed to be isentropic, and thermomechanical coupling is neglected. The model material considered here is aluminum, but the analysis is general and can be applied to any viscoplastic material subjected to moderate amplitude shocks. Comparisons with experimental data are made for the shock velocity, the particle velocity and the shock structure. The shock structure is obtained by quadrature of a first order differential equation, which provides analytical results under certain simplifying assumptions. The effects of material parameters and loading conditions on the shock kinetics and shock structure are discussed. The shock width is characterized by assuming an overstress formulation for the viscoplastic response. The effects on the shock structure of strain rate sensitivity are analyzed and the rationale for the J. W. Swegle and D. E. Grady [J. Appl. Phys. 58, 692 (1985)] universal scaling law for homogeneous materials is explored. Finally, the ability to deduce information on the viscoplastic response of materials subjected to very high strain rates from shock wave experiments is discussed.

Elastodynamic cloaking and field enhancement for soft spheres

NASA Astrophysics Data System (ADS)

Diatta, Andre; Guenneau, Sebastien

2016-11-01

We propose a spherical cloak described by a non-singular asymmetric elasticity tensor {C} depending upon a small parameter η, that defines the softness of a region one would like to conceal from elastodynamic waves. By varying η, we generate a class of soft spheres dressed by elastodynamic cloaks, which are shown to considerably reduce the scattering of the soft spheres. Importantly, such cloaks also provide some wave protection except for a countable set of frequencies, for which some large elastic field enhancement can be observed within the soft spheres. Through an investigation of trapped modes in elasticity, we supply a good approximation of such Mie-type resonances by some transcendental equation. Our results, unlike previous studies that focused merely on the invisibility aspects, shed light on potential pitfalls of elastodynamic cloaks for earthquake protection designed via geometric transforms: a seismic cloak needs to be designed in such a way that its inner resonances differ from eigenfrequencies of the building one wishes to protect. In order to circumvent this downfall of field enhancement inside the cloaked area, we introduce a novel generation of cloaks, named here, mixed cloaks. Such mixed cloaks consist of a shell that detours incoming waves, hence creating an invisibility region, and of a perfectly matched layer (PML, located at the inner boundary of the cloaks) that absorbs residual wave energy in such a way that aforementioned resonances in the soft sphere are strongly attenuated. The designs of mixed cloaks with a non-singular elasticity tensor combined with an inner PML and non-vanishing density bring seismic cloaks one step closer to a practical implementation. Note in passing that the concept of mixed cloaks also applies in the case of singular cloaks and can be translated in other wave areas for a similar purpose (i.e. to smear down inner resonances within the invisibility region).

Nonlinear Acoustic Propagation into the Seafloor

NASA Astrophysics Data System (ADS)

McDonald, B. Edward

2006-05-01

Explosions near the seafloor result in shock waves entering a much more complicated medium than water or air. Nonlinearities may be increased by two processes inherent to granular media: (1) a poroelastic nonlinearity comparable to the addition of bubbles to water, and (2) the Hertz force resulting from elastic deformation of grains, proportional to the Youngs modulus of the grains times the strain rate to the power 3/2. These two types of nonlinearity for shock propagation into the seafloor are investigated using a variant of the NPE model. The traditional Taylor series expansion of the equation of state (pressure as a function of density) is not appropriate to the Hertz force in the limit of small strain. We present a simple nonlinear wave equation model for compressional waves in marine sediments that retains the Hertz force explicitly with overdensity to the power 3/2. Numerical results for shock propagation are compared with similarity solutions for quadratic nonlinearity and for the fractional nonlinearity of the Hertz force.

Second-harmonic generation in shear wave beams with different polarizations

NASA Astrophysics Data System (ADS)

Spratt, Kyle S.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2015-10-01

A coupled pair of nonlinear parabolic equations was derived by Zabolotskaya [1] that model the transverse components of the particle motion in a collimated shear wave beam propagating in an isotropic elastic solid. Like the KZK equation, the parabolic equation for shear wave beams accounts consistently for the leading order effects of diffraction, viscosity and nonlinearity. The nonlinearity includes a cubic nonlinear term that is equivalent to that present in plane shear waves, as well as a quadratic nonlinear term that is unique to diffracting beams. The work by Wochner et al. [2] considered shear wave beams with translational polarizations (linear, circular and elliptical), wherein second-order nonlinear effects vanish and the leading order nonlinear effect is third-harmonic generation by the cubic nonlinearity. The purpose of the current work is to investigate the quadratic nonlinear term present in the parabolic equation for shear wave beams by considering second-harmonic generation in Gaussian beams as a second-order nonlinear effect using standard perturbation theory. In order for second-order nonlinear effects to be present, a broader class of source polarizations must be considered that includes not only the familiar translational polarizations, but also polarizations accounting for stretching, shearing and rotation of the source plane. It is found that the polarization of the second harmonic generated by the quadratic nonlinearity is not necessarily the same as the polarization of the source-frequency beam, and we are able to derive a general analytic solution for second-harmonic generation from a Gaussian source condition that gives explicitly the relationship between the polarization of the source-frequency beam and the polarization of the second harmonic.

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

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.

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.

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.

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

Silin, D.; Goloshubin, G.

Analysis of compression wave propagation in a poroelastic medium predicts a peak of reflection from a high-permeability layer in the low-frequency end of the spectrum. An explicit formula expresses the resonant frequency through the elastic moduli of the solid skeleton, the permeability of the reservoir rock, the fluid viscosity and compressibility, and the reservoir thickness. This result is obtained through a low-frequency asymptotic analysis of Biot's model of poroelasticity. A review of the derivation of the main equations from the Hooke's law, momentum and mass balance equations, and Darcy's law suggests an alternative new physical interpretation of some coefficients ofmore » the classical poroelasticity. The velocity of wave propagation, the attenuation factor, and the wave number, are expressed in the form of power series with respect to a small dimensionless parameter. The absolute value of this parameter is equal to the product of the kinematic reservoir fluid mobility and the wave frequency. Retaining only the leading terms of the series leads to explicit and relatively simple expressions for the reflection and transmission coefficients for a planar wave crossing an interface between two permeable media, as well as wave reflection from a thin highly-permeable layer (a lens). Practical applications of the obtained asymptotic formulae are seismic modeling, inversion, and at-tribute analysis.« less

Green's function and Bloch theory for the analysis of the dynamic response of a periodically supported beam to a moving load

NASA Astrophysics Data System (ADS)

Lassoued, R.; Lecheheb, M.; Bonnet, G.

2012-08-01

This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.

Wave propagation in a strongly heterogeneous elastic porous medium: Homogenization of Biot medium with double porosities

NASA Astrophysics Data System (ADS)

Rohan, Eduard; Naili, Salah; Nguyen, Vu-Hieu

2016-08-01

We study wave propagation in an elastic porous medium saturated with a compressible Newtonian fluid. The porous network is interconnected whereby the pores are characterized by two very different characteristic sizes. At the mesoscopic scale, the medium is described using the Biot model, characterized by a high contrast in the hydraulic permeability and anisotropic elasticity, whereas the contrast in the Biot coupling coefficient is only moderate. Fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. The homogenization method based on the asymptotic analysis is used to obtain a macroscopic model. To respect the high contrast in the material properties, they are scaled by the small parameter, which is involved in the asymptotic analysis and characterized by the size of the heterogeneities. Using the estimates of wavelengths in the double-porosity networks, it is shown that the macroscopic descriptions depend on the contrast in the static permeability associated with pores and micropores and on the frequency. Moreover, the microflow in the double porosity is responsible for fading memory effects via the macroscopic poroviscoelastic constitutive law. xml:lang="fr"

Amplitude various angles (AVA) phenomena in thin layer reservoir: Case study of various reservoirs

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

Nurhandoko, Bagus Endar B., E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com; Rock Fluid Imaging Lab., Bandung; Susilowati, E-mail: bagusnur@bdg.centrin.net.id, E-mail: bagusnur@rock-fluid.com

2015-04-16

Amplitude various offset is widely used in petroleum exploration as well as in petroleum development field. Generally, phenomenon of amplitude in various angles assumes reservoir’s layer is quite thick. It also means that the wave is assumed as a very high frequency. But, in natural condition, the seismic wave is band limited and has quite low frequency. Therefore, topic about amplitude various angles in thin layer reservoir as well as low frequency assumption is important to be considered. Thin layer reservoir means the thickness of reservoir is about or less than quarter of wavelength. In this paper, I studied aboutmore » the reflection phenomena in elastic wave which considering interference from thin layer reservoir and transmission wave. I applied Zoeppritz equation for modeling reflected wave of top reservoir, reflected wave of bottom reservoir, and also transmission elastic wave of reservoir. Results show that the phenomena of AVA in thin layer reservoir are frequency dependent. Thin layer reservoir causes interference between reflected wave of top reservoir and reflected wave of bottom reservoir. These phenomena are frequently neglected, however, in real practices. Even though, the impact of inattention in interference phenomena caused by thin layer in AVA may cause inaccurate reservoir characterization. The relation between classes of AVA reservoir and reservoir’s character are different when effect of ones in thin reservoir and ones in thick reservoir are compared. In this paper, I present some AVA phenomena including its cross plot in various thin reservoir types based on some rock physics data of Indonesia.« less

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.

Low-energy neutron-deuteron reactions with N 3LO chiral forces

DOE PAGES

Golak, J.; Skibinski, R.; Topolnicki, K.; ...

2014-11-27

Here, we solve three-nucleon Faddeev equations with nucleon-nucleon and three-nucleon forces derived consistently in the framework of chiral perturbation theory at next-to-next-to-next-to-leading order in the chiral expansion. In this first investigation we include only matrix elements of the three-nucleon force for partial waves with the total two-nucleon (three-nucleon) angular momenta up to 3 (5/2). Low-energy neutron-deuteron elastic scattering and deuteron breakup reaction are studied. Emphasis is put on A y puzzle in elastic scattering and cross sections in symmetric-space-star and neutron-neutron quasi-free-scattering breakup configurations, for which large discrepancies between data and theory have been reported.

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections. Part 1; Electron-Hydrogen Elastic Scattering

NASA Technical Reports Server (NTRS)

Bhatia, A. K.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2001-01-01

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

3-D FDTD simulation of shear waves for evaluation of complex modulus imaging.

PubMed

Orescanin, Marko; Wang, Yue; Insana, Michael

2011-02-01

The Navier equation describing shear wave propagation in 3-D viscoelastic media is solved numerically with a finite differences time domain (FDTD) method. Solutions are formed in terms of transverse scatterer velocity waves and then verified via comparison to measured wave fields in heterogeneous hydrogel phantoms. The numerical algorithm is used as a tool to study the effects on complex shear modulus estimation from wave propagation in heterogeneous viscoelastic media. We used an algebraic Helmholtz inversion (AHI) technique to solve for the complex shear modulus from simulated and experimental velocity data acquired in 2-D and 3-D. Although 3-D velocity estimates are required in general, there are object geometries for which 2-D inversions provide accurate estimations of the material properties. Through simulations and experiments, we explored artifacts generated in elastic and dynamic-viscous shear modulus images related to the shear wavelength and average viscosity.

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.

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

Ab Initio Study of the Electronic Structure, Elastic Properties, Magnetic Feature and Thermodynamic Properties of the Ba2NiMoO6 Material

NASA Astrophysics Data System (ADS)

Deluque Toro, C. E.; Mosquera Polo, A. S.; Gil Rebaza, A. V.; Landínez Téllez, D. A.; Roa-Rojas, J.

2018-04-01

We report first-principles calculations of the elastic properties, electronic structure and magnetic behavior performed over the Ba2NiMoO6 double perovskite. Calculations are carried out through the full-potential linear augmented plane-wave method within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient and Local Density Approximations, including spin polarization. The elastic properties calculated are bulk modulus (B), the elastic constants (C 11, C 12 and C 44), the Zener anisotropy factor (A), the isotropic shear modulus (G), the Young modulus (Y) and the Poisson ratio (υ). Structural parameters, total energies and cohesive properties of the perovskite are studied by means of minimization of internal parameters with the Murnaghan equation, where the structural parameters are in good agreement with experimental data. Furthermore, we have explored different antiferromagnetic configurations in order to describe the magnetic ground state of this compound. The pressure and temperature dependence of specific heat, thermal expansion coefficient, Debye temperature and Grüneisen parameter were calculated by DFT from the state equation using the quasi-harmonic model of Debye. A specific heat behavior C V ≈ C P was found at temperatures below T = 400 K, with Dulong-Petit limit values, which is higher than those, reported for simple perovskites.

Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential.

PubMed

Li, Min; Xu, Tao

2015-03-01

Via the Nth Darboux transformation, a chain of nonsingular localized-wave solutions is derived for a nonlocal nonlinear Schrödinger equation with the self-induced parity-time (PT) -symmetric potential. It is found that the Nth iterated solution in general exhibits a variety of elastic interactions among 2N solitons on a continuous-wave background and each interacting soliton could be the dark or antidark type. The interactions with an arbitrary odd number of solitons can also be obtained under different degenerate conditions. With N=1 and 2, the two-soliton and four-soliton interactions and their various degenerate cases are discussed in the asymptotic analysis. Numerical simulations are performed to support the analytical results, and the stability analysis indicates that the PT-symmetry breaking can also destroy the stability of the soliton interactions.

Revisit of the relationship between the elastic properties and sound velocities at high pressures

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

Wang, Chenju; Yan, Xiaozhen; Institute of Atomic and Molecular Sciences, Sichuan University, Chengdu 610065

2014-09-14

The second-order elastic constants and stress-strain coefficients are defined, respectively, as the second derivatives of the total energy and the first derivative of the stress with respect to strain. Since the Lagrangian and infinitesimal strain are commonly used in the two definitions above, the second-order elastic constants and stress-strain coefficients are separated into two categories, respectively. In general, any of the four physical quantities is employed to characterize the elastic properties of materials without differentiation. Nevertheless, differences may exist among them at non-zero pressures, especially high pressures. Having explored the confusing issue systemically in the present work, we find thatmore » the four quantities are indeed different from each other at high pressures and these differences depend on the initial stress applied on materials. Moreover, the various relations between the four quantities depicting elastic properties of materials and high-pressure sound velocities are also derived from the elastic wave equations. As examples, we calculated the high-pressure sound velocities of cubic tantalum and hexagonal rhenium using these nexus. The excellent agreement of our results with available experimental data suggests the general applicability of the relations.« less

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 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.

Density reconstruction in multiparameter elastic full-waveform inversion

NASA Astrophysics Data System (ADS)

Sun, Min'ao; Yang, Jizhong; Dong, Liangguo; Liu, Yuzhu; Huang, Chao

2017-12-01

Elastic full-waveform inversion (EFWI) is a quantitative data fitting procedure that recovers multiple subsurface parameters from multicomponent seismic data. As density is involved in addition to P- and S-wave velocities, the multiparameter EFWI suffers from more serious tradeoffs. In addition, compared with P- and S-wave velocities, the misfit function is less sensitive to density perturbation. Thus, a robust density reconstruction remains a difficult problem in multiparameter EFWI. In this paper, we develop an improved scattering-integral-based truncated Gauss-Newton method to simultaneously recover P- and S-wave velocities and density in EFWI. In this method, the inverse Gauss-Newton Hessian has been estimated by iteratively solving the Gauss-Newton equation with a matrix-free conjugate gradient algorithm. Therefore, it is able to properly handle the parameter tradeoffs. To give a detailed illustration of the tradeoffs between P- and S-wave velocities and density in EFWI, wavefield-separated sensitivity kernels and the Gauss-Newton Hessian are numerically computed, and their distribution characteristics are analyzed. Numerical experiments on a canonical inclusion model and a modified SEG/EAGE Overthrust model have demonstrated that the proposed method can effectively mitigate the tradeoff effects, and improve multiparameter gradients. Thus, a high convergence rate and an accurate density reconstruction can be achieved.

Comparison of exact solution with Eikonal approximation for elastic heavy ion scattering

NASA Technical Reports Server (NTRS)

Dubey, Rajendra R.; Khandelwal, Govind S.; Cucinotta, Francis A.; Maung, Khin Maung

1995-01-01

A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.

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.

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.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-10-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

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.

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions: Preprint

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

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

Effect of Second-Order and Fully Nonlinear Wave Kinematics on a Tension-Leg-Platform Wind Turbine in Extreme Wave Conditions

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

Robertson, Amy N; Jonkman, Jason; Pegalajar-Jurado, Antonio

In this study, we assess the impact of different wave kinematics models on the dynamic response of a tension-leg-platform wind turbine. Aero-hydro-elastic simulations of the floating wind turbine are carried out employing linear, second-order, and fully nonlinear kinematics using the Morison equation for the hydrodynamic forcing. The wave kinematics are computed from either theoretical or measured signals of free-surface elevation. The numerical results from each model are compared to results from wave basin tests on a scaled prototype. The comparison shows that sub and superharmonic responses can be introduced by second-order and fully nonlinear wave kinematics. The response at themore » wave frequency range is better reproduced when kinematics are generated from the measured surface elevation. In the future, the numerical response may be further improved by replacing the global, constant damping coefficients in the model by a more detailed, customizable definition of the user-defined numerical damping.« less

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.

Root finding in the complex plane for seismo-acoustic propagation scenarios with Green's function solutions.

PubMed

McCollom, Brittany A; Collis, Jon M

2014-09-01

A normal mode solution to the ocean acoustic problem of the Pekeris waveguide with an elastic bottom using a Green's function formulation for a compressional wave point source is considered. Analytic solutions to these types of waveguide propagation problems are strongly dependent on the eigenvalues of the problem; these eigenvalues represent horizontal wavenumbers, corresponding to propagating modes of energy. The eigenvalues arise as singularities in the inverse Hankel transform integral and are specified by roots to a characteristic equation. These roots manifest themselves as poles in the inverse transform integral and can be both subtle and difficult to determine. Following methods previously developed [S. Ivansson et al., J. Sound Vib. 161 (1993)], a root finding routine has been implemented using the argument principle. Using the roots to the characteristic equation in the Green's function formulation, full-field solutions are calculated for scenarios where an acoustic source lies in either the water column or elastic half space. Solutions are benchmarked against laboratory data and existing numerical solutions.

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

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

Mechanics of composite materials: Recent advances; Proceedings of the Symposium, Virginia Polytechnic Institute and State University, Blacksburg, VA, August 16-19, 1982

NASA Technical Reports Server (NTRS)

Hashin, Z. (Editor); Herakovich, C. T. (Editor)

1983-01-01

The present conference on the mechanics of composites discusses microstructure's influence on particulate and short fiber composites' thermoelastic and transport properties, the elastoplastic deformation of composites, constitutive equations for viscoplastic composites, the plasticity and fatigue of metal matrix composites, laminate damping mechanisms, the micromechanical modeling of Kevlar/epoxy composites' time-dependent failure, the variational characterization of waves in composites, and computational methods for eigenvalue problems in composite design. Also discussed are the elastic response of laminates, elastic coupling nonlinear effects in unsymmetrical laminates, elasticity solutions for laminate problems having stress singularities, the mechanics of bimodular composite structures, the optimization of laminated plates and shells, NDE for laminates, the role of matrix cracking in the continuum constitutive behavior of a damaged composite ply, and the energy release rates of various microcracks in short fiber composites.

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.)

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.

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.

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.

Propagation of acoustic-gravity waves in arctic zones with elastic ice-sheets

NASA Astrophysics Data System (ADS)

Kadri, Usama; Abdolali, Ali; Kirby, James T.

2017-04-01

We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation, as postulated by Refs. [1, 3]. References [1] U. Kadri, 2016. Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones. Advances in Acoustics and Vibration, 2016, Article ID 8076108, 7 pages http://dx.doi.org/10.1155/2016/8076108 [2] A. Abdolali, J. T. Kirby and G. Bellotti, 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, J. Fluid Mech., 766, R1 doi:10.1017/jfm.2015.37 [3] U. Kadri, 2014. Deep ocean water transportation by acoustic?gravity waves. J. Geophys. Res. Oceans, 119, doi:10.1002/ 2014JC010234

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.

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.

Abnormal Elasticity of Single-Crystal Magnesiosiderite across the Spin Transition in Earth's Lower Mantle

NASA Astrophysics Data System (ADS)

Fu, S.; Yang, J.; Lin, J. F.

2016-12-01

Carbon can be transported into deep Earth's interior via subduction of carbonated oceanic crust, hosted as Mg-Fe bearing carbonates. The existence of stable carbonate can significantly affect our understanding on geochemical and geophysical properties of the planet. Early studies have shown that iron spin-pairing transition could occur in the iron-enriched carbonates, generally called magnesiosiderite, under lower mantle conditions. The pressure-induced spin state change is accompanied by a sudden volume collaps. However, the effects of the spin-pairing transition on single-crystal elasticity of magnesiosiderite under high pressure conditions are still unclear. Understanding the elasticity of single-crystal magnesiosiderite at relevant lower mantle conditions plays an important role in better understanding the seismic signatures in the carbon-enriched region, and to constrain carbon storage and recycling in the mantle. In order to solve all individual elastic constants (C11, C22, C33, C44, C55, C66, C12, C23, and C13) of magnesiosiderite at high pressures via Christoffel's equations, we employed Brillouin Light Scattering (BLS) to measure shear wave (Vs) and compressional wave velocities (Vp) as a function of the azimuthal angle under lower mantle pressures, accompanied by Impulsive Stimulate Light Scattering (ISS) to measure the Vp when pressures are too high to measure it by BLS. A general thermoelastic modelling was developed to fit the elastic softening within the spin transition. We will further discuss the effects of pressures, as well as iron spin states, on the single-crystal elasticity and seismic parameters (Vp and Vs anisotropy AVp, AVs, etc) at lower mantle conditions. These results could provide clues in explaining regional seismic heterogeneities in deep mantle.

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. .

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.

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

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Balsara, Dinshaw S., E-mail: dbalsara@nd.edu

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearlymore » degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.« less

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.

Elasticity of superhydrous phase, B, Mg10Si3O14(OH)4

NASA Astrophysics Data System (ADS)

Mookherjee, Mainak; Tsuchiya, Jun

2015-01-01

We have used first principles simulation based on density functional theory to calculate the equation of state and elasticity of superhydrous phase B, Mg10Si3O14(OH)4. The pressure-volume results for superhydrous phase B is well represented by a third order Birch-Murnaghan formulation, with K0 = 161.8 (±0.2) GPa and K0‧ = 4.4 (±0.01). The calculated full elastic tensor at 0 GPa is in good agreement with Brillouin scattering results, with the compressional elastic constants: c11 = 329.5 GPa, c22 = 294.9 GPa, c33 = 306.8 GPa, the shear elastic constants - c44 = 99.8 GPa, c55 = 98 GPa, and c66 = 99 GPa; the off-diagonal elastic constants c12 = 82.5 GPa, c13 = 84.6 GPa, and c23 = 98.7 GPa. At the depths corresponding to the mantle transition zone, the aggregate sound wave velocities for superhydrous phase B is slower compared to dry ringwoodite which is the dominant mineral phase. However, hydrous ringwoodite bulk sound velocities are comparable to that of superhydrous phase B. Majoritic garnet, the second most abundant mineral in the transition zone, has bulk sound wave velocities slower than superhydrous phase B. An assemblage consisting of hydrous ringwoodite, superhydrous phase B, and majorite garnet could account for the low velocities observed in certain subduction zone settings at depths corresponding to the base of the transition zone and upper mantle. Superhydrous phase B exhibits moderate single-crystal elastic anisotropy with AVP ∼ 3% and AVS ∼ 5% at the base of the transition zone. Single-crystal elastic anisotropy of other dense hydrous magnesium silicate phases phase such as hydrous phase D is significantly larger at these conditions and might play a major role in explaining the observed mid mantle seismic anisotropy.

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.

Experimental and first-principles studies on the elastic properties of α-hafnium metal under pressure

DOE PAGES

Qi, Xintong; Wang, Xuebing; Chen, Ting; ...

2016-03-30

Compressional and shear wave velocities of the α phase of hafnium have been measured up to 10.4 GPa at room temperature using ultrasonic interferometry in a multi-anvil apparatus. A finite strain equation of state analysis yielded K s0 = 110.4 (5) GPa, G 0 = 54.7(5) GPa,K s0' = 3.7 and G 0' = 0.6 for the elastic bulk and shear moduli and their pressure derivatives at ambient conditions. Complementary to the experimental data, the single crystal elastic constants, elastic anisotropy and the unit cell axial ratio c/a of α-hafnium at high pressures were investigated by Density Functional Theory (DFT)more » based first principles calculations. A c/a value of 1.605 is predicted for α-Hf at 40 GPa, which is in excellent agreement with previous experimental results. The low-pressure derivative of the shear modulus observed in our experimental data up to 10 GPa was found to originate from the elastic constant C44 which exhibits negligible pressure dependence within the current experimental pressure range. At higher pressures (>10 GPa), C 44 was predicted to soften and the shear wave velocity ν S trended to decrease with pressure, which can be interpreted as a precursor to the α-ω transition similar to that observed in other group IV elements (titanium and zirconium). Here, the acoustic velocities, bulk and shear moduli, and the acoustic Debye temperature (θ D = 240.1 K) determined from the current experiments were all compared well with those predicted by our theoretical DFT calculations.« less

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.

A simple method of predicting S-wave velocity

USGS Publications Warehouse

Lee, M.W.

2006-01-01

Prediction of shear-wave velocity plays an important role in seismic modeling, amplitude analysis with offset, and other exploration applications. This paper presents a method for predicting S-wave velocity from the P-wave velocity on the basis of the moduli of dry rock. Elastic velocities of water-saturated sediments at low frequencies can be predicted from the moduli of dry rock by using Gassmann's equation; hence, if the moduli of dry rock can be estimated from P-wave velocities, then S-wave velocities easily can be predicted from the moduli. Dry rock bulk modulus can be related to the shear modulus through a compaction constant. The numerical results indicate that the predicted S-wave velocities for consolidated and unconsolidated sediments agree well with measured velocities if differential pressure is greater than approximately 5 MPa. An advantage of this method is that there are no adjustable parameters to be chosen, such as the pore-aspect ratios required in some other methods. The predicted S-wave velocity depends only on the measured P-wave velocity and porosity. ?? 2006 Society of Exploration Geophysicists.

Acoustic plane waves incident on an oblique clamped panel in a rectangular duct

NASA Technical Reports Server (NTRS)

Unz, H.; Roskam, J.

1980-01-01

The theory of acoustic plane waves incident on an oblique clamped panel in a rectangular duct was developed from basic theoretical concepts. The coupling theory between the elastic vibrations of the panel (plate) and the oblique incident acoustic plane wave in infinite space was considered in detail, and was used for the oblique clamped panel in the rectangular duct. The partial differential equation which governs the vibrations of the clamped panel (plate) was modified by adding to it stiffness (spring) forces and damping forces. The Transmission Loss coefficient and the Noise Reduction coefficient for oblique incidence were defined and derived in detail. The resonance frequencies excited by the free vibrations of the oblique finite clamped panel (plate) were derived and calculated in detail for the present case.

Geophysical Signatures to Monitor Fluids and Mineralization for CO2 Sequestration in Basalts

NASA Astrophysics Data System (ADS)

Otheim, L. T.; Adam, L.; Van Wijk, K.; Batzle, M. L.; Mcling, T. L.; Podgorney, R. K.

2011-12-01

Carbon dioxide sequestration in large reservoirs can reduce emissions of this green house gas into the atmosphere. Basalts are promising host rocks due to their volumetric extend, worldwide distribution, and recent observations that CO2-water mixtures react with basalt minerals to precipitate as carbonate minerals, trapping the CO2. The chemical reaction between carbonic acid and minerals rich in calcium, magnesium and iron precipitates carbonates in the pore space. This process would increase the elastic modulus and velocity of the rock. At the same time, the higher compressibility of CO2 over water changes the elastic properties of the rock, decreasing the saturated rock bulk modulus and the P-wave velocity. Reservoirs where the rock properties change as a result of fluid or pressure changes are commonly monitored with seismic methods. Here we present experiments to study the feasibility of monitoring CO2 migration in a reservoir and CO2-rock reactions for a sequestration scenario in basalts. Our goal is to measure the rock's elastic response to mineralization with non-contacting ultrasonic lasers, and the effect of fluid substitution at reservoir conditions at seismic and ultrasonic frequencies. For the fluid substitution experiment we observe changes in the P- and S-wave velocities when saturating the sample with super-critical (sc) CO2, CO2-water mixtures and water alone for different pore and confining pressures. The bulk modulus of the rock is significantly dependent on frequency in the 2~to 106~Hz range, for CO2-water mixtures and pure water saturations. Dry and pure CO2 (sc or gas) do not show a frequency dependence on the modulus. Moreover, the shear wave modulus is not dispersive for either fluid. The frequency dependence of the elastic parameters is related to the attenuation (1/Q) of the rock. We will show the correlation between frequency dependent moduli and attenuation data for the different elastic moduli of the rocks. Three other basalt samples were stored in a pressure chamber with a sc CO2-water solution to study the effect of mineralization on the elastic properties of the rock. The rock elastic properties are recorded with non-contacting ultrasonic lasers at room conditions. After 15 weeks the first post-mineralization scan showed differences in the rock velocities with respect to the pre-mineralization scan. The analysis is done through coda wave interferometry and direct arrivals. The samples were inserted back into the pressure vessel for continuing mineralization and subsequent scans. Finally, we will discuss the applicability of Gassmann's equation and how the combination of mineralization together with CO2-water mixture affects the velocity of waves in basalt rocks.

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.

Experimental validation of ultrasonic guided modes in electrical cables by optical interferometry.

PubMed

Mateo, Carlos; de Espinosa, Francisco Montero; Gómez-Ullate, Yago; Talavera, Juan A

2008-03-01

In this work, the dispersion curves of elastic waves propagating in electrical cables and in bare copper wires are obtained theoretically and validated experimentally. The theoretical model, based on Gazis equations formulated according to the global matrix methodology, is resolved numerically. Viscoelasticity and attenuation are modeled theoretically using the Kelvin-Voigt model. Experimental tests are carried out using interferometry. There is good agreement between the simulations and the experiments despite the peculiarities of electrical cables.

Quantitative assessment of corneal viscoelasticity using optical coherence elastography and a modified Rayleigh-Lamb equation

NASA Astrophysics Data System (ADS)

Han, Zhaolong; Aglyamov, Salavat R.; Li, Jiasong; Singh, Manmohan; Wang, Shang; Vantipalli, Srilatha; Wu, Chen; Liu, Chih-hao; Twa, Michael D.; Larin, Kirill V.

2015-02-01

We demonstrate the use of a modified Rayleigh-Lamb frequency equation in conjunction with noncontact optical coherence elastography to quantify the viscoelastic properties of the cornea. Phase velocities of air-pulse-induced elastic waves were extracted by spectral analysis and used for calculating the Young's moduli of the samples using the Rayleigh-Lamb frequency equation (RLFE). Validation experiments were performed on 2% agar phantoms (n=3) and then applied to porcine corneas (n=3) in situ. The Young's moduli of the porcine corneas were estimated to be ˜60 kPa with a shear viscosity ˜0.33 Pa.s. The results demonstrate that the RLFE is a promising method for noninvasive quantification of the corneal biomechanical properties and may potentially be useful for clinical ophthalmological applications.

Single-Crystal Elasticity of Iron-Bearing Bridgemanite in the Lower Mantle

NASA Astrophysics Data System (ADS)

Yang, J.; Lin, J. F.; Okuchi, T.; Tomioka, N.

2014-12-01

Bridgemanite is believed to be the most abundant mineral in the Earth's lower mantle. Knowing its elasticity is thus critical to our understanding of the lower-mantle seismology, geochemistry, and geophysics. Although single-crystal elasticity and elastic anisotropy of bridgemanite under high P-T have been reported theoretically, experimental results on the single-crystal elasticity of bridgemanite remain very limited[1, 2]. Published experimental results have been limited to ambient conditions due to technical challenges in high-pressure measurements to permit derivations of all nine elastic constants (C11, C22, C33, C44, C55, C66, C12, C23 and C13) of the crystal. A thorough understanding of the elastic properties of bridgemanite at relevant lower mantle conditions, as well as the effects of iron, is essentially needed to interpret seismic observations and to construct a reliable mineralogical and geochemical model. In order to solve all individual elastic constants of bridgemanite at high pressures via Christoffel's equations, we employed both Brillouin Light Scattering (BLS) which is sensitive to shear wave velocities (Vs) up to megabars, and Impulsive Stimulated Light Scattering (ISS) which is sensitive to compressional wave velocities (VP) at lower mantle pressures. The BLS and ISS allowed us to measure VP and VS sound velocities as a function of the azimuthal angle from two orientated single-crystal iron bearing bridgemanite platelets under lower mantle pressures. These experimental results permit the derivations of full elastic constants of single-crystal bridgemanite that are consistent with previous theoretical studies [3, 4]. We will discuss how pressure-temperature, as well as the iron spin/valence states and minor element aluminum, affect the single-crystal elasticity and seismic parameters (e.g. VP and VS anisotropy AVP, AVS) at lower mantle conditions. Within a pyrolite mineralogical model, these results are extrapolated using a thermoelastic model and compared with seismic profiles of the lower mantle to better understand the deep-mantle geophysics and geochemistry. References: Sinogeikon,S.V., et al., 2004, GRL 31. Yeganeh-Haeri, A., et al., 1994, PEPI 87. Wentzcovitch, R.M., et al., 1998, EPSL 164. Oganov, A.R., et al., 2001, Nature 411.

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.

Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior

NASA Technical Reports Server (NTRS)

Riff, R.; Carlson, R. L.; Simitses, G. J.

1985-01-01

The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.

Contact interaction of thin-walled elements with an elastic layer and an infinite circular cylinder under torsion

NASA Astrophysics Data System (ADS)

Kanetsyan, E. G.; Mkrtchyan, M. S.; Mkhitaryan, S. M.

2018-04-01

We consider a class of contact torsion problems on interaction of thin-walled elements shaped as an elastic thin washer – a flat circular plate of small height – with an elastic layer, in particular, with a half-space, and on interaction of thin cylindrical shells with a solid elastic cylinder, infinite in both directions. The governing equations of the physical models of elastic thin washers and thin circular cylindrical shells under torsion are derived from the exact equations of mathematical theory of elasticity using the Hankel and Fourier transforms. Within the framework of the accepted physical models, the solution of the contact problem between an elastic washer and an elastic layer is reduced to solving the Fredholm integral equation of the first kind with a kernel representable as a sum of the Weber–Sonin integral and some integral regular kernel, while solving the contact problem between a cylindrical shell and solid cylinder is reduced to a singular integral equation (SIE). An effective method for solving the governing integral equations of these problems are specified.

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.

Generalized thermoelastic diffusive waves in heat conducting materials

NASA Astrophysics Data System (ADS)

Sharma, J. N.

2007-04-01

Keeping in view the applications of diffusion processes in geophysics and electronics industry, the aim of the present paper is to give a detail account of the plane harmonic generalized thermoelastic diffusive waves in heat conducting solids. According to the characteristic equation, three longitudinal waves namely, elastodiffusive (ED), mass diffusion (MD-mode) and thermodiffusive (TD-mode), can propagate in such solids in addition to transverse waves. The transverse waves get decoupled from rest of the fields and hence remain unaffected due to temperature change and mass diffusion effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic diffusive waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. At low frequency mass diffusion and thermal waves do not exist but at high-frequency limits these waves propagate with infinite velocity being diffusive in character. Moreover, in the low-frequency regions, the disturbance is mainly dominant by mechanical process of transportation of energy and at high-frequency regions it is significantly dominated by a close to diffusive process (heat conduction or mass diffusion). Therefore, at low-frequency limits the waves like modes are identifiable with small amplitude waves in elastic materials that do not conduct heat. The general complex characteristic equation is solved by using irreducible case of Cardano's method with the help of DeMoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation of various modes. The propagation of waves in case of non-heat conducting solids is also discussed. Finally, the numerical solution is carried out for copper (solvent) and zinc (solute) materials and the obtained phase velocities, attenuation coefficients and specific loss factor of various thermoelastic diffusive waves are presented graphically.

Lithosphere-Atmosphere coupling: Spectral element modeling of the evolution of acoustic waves in the atmosphere from an underground source.

NASA Astrophysics Data System (ADS)

Averbuch, Gil; Price, Colin

2015-04-01

Lithosphere-Atmosphere coupling: Spectral element modeling of the evolution of acoustic waves in the atmosphere from an underground source. G. Averbuch, C. Price Department of Geosciences, Tel Aviv University, Israel Infrasound is one of the four Comprehensive Nuclear-Test Ban Treaty technologies for monitoring nuclear explosions. This technology measures the acoustic waves generated by the explosions followed by their propagation through the atmosphere. There are also natural phenomena that can act as an infrasound sources like sprites, volcanic eruptions and earthquakes. The infrasound waves generated from theses phenomena can also be detected by the infrasound arrays. In order to study the behavior of these waves, i.e. the physics of wave propagation in the atmosphere, their evolution and their trajectories, numerical methods are required. This presentation will deal with the evolution of acoustic waves generated by underground sources (earthquakes and underground explosions). A 2D Spectral elements formulation for lithosphere-atmosphere coupling will be presented. The formulation includes the elastic wave equation for the seismic waves and the momentum, mass and state equations for the acoustic waves in a moving stratified atmosphere. The coupling of the two media is made by boundary conditions that ensures the continuity of traction and velocity (displacement) in the normal component to the interface. This work has several objectives. The first is to study the evolution of acoustic waves in the atmosphere from an underground source. The second is to derive transmission coefficients for the energy flux with respect to the seismic magnitude and earth density. The third will be the generation of seismic waves from acoustic waves in the atmosphere. Is it possible?

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.

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

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.

Free vibration analysis of embedded magneto-electro-thermo-elastic cylindrical nanoshell based on the modified couple stress theory

NASA Astrophysics Data System (ADS)

Ghadiri, Majid; Safarpour, Hamed

2016-09-01

In this paper, size-dependent effect of an embedded magneto-electro-elastic (MEE) nanoshell subjected to thermo-electro-magnetic loadings on free vibration behavior is investigated. Also, the surrounding elastic medium has been considered as the model of Winkler characterized by the spring. The size-dependent MEE nanoshell is investigated on the basis of the modified couple stress theory. Taking attention to the first-order shear deformation theory (FSDT), the modeled nanoshell and its equations of motion are derived using principle of minimum potential energy. The accuracy of the presented model is validated with some cases in the literature. Finally, using the Navier-type method, an analytical solution of governing equations for vibration behavior of simply supported MEE cylindrical nanoshell under combined loadings is presented and the effects of material length scale parameter, temperature changes, external electric potential, external magnetic potential, circumferential wave numbers, constant of spring, shear correction factor and length-to-radius ratio of the nanoshell on natural frequency are identified. Since there has been no research about size-dependent analysis MEE cylindrical nanoshell under combined loadings based on FSDT, numerical results are presented to be served as benchmarks for future analysis of MEE nanoshells using the modified couple stress theory.

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.

Prestack reverse time migration for tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Jang, Seonghyung; Hien, Doan Huy

2013-04-01

According to having interest in unconventional resource plays, anisotropy problem is naturally considered as an important step for improving the seismic image quality. Although it is well known prestack depth migration for the seismic reflection data is currently one of the powerful tools for imaging complex geological structures, it may lead to migration error without considering anisotropy. Asymptotic analysis of wave propagation in transversely isotropic (TI) media yields a dispersion relation of couple P- and SV wave modes that can be converted to a fourth order scalar partial differential equation (PDE). By setting the shear wave velocity equal zero, the fourth order PDE, called an acoustic wave equation for TI media, can be reduced to couple of second order PDE systems and we try to solve the second order PDE by the finite difference method (FDM). The result of this P wavefield simulation is kinematically similar to elastic and anisotropic wavefield simulation. We develop prestack depth migration algorithm for tilted transversely isotropic media using reverse time migration method (RTM). RTM is a method for imaging the subsurface using inner product of source wavefield extrapolation in forward and receiver wavefield extrapolation in backward. We show the subsurface image in TTI media using the inner product of partial derivative wavefield with respect to physical parameters and observation data. Since the partial derivative wavefields with respect to the physical parameters require extremely huge computing time, so we implemented the imaging condition by zero lag crosscorrelation of virtual source and back propagating wavefield instead of partial derivative wavefields. The virtual source is calculated directly by solving anisotropic acoustic wave equation, the back propagating wavefield on the other hand is calculated by the shot gather used as the source function in the anisotropic acoustic wave equation. According to the numerical model test for a simple geological model including syncline and anticline, the prestack depth migration using TTI-RTM in weak anisotropic media shows the subsurface image is similar to the true geological model used to generate the shot gathers.

A first principles study of the mechanical, electronic, and vibrational properties of lead oxide

NASA Astrophysics Data System (ADS)

Zhuravlev, Yu. N.; Korabel'nikov, D. V.

2017-11-01

The first principles study of the crystal structure, chemical bonds, elastic and mechanical properties, electron energy band structure and density, and normal long-wave vibrations of nine phases of lead monoxide, dioxide, and tetraoxide has been performed under normal and external pressure within the framework of density functional theory (DFT) with the Perdew-Becke-Ernzerhof (PBE) gradient exchange-correlation functional and its hybrid version with a 25-% Hartree-Fock (HF) exchange contribution in the basis of localized atom orbitals. The behavior of physical parameters has been studied using the cold four- and threeparameter equations of state. The parameters of the crystal structures are in satisfactory agreement with experimental data, and elastic constants indicate their mechanical stability and anisotropy in the elastic properties. The elasticity, shear, and Young moduli, hardness, acoustic velocities, and Debye temperature of dioxide on the one hand and monoxide and tetraoxide on the other hand appreciably differ from each other. The difference between electron properties may be explained by the character of hybridization in the upper filled and lower empty energy bands as evident from the density of states. In monoxide, the indirect band gap width decreases with increasing pressure at a rate of 0.16 eV/GPa, and the direct band gap width increases at a rate of 0.13 eV/GPa. To identify crystalline phases, the frequencies and intensities of long-wave modes active in IR and Raman spectra have been calculated.

Porogranular materials composed of elastic Helmholtz resonators for acoustic wave absorption.

PubMed

Griffiths, Stéphane; Nennig, Benoit; Job, Stéphane

2017-01-01

A theoretical and experimental study of the acoustic absorption of granular porous media made of non-cohesive piles of spherical shells is presented. These shells are either rigid or elastic, possibly drilled with a neck (Helmholtz resonators), and either porous or impervious. A description is given of acoustic propagation through these media using the effective medium models proposed by Johnson (rigid particles) and Boutin (rigid Helmholtz resonators), which are extended to the configurations studied in this work. A solution is given for the local equation of elasticity of a shell coupled to the viscous flow of air through the neck and the micropores. The models and the simulations are compared to absorption spectra measured in reflection in an impedance tube. The effective medium models and the measurements show excellent agreement for configurations made of rigid particles and rigid Helmholtz resonators that induce an additional peak of absorption at low frequency. A shift of the Helmholtz resonance toward low frequencies, due to the softness of the shells is revealed by the experiments for elastic shells made of soft elastomer and is well reproduced by the simulations. It is shown that microporous shells enhance and broaden acoustic absorption compared to stiff or elastic resonators.

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

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.

An Laudau-Lifschitz theory based algorithm on calculating post-buckling configuration of a rod buckling in elastic media

NASA Astrophysics Data System (ADS)

Huang, Shicheng; Tan, Likun; Hu, Nan; Grover, Hannah; Chu, Kevin; Chen, Zi

This reserach introduces a new numerical approach of calculating the post-buckling configuration of a thin rod embedded in elastic media. The theoretical base is the governing ODEs describing the balance of forces and moments, the length conservation, and the physics of bending and twisting by Laudau and Lifschitz. The numerical methods applied in the calculation are continuation method and Newton's method of iteration in combination with spectrum method. To the authors' knowledge, it is the first trial of directly applying the L-L theory to numerically studying the phenomenon of rod buckling in elastic medium. This method accounts for nonlinearity of geometry, thus is capable of calculating large deformation. The stability of this method is another advantage achieved by expressing the governing equations in a set of first-order derivative form. The wave length, amplitude, and decay effect all agree with the experiment without any further assumptions. This program can be applied to different occasions with varying stiffness of the elastic medai and rigidity of the rod.

Long-Wavelength Elastic Wave Propagation Across Naturally Fractured Rock Masses

NASA Astrophysics Data System (ADS)

Mohd-Nordin, Mohd Mustaqim; Song, Ki-Il; Cho, Gye-Chun; Mohamed, Zainab

2014-03-01

Geophysical site investigation techniques based on elastic waves have been widely used to characterize rock masses. However, characterizing jointed rock masses by using such techniques remains challenging because of a lack of knowledge about elastic wave propagation in multi-jointed rock masses. In this paper, the roughness of naturally fractured rock joint surfaces is estimated by using a three-dimensional (3D) image-processing technique. The classification of the joint roughness coefficient (JRC) is enhanced by introducing the scan line technique. The peak-to-valley height is selected as a key indicator for JRC classification. Long-wavelength P-wave and torsional S-wave propagation across rock masses containing naturally fractured joints are simulated through the quasi-static resonant column (QSRC) test. In general, as the JRC increases, the S-wave velocity increases within the range of stress levels considered in this paper, whereas the P-wave velocity and the damping ratio of the shear wave decrease. In particular, the two-dimensional joint specimen underestimates the S-wave velocity while overestimating the P-wave velocity. This suggests that 3D joint surfaces should be implicated to obtain the reliable elastic wave velocity in jointed rock masses. The contact characteristic and degree of roughness and waviness of the joint surface are identified as a factor influencing P-wave and S-wave propagation in multi-jointed rock masses. The results indicate a need for a better understanding of the sensitivity of contact area alterations to the elastic wave velocity induced by changes in normal stress. This paper's framework can be a reference for future research on elastic wave propagation in naturally multi-jointed rock masses.

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

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.

Computation of Hypersonic Shock Wave Flows of Multi-Component Reactive Gas Mixtures Using the Generalized Boltzmann Equation

DTIC Science & Technology

2009-03-27

ones like the Lennard - Jones potential with established parameters for each gas (e.g. N2 and 02), and for inelastic collisions DSMC method employs...solution of the collision integral. Lennard - Jones potential with two free parameters is used to obtain the elastic cross-section of the gas molecules...and the so called "combinatory relations" are used to obtain parameters of Lennard - Jones potential for an interaction of molecule A with molecule B

CRUSTAL FAILURE DURING BINARY INSPIRAL

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

Penner, A. J.; Andersson, N.; Jones, D. I.

2012-04-20

We present the first fully relativistic calculations of the crustal strain induced in a neutron star by a binary companion at the late stages of inspiral, employing realistic equations of state for the fluid core and the solid crust. We show that while the deep crust is likely to fail only shortly before coalescence, there is a large variation in elastic strain, with the outermost layers failing relatively early on in the inspiral. We discuss the significance of the results for both electromagnetic and gravitational-wave astronomy.

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.

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 correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis.

PubMed

Goossens, Liesbet; Vanderoost, Jef; Jaecques, Siegfried; Boonen, Steven; D'hooge, Jan; Lauriks, Walter; Van der Perre, Georges

2008-01-01

For the clinical assessment of osteoporosis (i.e., a degenerative bone disease associated with increased fracture risk), ultrasound has been proposed as an alternative or supplement to the dual-energy X-ray absorptiometry (DEXA) technique. However, the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The present study aimed to improve this understanding by simulating ultrasound wave propagation in 15 trabecular bone samples from the human lumbar spine, using microcomputed tomography-based finite-element modeling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (E(s)), and the ultrasound propagation parameter speed of sound (SOS). Relations between BV/TV and E(s) were similar to published experimental relations. At 1 MHz, correlations between SOS and the structural parameters BV/TV and Es were rather weak, but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus E(i). In particular, the systematic differences between the three main directions provide information on the trabecular structure. In addition, at 1 MHz the correlation found between the simulated SOS values and those calculated from the simple bar equation was poor when the three directions are considered separately. Hence, under these conditions, the homogenization approach-including the bar equation-is not valid. However, at lower frequencies (50-300 kHz) this correlation significantly improved. It is concluded that detailed analysis of ultrasound wave propagation through the solid structure in various directions and with various frequencies, can yield much information on the structural and mechanical properties of trabecular bone.

Multifactor estimation of ecological risks using numerical simulation

NASA Astrophysics Data System (ADS)

Voskoboynikova, G.; Shalamov, K.; Khairetdinov, M.; Kovalevsky, V.

2017-10-01

In this paper, the problem of interaction of acoustic waves falling at a given angle on a snow layer on the ground and seismic waves arising both in this layer and in the ground is considered. A system of differential equations with boundary conditions describing the propagation of incident and reflected acoustic waves in the air refracted and reflected from the boundary of seismic waves in elastic media (snow and ground) is constructed and solved for a three-layer air-snow layer-ground model. The coefficients of reflection and refraction are calculated in the case of an acoustic wave falling onto both the ground and snow on the ground. The ratio of the energy of the refracted waves to the energy of the falling acoustic wave is obtained. It is noted that snow has a strong influence on the energy transfer into the ground, which can decrease by more than an order of magnitude. The numerical results obtained are consistent with the results of field experiments with a vibrational source performed by the Siberian Branch of the Russian Academy of Sciences.

Subsurface Void Characterization with 3-D Time Domain Full Waveform Tomography.

NASA Astrophysics Data System (ADS)

Nguyen, T. D.

2017-12-01

A new three dimensional full waveform inversion (3-D FWI) method is presented for subsurface site characterization at engineering scales (less than 30 m in depth). The method is based on a solution of 3-D elastic wave equations for forward modeling, and a cross-adjoint gradient approach for model updating. The staggered-grid finite-difference technique is used to solve the wave equations, together with implementation of the perfectly matched layer condition for boundary truncation. The gradient is calculated from the forward and backward wavefields. Reversed-in-time displacement residuals are induced as multiple sources at all receiver locations for the backward wavefield. The capability of the presented FWI method is tested on both synthetic and field experimental datasets. The test configuration uses 96 receivers and 117 shots at equal spacing (Fig 1). The inversion results from synthetic data show the ability of characterizing variable low- and high-velocity layers with embedded void (Figs 2-3). The synthetic study shows good potential for detection of voids and abnormalities in the field.

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.

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

Application of various elastic thin shell theories to blood flow problems

NASA Technical Reports Server (NTRS)

1972-01-01

Some existing theories, on elastic thin shells, are reviewed to ascertain their influence on the computation of phase velocities in fluid filled cylinders representing certain aspects of the behavior of arteries and veins in vivo. For physiologically meaningful parameters, including moderately large in plane prestrain that occurs in mammals, the results suggest that with one exception, the small differences in the formulations exercise little influence on the phase velocities. However, it is demonstrated that inclusion of the forces induced by the rotation of the hydrostatic pressure is essential or significantly erroneous torsional wave speeds result. Also the introduction of moderate implane prestrains that are present in living mammals is shown to lead to nonselfadjoint differential equations of motion, whose biorthogonal eigenvectors differ slightly from each other.

Absorption effects in electron-sulfur-dioxide collisions

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

Machado, L. E.; Sugohara, R. T.; Santos, A. S. dos

2011-09-15

A joint experimental-theoretical study on electron-SO{sub 2} collisions in the low and intermediate energy range is reported. More specifically, experimental elastic differential, integral, and momentum transfer cross sections in absolute scale are measured in the 100-1000 eV energy range using the relative-flow technique. Calculated elastic differential, integral, and momentum transfer cross sections as well as grand-total and total absorption cross sections are also presented in the 1-1000 eV energy range. A complex optical potential is used to represent the electron-molecule interaction dynamics, whereas the Schwinger variational iterative method combined with the distorted-wave approximation is used to solve the scattering equations.more » Comparison of the present results is made with the theoretical and experimental results available in the literature.« less

Comparative study for elastic electron collisions on C{sub 2}N{sub 2} isomers

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

Michelin, S. E.; Falck, A. S.; Mazon, K. T.

2006-08-15

In this work, we present a theoretical study on elastic electron collisions with the four C{sub 2}N{sub 2} isomers. More specifically, calculated differential, integral, and momentum transfer cross sections are reported in the 1-100 eV energy range. Calculations are performed at both the static-exchange-absorption and the static-exchange-polarization-absorption levels. The iterative Schwinger variational method combined with the distorted wave approximation is used to solve the scattering equations. Our study reveals an interesting trend of the calculated cross sections for the four isomers. In particular, strong isomer effect is seen at low incident energies. Also, we have identified a shape resonance whichmore » leads to a depression in the calculated partial integral cross section.« less

Seismic waves in heterogeneous material: subcell resolution of the discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Castro, Cristóbal E.; Käser, Martin; Brietzke, Gilbert B.

2010-07-01

We present an important extension of the arbitrary high-order discontinuous Galerkin (DG) finite-element method to model 2-D elastic wave propagation in highly heterogeneous material. In this new approach we include space-variable coefficients to describe smooth or discontinuous material variations inside each element using the same numerical approximation strategy as for the velocity-stress variables in the formulation of the elastic wave equation. The combination of the DG method with a time integration scheme based on the solution of arbitrary accuracy derivatives Riemann problems still provides an explicit, one-step scheme which achieves arbitrary high-order accuracy in space and time. Compared to previous formulations the new scheme contains two additional terms in the form of volume integrals. We show that the increasing computational cost per element can be overcompensated due to the improved material representation inside each element as coarser meshes can be used which reduces the total number of elements and therefore computational time to reach a desired error level. We confirm the accuracy of the proposed scheme performing convergence tests and several numerical experiments considering smooth and highly heterogeneous material. As the approximation of the velocity and stress variables in the wave equation and of the material properties in the model can be chosen independently, we investigate the influence of the polynomial material representation on the accuracy of the synthetic seismograms with respect to computational cost. Moreover, we study the behaviour of the new method on strong material discontinuities, in the case where the mesh is not aligned with such a material interface. In this case second-order linear material approximation seems to be the best choice, with higher-order intra-cell approximation leading to potential instable behaviour. For all test cases we validate our solution against the well-established standard fourth-order finite difference and spectral element method.

Numerical simulations of earthquakes and the dynamics of fault systems using the Finite Element method.

NASA Astrophysics Data System (ADS)

Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.

2006-12-01

Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.

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.

Evaluating the Effects of Riboflavin/UV-A and Rose-Bengal/Green Light Cross-Linking of the Rabbit Cornea by Noncontact Optical Coherence Elastography

PubMed Central

Singh, Manmohan; Li, Jiasong; Han, Zhaolong; Vantipalli, Srilatha; Liu, Chih-Hao; Wu, Chen; Raghunathan, Raksha; Aglyamov, Salavat R.; Twa, Michael D.; Larin, Kirill V.

2016-01-01

Purpose The purpose of this study was to use noncontact optical coherence elastography (OCE) to evaluate and compare changes in biomechanical properties that occurred in rabbit cornea in situ after corneal collagen cross-linking by either of two techniques: ultraviolet-A (UV-A)/riboflavin or rose-Bengal/green light. Methods Low-amplitude (≤10 μm) elastic waves were induced in mature rabbit corneas by a focused air pulse. Elastic wave propagation was imaged by a phase-stabilized swept source OCE (PhS-SSOCE) system. Corneas were then cross-linked by either of two methods: UV-A/riboflavin (UV-CXL) or rose-Bengal/green light (RGX). Phase velocities of the elastic waves were fitted to a previously developed modified Rayleigh-Lamb frequency equation to obtain the viscoelasticity of the corneas before and after the cross-linking treatments. Micro-scale depth-resolved phase velocity distribution revealed the depth-wise heterogeneity of both cross-linking techniques. Results Under standard treatment settings, UV-CXL significantly increased the stiffness of the corneas by ∼47% (P < 0.05), but RGX did not produce statistically significant increases. The shear viscosities were unaffected by either cross-linking technique. The depth-wise phase velocities showed that UV-CXL affected the anterior ∼34% of the corneas, whereas RGX affected only the anterior ∼16% of the corneas. Conclusions UV-CXL significantly strengthens the cornea, whereas RGX does not, and the effects of cross-linking by UV-CXL reach deeper into the cornea than cross-linking effects of RGX under similar conditions. PMID:27409461

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.

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.

CCKT Calculation of e-H Total Cross Sections

NASA Technical Reports Server (NTRS)

Bhatia, Aaron K.; Schneider, B. I.; Temkin, A.; Fisher, Richard R. (Technical Monitor)

2002-01-01

We are in the process of carrying out calculations of e-H total cross sections using the 'complex-correlation Kohn-T' (CCKT) method. In a later paper, we described the methodology more completely, but confined calculations to the elastic scattering region, with definitive, precision results for S-wave phase shifts. Here we extend the calculations to the (low) continuum (1 much less than k(exp 2) much less than 3) using a Green's function formulation. This avoids having to solve integro-differential equations; rather we evaluate indefinite integrals involving appropriate Green's functions and the (complex) optical potential to find the scattering function u(r). From the asymptotic form of u(r) we extract a T(sub L) which is a complex number. From T(sub L), elastic sigma(sub L)(elastic) = 4pi(2L+1)((absolute value of T(sub L))(exp 2)), and total sigma (sub L)(total) = 4pi/k(2L+1)Im(T(sub L)) cross sections follow.

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.

Longitudinal wave propagation in multi cylindrical viscoelastic matching layers of airborne ultrasonic transducer: new method to consider the matching layer's diameter (frequency <100 kHz).

PubMed

Saffar, Saber; Abdullah, Amir

2013-08-01

Wave propagation in viscoelastic disk layers is encountered in many applications including studies of airborne ultrasonic transducers. For viscoelastic materials, both material and geometric dispersion are possible when the diameter of the matching layer is of the same order as the wavelength. Lateral motions of the matching layer(s) that result from the Poisson effect are accounted by using a new concept called the "effective-density". A new wave equation is derived for both metallic and non-metallic (polymeric) materials, usually employed for the matching layers of airborne ultrasonic transducer. The material properties are modeled by using the Kelvin model for metals and Linear Solid Standard model for non-metallic (polymeric) matching layers. The utilized model of the material of the matching layers has influence on amount and trend of variation in speed ratio. In this regard, 60% reduction in speed ratio is observed for Kelvin model for aluminum with diameter of 80 mm at 100 kHz while for a similar diameter but Standard Linear Model, the speed ratio increase to twice value at 15 kHz, and then reduced until 70% at 67 kHz for Polypropylene. The new wave theory simplifies to the one-dimensional solution for waves in metallic or polymeric matching layers if the Poisson ratio is set to zero. The predictions simplify to Love's equation for stress waves in elastic disks when loss term is removed from equations for both models. Afterwards, the new wave theory is employed to determine the airborne ultrasonic matching layers to maximize the energy transmission to the air. The optimal matching layers are determined by using genetic algorithm theory for 1, 2 and 3 airborne matching layers. It has been shown that 1-D equation is useless at frequencies less than 100 kHz and the effect of diameter of the matching layers must be considered to determine the acoustic impedances (matching layers) to design airborne ultrasonic transducers. Copyright © 2013 Elsevier B.V. All rights reserved.

Effect of elastic boundaries in hydrostatic problems

NASA Astrophysics Data System (ADS)

Volobuev, A. N.; Tolstonogov, A. P.

2010-03-01

The possibility and conditions of use of the Bernoulli equation for description of an elastic pipeline were considered. It is shown that this equation is identical in form to the Bernoulli equation used for description of a rigid pipeline. It has been established that the static pressure entering into the Bernoulli equation is not identical to the pressure entering into the impulse-momentum equation. The hydrostatic problem on the pressure distribution over the height of a beaker with a rigid bottom and elastic walls, filled with a liquid, was solved.

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

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.

Performance of parallel computation using CUDA for solving the one-dimensional elasticity equations

NASA Astrophysics Data System (ADS)

Darmawan, J. B. B.; Mungkasi, S.

2017-01-01

In this paper, we investigate the performance of parallel computation in solving the one-dimensional elasticity equations. Elasticity equations are usually implemented in engineering science. Solving these equations fast and efficiently is desired. Therefore, we propose the use of parallel computation. Our parallel computation uses CUDA of the NVIDIA. Our research results show that parallel computation using CUDA has a great advantage and is powerful when the computation is of large scale.

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.

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.

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

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

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Goodman, Harvey E.; ...

2017-10-18

Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classicalmore » nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.« less

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

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

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.

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.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

High-Frequency Normal Mode Propagation in Aluminum Cylinders

USGS Publications Warehouse

Lee, Myung W.; Waite, William F.

2009-01-01

Acoustic measurements made using compressional-wave (P-wave) and shear-wave (S-wave) transducers in aluminum cylinders reveal waveform features with high amplitudes and with velocities that depend on the feature's dominant frequency. In a given waveform, high-frequency features generally arrive earlier than low-frequency features, typical for normal mode propagation. To analyze these waveforms, the elastic equation is solved in a cylindrical coordinate system for the high-frequency case in which the acoustic wavelength is small compared to the cylinder geometry, and the surrounding medium is air. Dispersive P- and S-wave normal mode propagations are predicted to exist, but owing to complex interference patterns inside a cylinder, the phase and group velocities are not smooth functions of frequency. To assess the normal mode group velocities and relative amplitudes, approximate dispersion relations are derived using Bessel functions. The utility of the normal mode theory and approximations from a theoretical and experimental standpoint are demonstrated by showing how the sequence of P- and S-wave normal mode arrivals can vary between samples of different size, and how fundamental normal modes can be mistaken for the faster, but significantly smaller amplitude, P- and S-body waves from which P- and S-wave speeds are calculated.

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.

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.

Shear wave speed recovery using moving interference patterns obtained in sonoelastography experiments.

PubMed

McLaughlin, Joyce; Renzi, Daniel; Parker, Kevin; Wu, Zhe

2007-04-01

Two new experiments were created to characterize the elasticity of soft tissue using sonoelastography. In both experiments the spectral variance image displayed on a GE LOGIC 700 ultrasound machine shows a moving interference pattern that travels at a very small fraction of the shear wave speed. The goal of this paper is to devise and test algorithms to calculate the speed of the moving interference pattern using the arrival times of these same patterns. A geometric optics expansion is used to obtain Eikonal equations relating the moving interference pattern arrival times to the moving interference pattern speed and then to the shear wave speed. A cross-correlation procedure is employed to find the arrival times; and an inverse Eikonal solver called the level curve method computes the speed of the interference pattern. The algorithm is tested on data from a phantom experiment performed at the University of Rochester Center for Biomedical Ultrasound.

A time reversal algorithm in acoustic media with Dirac measure approximations

NASA Astrophysics Data System (ADS)

Bretin, Élie; Lucas, Carine; Privat, Yannick

2018-04-01

This article is devoted to the study of a photoacoustic tomography model, where one is led to consider the solution of the acoustic wave equation with a source term writing as a separated variables function in time and space, whose temporal component is in some sense close to the derivative of the Dirac distribution at t  =  0. This models a continuous wave laser illumination performed during a short interval of time. We introduce an algorithm for reconstructing the space component of the source term from the measure of the solution recorded by sensors during a time T all along the boundary of a connected bounded domain. It is based at the same time on the introduction of an auxiliary equivalent Cauchy problem allowing to derive explicit reconstruction formula and then to use of a deconvolution procedure. Numerical simulations illustrate our approach. Finally, this algorithm is also extended to elasticity wave systems.

Effect of inhomogeneity due to temperature on the propagation of shear waves in an anisotropic layer

NASA Astrophysics Data System (ADS)

Prasad, Bishwanath; Pal, Prakash Chandra; Kundu, Santimoy; Prasad, Narayan

2017-07-01

The present paper is concerned with the propagation of shear waves in an anisotropic inhomogeneous layer whose elastic constants are functions of temperature. The dependence of material properties on temperature gives rise to inhomogeneity of the layer which is one of the trivial characteristics of the constituent layers of earth which may cause due to the presence of various types of elements and compounds beneath the earth. The layer is lying over a rigid foundation and there is no loading on the upper boundary. The dispersion equation of shear waves has been obtained in closed form. Numerical computations are performed and graphs are plotted to show the effect of inhomogeneity and anisotropy factors on the dimensionless phase velocity. It is found that the phase velocity is considerably influenced by the inhomogeneity and anisotropy of the layer.

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.

Laser-launched flyer plate and confined laser ablation for shock wave loading: validation and applications.

PubMed

Paisley, Dennis L; Luo, Sheng-Nian; Greenfield, Scott R; Koskelo, Aaron C

2008-02-01

We present validation and some applications of two laser-driven shock wave loading techniques: laser-launched flyer plate and confined laser ablation. We characterize the flyer plate during flight and the dynamically loaded target with temporally and spatially resolved diagnostics. With transient imaging displacement interferometry, we demonstrate that the planarity (bow and tilt) of the loading induced by a spatially shaped laser pulse is within 2-7 mrad (with an average of 4+/-1 mrad), similar to that in conventional techniques including gas gun loading. Plasma heating of target is negligible, in particular, when a plasma shield is adopted. For flyer plate loading, supported shock waves can be achieved. Temporal shaping of the drive pulse in confined laser ablation allows for flexible loading, e.g., quasi-isentropic, Taylor-wave, and off-Hugoniot loading. These techniques can be utilized to investigate such dynamic responses of materials as Hugoniot elastic limit, plasticity, spall, shock roughness, equation of state, phase transition, and metallurgical characteristics of shock-recovered samples.

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

Rayleigh wave behavior in functionally graded magneto-electro-elastic material

NASA Astrophysics Data System (ADS)

Ezzin, Hamdi; Mkaoir, Mohamed; Amor, Morched Ben

2017-12-01

Piezoelectric-piezomagnetic functionally graded materials, with a gradual change of the mechanical and electromagnetic properties have greatly applying promises. Based on the ordinary differential equation and stiffness matrix methods, a dynamic solution is presented for the propagation of the wave on a semi-infinite piezomagnetic substrate covered with a functionally graded piezoelectric material (FGPM) layer. The materials properties are assumed to vary in the direction of the thickness according to a known variation law. The phase and group velocity of the Rayleigh wave is numerically calculated for the magneto-electrically open and short cases, respectively. The effect of gradient coefficients on the phase velocity, group velocity, coupled magneto-electromechanical factor, on the stress fields, the magnetic potential and the mechanical displacement are discussed, respectively. Illustration is achieved on the hetero-structure PZT-5A/CoFe2O4; the obtained results are especially useful in the design of high-performance acoustic surface devices and accurately prediction of the Rayleigh wave propagation behavior.

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.

Couple stress theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and rotation along with body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby, all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of elasticity, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scales when taking into account couple stress and rotation effects.

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.

Sound Transmission Through Multi-Panel Structures Lined with Elastic Porous Materials

NASA Astrophysics Data System (ADS)

Bolton, J. S.; Shiau, N.-M.; Kang, Y. J.

1996-04-01

Theory and measurements related to sound transmission through double panels lined with elastic porous media are presented. The information has application to the design of noise control barriers and to the optimization of aircraft fuselage transmission loss, for example. The major difference between the work described here and earlier research in this field relates to the treatment of the porous material that is used to line the cavity between the two panels of the double panel structure. Here we have used the porous material theory proposed by Biot since it takes explicit account of all the wave types known to propagate in elastic porous materials. As a result, it is possible to use the theory presented here to calculate the transmission loss of lined double panels at arbitrary angles of incidence; results calculated over a range of incidence angles may then be combined to yield the random incidence transmission loss. In this paper, the equations governing wave propagation in an elastic porous material are first considered briefly and then the general forms for the stresses and displacements within the porous material are given. Those solutions are expressed in terms of a number of constants that can be determined by application of appropriate boundary conditions. The boundary conditions required to model double panels having linings that are either directly attached to the facing panels or separated?!from them by air gaps are presented and discussed. Measurements of the random incidence transmission loss of aluminium double-panel structures lined with polyurethane foam are presented and have been found to be in good agreement with theoretical predictions. Both the theoretical predictions and the measured results have shown that the method by which an elastic porous lining material is attached to the facing panels can have a profound influence on the transmission loss of the panel system. It has been found, for example, that treatments in which the lining material is not directly attached to the facing panels are generally to be preferred to those in which the lining is directly bonded to the panels. These effects may be explained by considering the degree to which the various wave types within the elastic porous material are excited, which in turn can be related to the method by which the lining is mounted to the facing panels.

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.

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

NASA Technical Reports Server (NTRS)

Nemeth, Michael P.

2011-01-01

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

First-principles study on elastic and superconducting properties of Nb3Sn and Nb3Al under hydrostatic pressure

NASA Astrophysics Data System (ADS)

Zhang, Rui; Gao, Peifeng; Wang, Xingzhe; Zhou, Youhe

2015-10-01

The low temperature superconducting materials, such as Nb3Sn and Nb3Al, have similar crystal structures and elastic properties. However, their critical-temperature degradations always show the distinct way under mechanical stresses. In this study, first-principles calculations for the low temperature superconductors based on plane-wave pseudo-potential density functional theory within the generalized gradient approximation are implemented, and the elastic moduli of Nb3Sn and Nb3Al and those superconductivities in the presence of hydrostatic pressure are evaluated. The Debye temperatures are obtained by the bulk moduli and shear moduli of superconducting materials. The MacMillan equation is further used to acquire the critical temperatures of Nb3Sn and Nb3Al under different hydrostatic pressures. It is found that the elastic constants and bulk moduli of the low temperature superconductors are enhanced by the applied hydrostatic pressure, while the critical temperatures usually are decreased with the pressure. Additionally, the decrease of critical-temperature for Nb3Sn is more sensitive to the hydrostatic pressure than the one for Nb3Al. The prediction results show good agreement with the experimental results in the literatures qualitatively.

Development and Application of Acoustic Metamaterials with Locally Resonant Microstructures

DTIC Science & Technology

2014-10-21

the effective Young’s modulus of the solid is found frequency-dependent in the form       − += 12 1 2 2 31 η ηµδNYM st NYM eff EE ...22 1 2 2 031 <=< + NYMω ωη µδ (5.15) The wave equation takes the form of Eq. (5.7), in which the effective Young’s modulus, NYM effeff EE ...effeff EEE == , respectively. Consequently, the dispersion relation of the representative elastic solid is obtained as ( ) 0/),( 22220 =−= LEG

A Laboratory Study of the Effect of Stress State on the Elastic Moduli of Sand

DTIC Science & Technology

1990-01-01

the sand column and had no provisions to confine the sand other than under its own weight. The growth of the nuclear power industry in the 1960’ s ...discovery in the early 1980’ s of how stress state impacts the magnitude of the shear modulus. In particular, it was determined that shear wave velocity...z,t) goes to infinity, a condition analogous to "resonance." If the determinant is set equal to zero, it yields the following equation, (mo)2+ ikEA

Least-squares reverse time migration in elastic media

NASA Astrophysics Data System (ADS)

Ren, Zhiming; Liu, Yang; Sen, Mrinal K.

2017-02-01

Elastic reverse time migration (RTM) can yield accurate subsurface information (e.g. PP and PS reflectivity) by imaging the multicomponent seismic data. However, the existing RTM methods are still insufficient to provide satisfactory results because of the finite recording aperture, limited bandwidth and imperfect illumination. Besides, the P- and S-wave separation and the polarity reversal correction are indispensable in conventional elastic RTM. Here, we propose an iterative elastic least-squares RTM (LSRTM) method, in which the imaging accuracy is improved gradually with iteration. We first use the Born approximation to formulate the elastic de-migration operator, and employ the Lagrange multiplier method to derive the adjoint equations and gradients with respect to reflectivity. Then, an efficient inversion workflow (only four forward computations needed in each iteration) is introduced to update the reflectivity. Synthetic and field data examples reveal that the proposed LSRTM method can obtain higher-quality images than the conventional elastic RTM. We also analyse the influence of model parametrizations and misfit functions in elastic LSRTM. We observe that Lamé parameters, velocity and impedance parametrizations have similar and plausible migration results when the structures of different models are correlated. For an uncorrelated subsurface model, velocity and impedance parametrizations produce fewer artefacts caused by parameter crosstalk than the Lamé coefficient parametrization. Correlation- and convolution-type misfit functions are effective when amplitude errors are involved and the source wavelet is unknown, respectively. Finally, we discuss the dependence of elastic LSRTM on migration velocities and its antinoise ability. Imaging results determine that the new elastic LSRTM method performs well as long as the low-frequency components of migration velocities are correct. The quality of images of elastic LSRTM degrades with increasing noise.

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.

Distributed Seismic Moment Fault Model, Spectral Characteristics and Radiation Patterns

NASA Astrophysics Data System (ADS)

Shani-Kadmiel, Shahar; Tsesarsky, Michael; Gvirtzman, Zohar

2014-05-01

We implement a Distributed Seismic Moment (DSM) fault model, a physics-based representation of an earthquake source based on a skewed-Gaussian slip distribution over an elliptical rupture patch, for the purpose of forward modeling of seismic-wave propagation in 3-D heterogeneous medium. The elliptical rupture patch is described by 13 parameters: location (3), dimensions of the patch (2), patch orientation (1), focal mechanism (3), nucleation point (2), peak slip (1), rupture velocity (1). A node based second order finite difference approach is used to solve the seismic-wave equations in displacement formulation (WPP, Nilsson et al., 2007). Results of our DSM fault model are compared with three commonly used fault models: Point Source Model (PSM), Haskell's fault Model (HM), and HM with Radial (HMR) rupture propagation. Spectral features of the waveforms and radiation patterns from these four models are investigated. The DSM fault model best incorporates the simplicity and symmetry of the PSM with the directivity effects of the HMR while satisfying the physical requirements, i.e., smooth transition from peak slip at the nucleation point to zero at the rupture patch border. The implementation of the DSM in seismic-wave propagation forward models comes at negligible computational cost. Reference: Nilsson, S., Petersson, N. A., Sjogreen, B., and Kreiss, H.-O. (2007). Stable Difference Approximations for the Elastic Wave Equation in Second Order Formulation. SIAM Journal on Numerical Analysis, 45(5), 1902-1936.

Stochastic Representations of Seismic Anisotropy: Verification of Effective Media Models and Application to the Continental Crust

NASA Astrophysics Data System (ADS)

Song, X.; Jordan, T. H.

2017-12-01

The seismic anisotropy of the continental crust is dominated by two mechanisms: the local (intrinsic) anisotropy of crustal rocks caused by the lattice-preferred orientation of their constituent minerals, and the geometric (extrinsic) anisotropy caused by the alignment and layering of elastic heterogeneities by sedimentation and deformation. To assess the relative importance of these mechanisms, we have applied Jordan's (GJI, 2015) self-consistent, second-order theory to compute the effective elastic parameters of stochastic media with hexagonal local anisotropy and small-scale 3D heterogeneities that have transversely isotropic (TI) statistics. The theory pertains to stochastic TI media in which the eighth-order covariance tensor of the elastic moduli can be separated into a one-point variance tensor that describes the local anisotropy in terms of a anisotropy orientation ratio (ξ from 0 to ∞), and a two-point correlation function that describes the geometric anisotropy in terms of a heterogeneity aspect ratio (η from 0 to ∞). If there is no local anisotropy, then, in the limiting case of a horizontal stochastic laminate (η→∞), the effective-medium equations reduce to the second-order equations derived by Backus (1962) for a stochastically layered medium. This generalization of the Backus equations to 3D stochastic media, as well as the introduction of local, stochastically rotated anisotropy, provides a powerful theory for interpreting the anisotropic signatures of sedimentation and deformation in continental environments; in particular, the parameterizations that we propose are suitable for tomographic inversions. We have verified this theory through a series high-resolution numerical experiments using both isotropic and anisotropic wave-propagation codes.

Fluid-structure interaction in Taylor-Couette flow

NASA Astrophysics Data System (ADS)

Kempf, Martin Horst Willi

1998-10-01

The linear stability of a viscous fluid between two concentric, rotating cylinders is considered. The inner cylinder is a rigid boundary and the outer cylinder has an elastic layer exposed to the fluid. The subject is motivated by flow between two adjoining rollers in a printing press. The governing equations of the fluid layer are the incompressible Navier-Stokes equations, and the governing equations of the elastic layer are Navier's equations. A narrow gap, neutral stability, and axisymmetric disturbances are assumed. The solution involves a novel technique for treating two layer stability problems, where an exact solution in the elastic layer is used to isolate the problem in the fluid layer. The results show that the presence of the elastic layer has only a slight effect on the critical Taylor numbers for the elastic parameters of modern printing presses. However, there are parameter values where the critical Taylor number is dramatically different than the classical Taylor-Couette problem.

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.

Wave energy trapping and localization in a plate with a delamination

NASA Astrophysics Data System (ADS)

Glushkov, Evgeny; Glushkova, Natalia; Golub, Mikhail V.; Moll, Jochen; Fritzen, Claus-Peter

2012-12-01

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

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

Equations of motion for a flexible spacecraft-lumped parameter idealization

NASA Technical Reports Server (NTRS)

Storch, Joel; Gates, Stephen

1982-01-01

The equations of motion for a flexible vehicle capable of arbitrary translational and rotational motions in inertial space accompanied by small elastic deformations are derived in an unabridged form. The vehicle is idealized as consisting of a single rigid body with an ensemble of mass particles interconnected by massless elastic structure. The internal elastic restoring forces are quantified in terms of a stiffness matrix. A transformation and truncation of elastic degrees of freedom is made in the interest of numerical integration efficiency. Deformation dependent terms are partitioned into a hierarchy of significance. The final set of motion equations are brought to a fully assembled first order form suitable for direct digital implementation. A FORTRAN program implementing the equations is given and its salient features described.

A finite difference scheme for the equilibrium equations of elastic bodies

NASA Technical Reports Server (NTRS)

Phillips, T. N.; Rose, M. E.

1984-01-01

A compact difference scheme is described for treating the first-order system of partial differential equations which describe the equilibrium equations of an elastic body. An algebraic simplification enables the solution to be obtained by standard direct or iterative techniques.

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.

Sine-Gordon equation and its application to tectonic stress transfer

NASA Astrophysics Data System (ADS)

Bykov, Victor G.

2014-07-01

An overview is given on remarkable progress that has been made in theoretical studies of solitons and other nonlinear wave patterns, excited during the deformation of fault block (fragmented) geological media. The models that are compliant with the classical and perturbed sine-Gordon equations have only been chosen. In these mathematical models, the rotation angle of blocks (fragments) and their translatory displacement of the medium are used as dynamic variables. A brief description of the known models and their geophysical and geodynamic applications is given. These models reproduce the kinematic and dynamic features of the traveling deformation front (kink, soliton) generated in the fragmented media. It is demonstrated that the sine-Gordon equation is applicable to the description of series of the observed seismic data, modeling of strain waves, as well as the features related to fault dynamics and the subduction slab, including slow earthquakes, periodicity of episodic tremor and slow slip (ETS) events, and migration pattern of tremors. The study shows that simple heuristic models and analytical and numerical computations can explain triggering of seismicity by transient processes, such as stress changes associated with solitary strain waves in crustal faults. The need to develop the above-mentioned new (nonlinear) mathematical models of the deformed fault and fragmented media was caused by the reason that it is impossible to explain a lot of the observed effects, particularly, slow redistribution and migration of stresses in the lithosphere, within the framework of the linear elasticity theory.

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

Nonlocal theory of curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-09-01

New models for plane curved rods based on linear nonlocal theory of elasticity have been developed. The 2-D theory is developed from general 2-D equations of linear nonlocal elasticity using a special curvilinear system of coordinates related to the middle line of the rod along with special hypothesis based on assumptions that take into account the fact that the rod is thin. High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First, stress and strain tensors, vectors of displacements and body forces have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby, all equations of elasticity including nonlocal constitutive relations have been transformed to the corresponding equations for Fourier coefficients. Then, in the same way as in the theory of local elasticity, a system of differential equations in terms of displacements for Fourier coefficients has been obtained. First and second order approximations have been considered in detail. Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear nonlocal theory of elasticity which are considered in a special curvilinear system of coordinates related to the middle line of the rod. The obtained equations can be used to calculate stress-strain and to model thin walled structures in micro- and nanoscales when taking into account size dependent and nonlocal effects.

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

NASA Astrophysics Data System (ADS)

Volchkov, Yu. M.

2017-09-01

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.

Micropolar curved rods. 2-D, high order, Timoshenko's and Euler-Bernoulli models

NASA Astrophysics Data System (ADS)

Zozulya, V. V.

2017-01-01

New models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke's law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko's and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

A comparison of viscous-plastic sea ice solvers with and without replacement pressure

NASA Astrophysics Data System (ADS)

Kimmritz, Madlen; Losch, Martin; Danilov, Sergey

2017-07-01

Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian-free Newton-Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them.

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.

Approximate method for predicting the permanent set in a beam in vacuo and in water subject to a shock wave

NASA Technical Reports Server (NTRS)

Stiehl, A. L.; Haberman, R. C.; Cowles, J. H.

1988-01-01

An approximate method to compute the maximum deformation and permanent set of a beam subjected to shock wave laoding in vacuo and in water was investigated. The method equates the maximum kinetic energy of the beam (and water) to the elastic plastic work done by a static uniform load applied to a beam. Results for the water case indicate that the plastic deformation is controlled by the kinetic energy of the water. The simplified approach can result in significant savings in computer time or it can expediently be used as a check of results from a more rigorous approach. The accuracy of the method is demonstrated by various examples of beams with simple support and clamped support boundary conditions.

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.

Hybrid multicore/vectorisation technique applied to the elastic wave equation on a staggered grid

NASA Astrophysics Data System (ADS)

Titarenko, Sofya; Hildyard, Mark

2017-07-01

In modern physics it has become common to find the solution of a problem by solving numerically a set of PDEs. Whether solving them on a finite difference grid or by a finite element approach, the main calculations are often applied to a stencil structure. In the last decade it has become usual to work with so called big data problems where calculations are very heavy and accelerators and modern architectures are widely used. Although CPU and GPU clusters are often used to solve such problems, parallelisation of any calculation ideally starts from a single processor optimisation. Unfortunately, it is impossible to vectorise a stencil structured loop with high level instructions. In this paper we suggest a new approach to rearranging the data structure which makes it possible to apply high level vectorisation instructions to a stencil loop and which results in significant acceleration. The suggested method allows further acceleration if shared memory APIs are used. We show the effectiveness of the method by applying it to an elastic wave propagation problem on a finite difference grid. We have chosen Intel architecture for the test problem and OpenMP (Open Multi-Processing) since they are extensively used in many applications.

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.

Elasticity of ferropericlase and seismic heterogeneity in the Earth's lower mantle: Ferropericlase High Pressure-Temperature Elasticity

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

Yang, Jing; Lin, Jung-Fu; Jacobsen, Steven D.

2016-12-16

Deciphering the origin of seismic heterogeneity has been one of the major challenges in understanding the geochemistry and geodynamics of the deep mantle. Fully anisotropic elastic properties of constituent minerals at relevant pressure-temperature conditions of the lower mantle can be used to calculate seismic heterogeneity parameters in order to better understand chemically and thermally induced seismic heterogeneities. In this study, the single-crystal elastic properties of ferropericlase (Mg0.94Fe0.06)O were measured using Brillouin spectroscopy and X-ray diffraction at conditions up to 50 GPa and 900 K. The velocity-density results were modeled using third-order finite-strain theory and thermoelastic equations along a representative geothermmore » to investigate high pressure-temperature and compositional effects on the seismic heterogeneity parameters. Our results demonstrate that from 660 to 2000 km, compressional wave anisotropy of ferropericlase increased from 4% to 9.7%, while shear wave anisotropy increased from 9% to as high as 22.5%. The thermally induced lateral heterogeneity ratio (RS/P = ∂lnVS/∂lnVP) of ferropericlase was calculated to be 1.48 at ambient pressure but decreased to 1.43 at 40 GPa along a representative geotherm. The RS/P of a simplified pyrolite model consisting of 80% bridgmanite and 20% ferropericlase was approximately 1.5, consistent with seismic models at depths from 670 to 1500 km, but showed an increased mismatch at lower mantle depths below ~1500 km. This discrepancy below mid-lower mantle could be due to either a contribution from chemically induced heterogeneity or the effects of the Fe spin transition in the deeper parts of the Earth's lower mantle.« less

A recursive approach to the equations of motion for the maneuvering and control of flexible multi-body systems

NASA Technical Reports Server (NTRS)

Kwak, Moon K.; Meirovitch, Leonard

1991-01-01

Interest lies in a mathematical formulation capable of accommodating the problem of maneuvering a space structure consisting of a chain of articulated flexible substructures. Simultaneously, any perturbations from the 'rigid body' maneuvering and any elastic vibration must be suppressed. The equations of motion for flexible bodies undergoing rigid body motions and elastic vibrations can be obtained conveniently by means of Lagrange's equations in terms of quasi-coordinates. The advantage of this approach is that it yields equations in terms of body axes, which are the same axes that are used to express the control forces and torques. The equations of motion are nonlinear hybrid differential quations. The partial differential equations can be discretized (in space) by means of the finite element method or the classical Rayleigh-Ritz method. The result is a set of nonlinear ordinary differential equations of high order. The nonlinearity can be traced to the rigid body motions and the high order to the elastic vibration. Elastic motions tend to be small when compared with rigid body motions.

Diameter effect on stress-wave evaluation of modulus of elasticity of logs

Treesearch

Xiping Wang; Robert J. Ross; Brian K. Brashaw; John Punches; John R. Erickson; John W. Forsman; Roy E. Pellerin

2004-01-01

Recent studies on nondestructive evaluation (NDE) of logs have shown that a longitudinal stress-wave method can be used to nondestructively evaluate the modulus of elasticity (MOE) of logs. A strong relationship has been found between stress-wave MOE and static MOE of logs, but a significant deviation was observed between stress-wave and static values. The objective of...

Diameter effect on stress-wave evaluation of modulus of elasticity of logs

Treesearch

Xiping Wang; Robert J. Ross; Brian K. Brashaw; John R. Erickson; John W. Forsman; Roy Pellerin

2003-01-01

Recent studies on nondestructive evaluation (NDE) of logs have shown that a longitudinal stress-wave method can be used to nondestructively evaluate the modulus of elasticity (MOE) of logs. A strong relationship has been found between stress-wave MOE and static MOE of logs, but a significant deviation was observed between stress-wave and static values. The objective of...

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

A study on Rayleigh wave dispersion in bone according to Mindlin's Form II gradient elasticity.

PubMed

Vavva, Maria G; Gergidis, Leonidas N; Protopappas, Vasilios C; Charalambopoulos, Antonios; Polyzos, Demosthenes; Fotiadis, Dimitrios I

2014-05-01

The classical elasticity cannot effectively describe bone's mechanical behavior since only homogeneous media and local stresses are assumed. Additionally, it cannot predict the dispersive nature of the Rayleigh wave which has been reported in experimental studies and was also demonstrated in a previous computational study by adopting Mindlin's Form II gradient elasticity. In this work Mindlin's theory is employed to analytically determine the dispersion of Rayleigh waves in a strain gradient elastic half-space. An isotropic semi-infinite space is considered with properties equal to those of bone and dynamic behavior suffering from microstructural effects. Microstructural effects are considered by incorporating four intrinsic parameters in the stress analysis. The results are presented in the form of group and phase velocity dispersion curves and compared with existing computational results and semi-analytical curves calculated for a simpler case of Rayleigh waves in dipolar gradient elastic half-spaces. Comparisons are also performed with the velocity of the first-order antisymmetric mode propagating in a dipolar plate so as to observe the Rayleigh asymptotic behavior. It is shown that Mindlin's Form II gradient elasticity can effectively describe the dispersive nature of Rayleigh waves. This study could be regarded as a step toward the ultrasonic characterization of bone.

Creeping gaseous flows through elastic tube and annulus micro-configurations

NASA Astrophysics Data System (ADS)

Elbaz, Shai; Jacob, Hila; Gat, Amir

2016-11-01

Gaseous flows in elastic micro-configurations is relevant to biological systems (e.g. alveolar ducts in the lungs) as well as to applications such as gas actuated soft micro-robots. We here examine the effect of low-Mach-number compressibility on creeping gaseous axial flows through linearly elastic tube and annulus micro-configurations. For steady flows, the leading-order effects of elasticity on the pressure distribution and mass-flux are obtained. For transient flow in a tube with small deformations, elastic effects are shown to be negligible in leading order due to compressibility. We then examine transient flows in annular configurations where the deformation is significant compared with the gap between the inner and outer cylinders defining the annulus. Both compressibility and elasticity are obtained as dominant terms interacting with viscosity. For a sudden flux impulse, the governing non-linear leading order diffusion equation is initially approximated by a porous-medium-equation of order 2.5 for the pressure square. However, as the fluid expand and the pressure decreases, the governing equation degenerates to a porous-medium-equation of order 2 for the pressure.

A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium

NASA Astrophysics Data System (ADS)

Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean

2016-10-01

In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.

Seismic Wave Propagation in Fully Anisotropic Axisymmetric Media: Applications and Practical Considerations

NASA Astrophysics Data System (ADS)

van Driel, Martin; Nissen-Meyer, Tarje; Stähler, Simon; Waszek, Lauren; Hempel, Stefanie; Auer, Ludwig; Deuss, Arwen

2014-05-01

We present a numerical method to compute high-frequency 3D elastic waves in fully anisotropic axisymmetric media. The method is based on a decomposition of the wavefield into a series of uncoupled 2D equations, for which the dependence of the wavefield on the azimuth can be solved analytically. The remaining 2D problems are then solved using a spectral element method (AxiSEM). AxiSEM was recently published open-source (Nissen-Meyer et al. 2014) as a production ready code capable to compute global seismic wave propagation up to frequencies of ~2Hz. It accurately models visco-elastic dissipation and anisotropy (van Driel et al., submitted to GJI) and runs efficiently on HPC resources using up to 10K cores. At very short period, the Fresnel Zone of body waves is narrow and sensitivity is focused around the geometrical ray. In cases where the azimuthal variations of structural heterogeneity exhibit long spatial wavelengths, so called 2.5D simulations (3D wavefields in 2D models) provide a good approximation. In AxiSEM, twodimensional variations in the source-receiver plane are effectively modelled as ringlike structures extending in the out-of-plane direction. In contrast to ray-theory, which is widely used in high-frequency applications, AxiSEM provides complete waveforms, thus giving access to frequency dependency, amplitude variations, and peculiar wave effects such as diffraction and caustics. Here we focus on the practical implications of the inherent axisymmetric geometry and show how the 2.5D-features of our method method can be used to model realistic anisotropic structures, by applying it to problems such as the D" region and the inner core.

Ultrasonic input-output for transmitting and receiving longitudinal transducers coupled to same face of isotropic elastic plate

NASA Technical Reports Server (NTRS)

Williams, J. H., Jr.; Karagulle, H.; Lee, S. S.

1982-01-01

The quantitative understanding of ultrasonic nondestructive evaluation parameters such as the stress wave factor were studied. Ultrasonic input/output characteristics for an isotropic elastic plate with transmitting and receiving longitudinal transducers coupled to the same face were analyzed. The asymptotic normal stress is calculated for an isotropic elastic half space subjected to a uniform harmonic normal stress applied to a circular region at the surface. The radiated stress waves are traced within the plate by considering wave reflections at the top and bottom faces. The output voltage amplitude of the receiving transducer is estimated by considering only longitudinal waves. Agreement is found between the output voltage wave packet amplitudes and times of arrival due to multiple reflections of the longitudinal waves.

A phase-plane analysis of localized frictional waves

NASA Astrophysics Data System (ADS)

Putelat, T.; Dawes, J. H. P.; Champneys, A. R.

2017-07-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

A phase-plane analysis of localized frictional waves

PubMed Central

Dawes, J. H. P.; Champneys, A. R.

2017-01-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick–slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types. PMID:28804255

A phase-plane analysis of localized frictional waves.

PubMed

Putelat, T; Dawes, J H P; Champneys, A R

2017-07-01

Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.

Fabric dependence of wave propagation in anisotropic porous media

PubMed Central

Cowin, Stephen C.; Cardoso, Luis

2012-01-01

Current diagnosis of bone loss and osteoporosis is based on the measurement of the Bone Mineral Density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as Speed of Sound (SOS) and Broadband Ultrasound Attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot’s poroelastic wave propagation theory. In this paper the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric - a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone. PMID:20461539

Quasi-Elastic Neutron Scattering Studies of the Slow Dynamics of Supercooled and Glassy Aspirin

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

Zhang, Yang; Tyagi, M.; Mamontov, Eugene

Aspirin, also known as acetylsalicylic acid (ASA), is not only a wonderful drug, but also a good glass former. Therefore, it serves as an important molecular system to study the near-arrest and arrested phenomena. In this paper, a high-resolution quasi-elastic neutron scattering (QENS) technique is used to investigate the slow dynamics of supercooled liquid and glassy aspirin from 410 K down to 350 K. The measured QENS spectra can be analyzed with a stretched exponential model. We find that (i) the stretched exponent (Q) is independent of the wave vector transfer Q in the measured Q-range, and (ii) the structuralmore » relaxation time (Q) follows a power law dependence on Q. Consequently, the Q-independent structural relaxation time 0 can be extracted for each temperature to characterize the slow dynamics of aspirin. The temperature dependence of 0 can be fitted with the mode coupling power law, the Vogel-Fulcher-Tammann equation and a universal equation for fragile glass forming liquids recently proposed by M. Tokuyama in the measured temperature range. The calculated dynamic response function T(Q,t) using the experimentally determined self-intermediate scattering function of the hydrogen atoms of aspirin shows a direct evidence of the enhanced dynamic fluctuations as the aspirin is increasingly supercooled, in agreement with the fixed-time mean squared displacement x2 and non-Gaussian parameter 2 extracted from the elastic scattering.« less

Strain and thermally induced magnetic dynamics and spin current in magnetic insulators subject to transient optical grating

NASA Astrophysics Data System (ADS)

Wang, Xi-Guang; Chotorlishvili, Levan; Berakdar, Jamal

2017-07-01

We analyze the magnetic dynamics and particularlythe spin current in an open-circuit ferromagnetic insulator irradiated by two intense, phase-locked laser pulses. The interference of the laser beams generates a transient optical grating and a transient spatio-temporal temperature distribution. Both effects lead to elastic and heat waves at the surface and into the bulk of the sample. The strain induced spin current as well as the thermally induced magnonic spin current are evaluated numerically on the basis of micromagnetic simulations using solutions of the heat equation. We observe that the thermo-elastically induced magnonic spin current propagates on a distance larger than the characteristic size of thermal profile, an effect useful for applications in remote detection of spin caloritronics phenomena. Our findings point out that exploiting strain adds a new twist to heat-assisted magnetic switching and spin-current generation for spintronic applications.

Effect of Initial Stress on the Dynamic Response of a Multi-Layered Plate-Strip Subjected to an Arbitrary Inclined Time-Harmonic Force

NASA Astrophysics Data System (ADS)

Daşdemir, A.

2017-08-01

The forced vibration of a multi-layered plate-strip with initial stress under the action of an arbitrary inclined time-harmonic force resting on a rigid foundation is considered. Within the framework of the piecewise homogeneous body model with the use of the three-dimensional linearized theory of elastic waves in initially stressed bodies (TLTEWISB), a mathematical modelling is presented in plane strain state. It is assumed that there exists the complete contact interaction at the interface between the layers and the materials of the layer are linearly elastic, homogeneous and isotropic. The governing system of the partial differential equations of motion for the considered problem is solved approximately by employing the Finite Element Method (FEM). Further, the influence of the initial stress parameter on the dynamic response of the plate-strip is presented.

Acoustic Velocity Log Numerical Simulation and Saturation Estimation of Gas Hydrate Reservoir in Shenhu Area, South China Sea

PubMed Central

Xiao, Kun; Zou, Changchun; Xiang, Biao; Liu, Jieqiong

2013-01-01

Gas hydrate model and free gas model are established, and two-phase theory (TPT) for numerical simulation of elastic wave velocity is adopted to investigate the unconsolidated deep-water sedimentary strata in Shenhu area, South China Sea. The relationships between compression wave (P wave) velocity and gas hydrate saturation, free gas saturation, and sediment porosity at site SH2 are studied, respectively, and gas hydrate saturation of research area is estimated by gas hydrate model. In depth of 50 to 245 m below seafloor (mbsf), as sediment porosity decreases, P wave velocity increases gradually; as gas hydrate saturation increases, P wave velocity increases gradually; as free gas saturation increases, P wave velocity decreases. This rule is almost consistent with the previous research result. In depth of 195 to 220 mbsf, the actual measurement of P wave velocity increases significantly relative to the P wave velocity of saturated water modeling, and this layer is determined to be rich in gas hydrate. The average value of gas hydrate saturation estimated from the TPT model is 23.2%, and the maximum saturation is 31.5%, which is basically in accordance with simplified three-phase equation (STPE), effective medium theory (EMT), resistivity log (Rt), and chloride anomaly method. PMID:23935407

Topologically protected edge states for out-of-plane and in-plane bulk elastic waves.

PubMed

Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo

2018-04-11

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

Topologically protected edge states for out-of-plane and in-plane bulk elastic waves

NASA Astrophysics Data System (ADS)

Huo, Shao-Yong; Chen, Jiu-Jiu; Huang, Hong-Bo

2018-04-01

Topological phononic insulators (TPnIs) show promise for application in the manipulation of acoustic waves for the design of low-loss transmission and perfectly integrated communication devices. Since solid phononic crystals exist as a transverse polarization mode and a mixed longitudinal-transverse polarization mode, the realization of topological edge states for both out-of-plane and in-plane bulk elastic waves is desirable to enhance the controllability of the edge waves in solid systems. In this paper, a two-dimensional (2D) solid/solid hexagonal-latticed phononic system that simultaneously supports the topologically protected edge states for out-of-plane and in-plane bulk elastic waves is investigated. Firstly, two pairs of two-fold Dirac cones, respectively corresponding to the out-of-plane and in-plane waves, are obtained at the same frequency by tuning the crystal parameters. Then, a strategy of zone folding is invoked to form double Dirac cones. By shrinking and expanding the steel scatterer, the lattice symmetry is broken, and band inversions induced, giving rise to an intriguing topological phase transition. Finally, the topologically protected edge states for both out-of-plane and in-plane bulk elastic waves, which can be simultaneously located at the frequency range from 1.223 to 1.251 MHz, are numerically observed. Robust pseudospin-dependent elastic edge wave propagation along arbitrary paths is further demonstrated. Our results will significantly broaden its practical application in the engineering field.

An irregular lattice method for elastic wave propagation

NASA Astrophysics Data System (ADS)

O'Brien, Gareth S.; Bean, Christopher J.

2011-12-01

Lattice methods are a class of numerical scheme which represent a medium as a connection of interacting nodes or particles. In the case of modelling seismic wave propagation, the interaction term is determined from Hooke's Law including a bond-bending term. This approach has been shown to model isotropic seismic wave propagation in an elastic or viscoelastic medium by selecting the appropriate underlying lattice structure. To predetermine the material constants, this methodology has been restricted to regular grids, hexagonal or square in 2-D or cubic in 3-D. Here, we present a method for isotropic elastic wave propagation where we can remove this lattice restriction. The methodology is outlined and a relationship between the elastic material properties and an irregular lattice geometry are derived. The numerical method is compared with an analytical solution for wave propagation in an infinite homogeneous body along with comparing the method with a numerical solution for a layered elastic medium. The dispersion properties of this method are derived from a plane wave analysis showing the scheme is more dispersive than a regular lattice method. Therefore, the computational costs of using an irregular lattice are higher. However, by removing the regular lattice structure the anisotropic nature of fracture propagation in such methods can be removed.

Strength and deformation of shocked diamond single crystals: Orientation dependence

DOE PAGES

Lang, John Michael Jr.; Winey, J. M.; Gupta, Y. M.

2018-03-01

Understanding and quantifying the strength or elastic limit of diamond single crystals is of considerable scientific and technological importance, and has been a subject of long standing theoretical and experimental interest. To examine the effect of crystalline anisotropy on strength and deformation of shocked diamond single crystals, plate impact experiments were conducted to measure wave profiles at various elastic impact stresses up to ~120 GPa along [110] and [111] crystal orientations. Using laser interferometry, particle velocity histories and shock velocities in the diamond samples were measured and were compared with similar measurements published previously for shock compression along the [100]more » direction. Wave profiles for all three orientations showed large elastic wave amplitudes followed by time-dependent inelastic deformation. From the measured wave profiles, the elastic limits were determined under well characterized uniaxial strain loading conditions. The measured elastic wave amplitudes for the [110] and [111] orientations were lower for higher elastic impact stress (stress attained for an elastic diamond response), consistent with the result reported previously for [100] diamond. The maximum resolved shear stress (MRSS) on the {111}<110> slip systems was determined for each orientation, revealing significant orientation dependence. The MRSS values for the [100] and [110] orientations (~33 GPa) are 25-30% of theoretical estimates; the MRSS value for the [111] orientation is significantly lower (~23 GPa). Our results demonstrate that the MRSS depends strongly on the stress component normal to the {111} planes or the resolved normal stress (RNS), suggesting that the RNS plays a key role in inhibiting the onset of inelastic deformation. Lower elastic wave amplitudes at higher peak stress and the effect of the RNS are inconsistent with typical dislocation slip mechanisms of inelastic deformation, suggesting instead an inelastic response characteristic of shocked brittle solids. The present results show that the elastic limit (or material strength) of diamond single crystals cannot be described using traditional isotropic approaches, and typical plasticity models cannot be used to describe the inelastic deformation of diamond. Analysis of the measured wave profiles beyond the elastic limit, including characterization of the peak state, requires numerical simulations that incorporate a time-dependent, anisotropic, inelastic deformation response. Development of such a material description for diamond is an important need.« less

Strength and deformation of shocked diamond single crystals: Orientation dependence

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

Lang, John Michael Jr.; Winey, J. M.; Gupta, Y. M.

Understanding and quantifying the strength or elastic limit of diamond single crystals is of considerable scientific and technological importance, and has been a subject of long standing theoretical and experimental interest. To examine the effect of crystalline anisotropy on strength and deformation of shocked diamond single crystals, plate impact experiments were conducted to measure wave profiles at various elastic impact stresses up to ~120 GPa along [110] and [111] crystal orientations. Using laser interferometry, particle velocity histories and shock velocities in the diamond samples were measured and were compared with similar measurements published previously for shock compression along the [100]more » direction. Wave profiles for all three orientations showed large elastic wave amplitudes followed by time-dependent inelastic deformation. From the measured wave profiles, the elastic limits were determined under well characterized uniaxial strain loading conditions. The measured elastic wave amplitudes for the [110] and [111] orientations were lower for higher elastic impact stress (stress attained for an elastic diamond response), consistent with the result reported previously for [100] diamond. The maximum resolved shear stress (MRSS) on the {111}<110> slip systems was determined for each orientation, revealing significant orientation dependence. The MRSS values for the [100] and [110] orientations (~33 GPa) are 25-30% of theoretical estimates; the MRSS value for the [111] orientation is significantly lower (~23 GPa). Our results demonstrate that the MRSS depends strongly on the stress component normal to the {111} planes or the resolved normal stress (RNS), suggesting that the RNS plays a key role in inhibiting the onset of inelastic deformation. Lower elastic wave amplitudes at higher peak stress and the effect of the RNS are inconsistent with typical dislocation slip mechanisms of inelastic deformation, suggesting instead an inelastic response characteristic of shocked brittle solids. The present results show that the elastic limit (or material strength) of diamond single crystals cannot be described using traditional isotropic approaches, and typical plasticity models cannot be used to describe the inelastic deformation of diamond. Analysis of the measured wave profiles beyond the elastic limit, including characterization of the peak state, requires numerical simulations that incorporate a time-dependent, anisotropic, inelastic deformation response. Development of such a material description for diamond is an important need.« less

Strength and deformation of shocked diamond single crystals: Orientation dependence

NASA Astrophysics Data System (ADS)

Lang, J. M.; Winey, J. M.; Gupta, Y. M.

2018-03-01

Understanding and quantifying the strength or elastic limit of diamond single crystals is of considerable scientific and technological importance, and has been a subject of long standing theoretical and experimental interest. To examine the effect of crystalline anisotropy on strength and deformation of shocked diamond single crystals, plate impact experiments were conducted to measure wave profiles at various elastic impact stresses up to ˜120 GPa along [110] and [111] crystal orientations. Using laser interferometry, particle velocity histories and shock velocities in the diamond samples were measured and were compared with similar measurements published previously for shock compression along the [100] direction. Wave profiles for all three orientations showed large elastic wave amplitudes followed by time-dependent inelastic deformation. From the measured wave profiles, the elastic limits were determined under well characterized uniaxial strain loading conditions. The measured elastic wave amplitudes for the [110] and [111] orientations were lower for higher elastic impact stress (stress attained for an elastic diamond response), consistent with the result reported previously for [100] diamond. The maximum resolved shear stress (MRSS) on the {111}⟨110⟩ slip systems was determined for each orientation, revealing significant orientation dependence. The MRSS values for the [100] and [110] orientations (˜33 GPa) are 25%-30% of theoretical estimates; the MRSS value for the [111] orientation is significantly lower (˜23 GPa). Our results demonstrate that the MRSS depends strongly on the stress component normal to the {111} planes or the resolved normal stress (RNS), suggesting that the RNS plays a key role in inhibiting the onset of inelastic deformation. Lower elastic wave amplitudes at higher peak stress and the effect of the RNS are inconsistent with typical dislocation slip mechanisms of inelastic deformation, suggesting instead an inelastic response characteristic of shocked brittle solids. The present results show that the elastic limit (or material strength) of diamond single crystals cannot be described using traditional isotropic approaches, and typical plasticity models cannot be used to describe the inelastic deformation of diamond. Analysis of the measured wave profiles beyond the elastic limit, including characterization of the peak state, requires numerical simulations that incorporate a time-dependent, anisotropic, inelastic deformation response. Development of such a material description for diamond is an important need.

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.

Simultaneous large band gaps and localization of electromagnetic and elastic waves in defect-free quasicrystals.

PubMed

Yu, Tianbao; Wang, Zhong; Liu, Wenxing; Wang, Tongbiao; Liu, Nianhua; Liao, Qinghua

2016-04-18

We report numerically large and complete photonic and phononic band gaps that simultaneously exist in eight-fold phoxonic quasicrystals (PhXQCs). PhXQCs can possess simultaneous photonic and phononic band gaps over a wide range of geometric parameters. Abundant localized modes can be achieved in defect-free PhXQCs for all photonic and phononic polarizations. These defect-free localized modes exhibit multiform spatial distributions and can confine simultaneously electromagnetic and elastic waves in a large area, thereby providing rich selectivity and enlarging the interaction space of optical and elastic waves. The simulated results based on finite element method show that quasiperiodic structures formed of both solid rods in air and holes in solid materials can simultaneously confine and tailor electromagnetic and elastic waves; these structures showed advantages over the periodic counterparts.

Shear elastic modulus estimation from indentation and SDUV on gelatin phantoms

PubMed Central

Amador, Carolina; Urban, Matthew W.; Chen, Shigao; Chen, Qingshan; An, Kai-Nan; Greenleaf, James F.

2011-01-01

Tissue mechanical properties such as elasticity are linked to tissue pathology state. Several groups have proposed shear wave propagation speed to quantify tissue mechanical properties. It is well known that biological tissues are viscoelastic materials; therefore velocity dispersion resulting from material viscoelasticity is expected. A method called Shearwave Dispersion Ultrasound Vibrometry (SDUV) can be used to quantify tissue viscoelasticity by measuring dispersion of shear wave propagation speed. However, there is not a gold standard method for validation. In this study we present an independent validation method of shear elastic modulus estimation by SDUV in 3 gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of elasticity derived from shear wave group velocities. The shear elastic moduli from indentation were 1.16, 3.40 and 5.6 kPa for a 7, 10 and 15% gelatin phantom respectively. SDUV measurements were 1.61, 3.57 and 5.37 kPa for the gelatin phantoms respectively. Shear elastic moduli derived from shear wave group velocities were 1.78, 5.2 and 7.18 kPa for the gelatin phantoms respectively. The shear elastic modulus estimated from the SDUV, matched the elastic modulus measured by indentation. On the other hand, shear elastic modulus estimated by group velocity did not agree with indentation test estimations. These results suggest that shear elastic modulus estimation by group velocity will be bias when the medium being investigated is dispersive. Therefore a rheological model should be used in order to estimate mechanical properties of viscoelastic materials. PMID:21317078

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.

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.

Corneal elastic anisotropy and hysteresis as a function of IOP assessed by optical coherence elastography

NASA Astrophysics Data System (ADS)

Li, Jiasong; Singh, Manmohan; Han, Zhaolong; Wu, Chen; Raghunathan, Raksha; Liu, Chih-Hao; Nair, Achuth; Noorani, Shezaan; Aglyamov, Salavat R.; Twa, Michael D.; Larin, Kirill V.

2016-03-01

The mechanical anisotropic properties of the cornea can be an important indicator for determining the onset and severity of different diseases and can be used to assess the efficacy of various therapeutic interventions, such as cross-linking and LASIK surgery. In this work, we introduce a noncontact method of assessing corneal mechanical anisotropy as a function of intraocular pressure (IOP) using optical coherence elastography (OCE). A focused air-pulse induced low amplitude (<10 μm) elastic waves in fresh porcine corneas in the whole eye-globe configuration in situ. A phase-stabilized swept source optical coherence elastography (PhS-SSOCE) system imaged the elastic wave propagation at stepped radial angles, and the OCE measurements were repeated as the IOP was cycled. The elastic wave velocity was then quantified to determine the mechanical anisotropy and hysteresis of the cornea. The results show that the elastic anisotropy at the corneal of the apex of the cornea becomes more pronounced at higher IOPs, and that there are distinct radial angles of higher and lower stiffness. Due to the noncontact nature and small amplitude of the elastic wave, this method may be useful for characterizing the elastic anisotropy of ocular and other tissues in vivo completely noninvasively.

The effects of plastic waves on the numerical convergence of the viscous-plastic and elastic-viscous-plastic sea-ice models

NASA Astrophysics Data System (ADS)

Williams, James; Tremblay, L. Bruno; Lemieux, Jean-François

2017-07-01

The plastic wave speed is derived from the linearized 1-D version of the widely used viscous-plastic (VP) and elastic-viscous-plastic (EVP) sea-ice models. Courant-Friedrichs-Lewy (CFL) conditions are derived using the propagation speed of the wave. 1-D numerical experiments of the VP, EVP and EVP* models successfully recreate a reference solution when the CFL conditions are satisfied, in agreement with the theory presented. The IMplicit-EXplicit (IMEX) method is shown to effectively alleviate the plastic wave CFL constraint on the timestep in the implicitly solved VP model in both 1-D and 2-D. In 2-D, the EVP and EVP* models show first order error in the simulated velocity field when the plastic wave is not resolved. EVP simulations are performed with various advective timestep, number of subcycles, and elastic-wave damping timescales. It is found that increasing the number of subcycles beyond that needed to resolve the elastic wave does not improve the quality of the solution. It is found that reducing the elastic wave damping timescale reduces the spatial extent of first order errors cause by the unresolved plastic wave. Reducing the advective timestep so that the plastic wave is resolved also reduces the velocity error in terms of magnitude and spatial extent. However, the parameter set required for convergence to within the error bars of satellite (RGPS) deformation fields is impractical for use in climate model simulations. The behavior of the EVP* method is analogous to that of the EVP method except that it is not possible to reduce the damping timescale with α = β.

An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media

DOE PAGES

Gao, Kai; Huang, Lianjie

2017-08-31

The rotated staggered-grid (RSG) finite-difference method is a powerful tool for elastic-wave modeling in 2D anisotropic media where the symmetry axes of anisotropy are not aligned with the coordinate axes. We develop an improved RSG scheme with fourth-order temporal accuracy to reduce the numerical dispersion associated with prolonged wave propagation or a large temporal step size. The high-order temporal accuracy is achieved by including high-order temporal derivatives, which can be converted to high-order spatial derivatives to reduce computational cost. Dispersion analysis and numerical tests show that our method exhibits very low temporal dispersion even with a large temporal step sizemore » for elastic-wave modeling in complex anisotropic media. Using the same temporal step size, our method is more accurate than the conventional RSG scheme. In conclusion, our improved RSG scheme is therefore suitable for prolonged modeling of elastic-wave propagation in 2D anisotropic media.« less

An improved rotated staggered-grid finite-difference method with fourth-order temporal accuracy for elastic-wave modeling in anisotropic media

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

Gao, Kai; Huang, Lianjie

The rotated staggered-grid (RSG) finite-difference method is a powerful tool for elastic-wave modeling in 2D anisotropic media where the symmetry axes of anisotropy are not aligned with the coordinate axes. We develop an improved RSG scheme with fourth-order temporal accuracy to reduce the numerical dispersion associated with prolonged wave propagation or a large temporal step size. The high-order temporal accuracy is achieved by including high-order temporal derivatives, which can be converted to high-order spatial derivatives to reduce computational cost. Dispersion analysis and numerical tests show that our method exhibits very low temporal dispersion even with a large temporal step sizemore » for elastic-wave modeling in complex anisotropic media. Using the same temporal step size, our method is more accurate than the conventional RSG scheme. In conclusion, our improved RSG scheme is therefore suitable for prolonged modeling of elastic-wave propagation in 2D anisotropic media.« less

Identification and control of structures in space

NASA Technical Reports Server (NTRS)

Meirovitch, L.; Quinn, R. D.; Norris, M. A.

1984-01-01

The derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) is reported and the equations of motion of a similar structure orbiting the earth are also derived. The structure is assumed to undergo large rigid-body maneuvers and small elastic deformations. A perturbation approach is proposed whereby the quantities defining the rigid-body maneuver are assumed to be relatively large, with the elastic deformations and deviations from the rigid-body maneuver being relatively small. The perturbation equations have the form of linear equations with time-dependent coefficients. An active control technique can then be formulated to permit maneuvering of the spacecraft and simultaneously suppressing the elastic vibration.

Statistical analysis of vibration in tyres

NASA Astrophysics Data System (ADS)

Le Bot, Alain; Bazari, Zakia; Klein, Philippe; Lelong, Joël

2017-03-01

The vibration in tyres submitted to random forces in the contact zone is investigated with the model of prestressed orthotropic plate on visco-elastic foundation. It is shown that beyond a cut-on frequency a single wave propagates whose speed is directional-dependent. A systematic numerical exploration of the governing equation solutions shows that three regimes may exist in such plates. These are modal field, diffuse field and free field. For actual tyres which present a high level of damping, the passage from low to high frequencies generally explores the modal and free field regimes but not the diffuse field regime.

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

Adaptive elastic metasurfaces for wave front manipulation

NASA Astrophysics Data System (ADS)

Li, Shilong; Xu, Jiawen; Tang, Jiong

2018-04-01

In this research, by combining the concept of elastic metasurfaces with piezoelectric transducer with shunted circuitry, we investigate the designs of elastic metasurfaces, consisting of an array of piezoelectric transducers shunted with negative capacitance, which is capable of modulating wave fronts adaptively. In order to construct different adaptive elastic metasurfaces, different phase profiles along the interface can be framed through properly adjusting the negative capacitance values. Flat planar lenses for focusing transmitted A0 Lamb waves are achieved, and possess the flexibility of changing focal locations through electromechanical tunings. Additionally, nonparaxial self-bending beams with arbitrary trajectories and source illusion devices can also be accomplished owing to the free manipulation of phase shifts. With their versatility and tunability, the adaptive elastic metasurfaces could pave new avenues to a wide variety of potential applications, such as nondestructive testing, ultrasound imaging, and caustic engineering.

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.

Effect of viscosity on the wave propagation: Experimental determination of compression and expansion pulse wave velocity in fluid-fill elastic tube.

PubMed

Stojadinović, Bojana; Tenne, Tamar; Zikich, Dragoslav; Rajković, Nemanja; Milošević, Nebojša; Lazović, Biljana; Žikić, Dejan

2015-11-26

The velocity by which the disturbance travels through the medium is the wave velocity. Pulse wave velocity is one of the main parameters in hemodynamics. The study of wave propagation through the fluid-fill elastic tube is of great importance for the proper biophysical understanding of the nature of blood flow through of cardiovascular system. The effect of viscosity on the pulse wave velocity is generally ignored. In this paper we present the results of experimental measurements of pulse wave velocity (PWV) of compression and expansion waves in elastic tube. The solutions with different density and viscosity were used in the experiment. Biophysical model of the circulatory flow is designed to perform measurements. Experimental results show that the PWV of the expansion waves is higher than the compression waves during the same experimental conditions. It was found that the change in viscosity causes a change of PWV for both waves. We found a relationship between PWV, fluid density and viscosity. Copyright © 2015 Elsevier Ltd. All rights reserved.

Second order Method for Solving 3D Elasticity Equations with Complex Interfaces

PubMed Central

Wang, Bao; Xia, Kelin; Wei, Guo-Wei

2015-01-01

Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson’s ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins.. PMID:25914422

Elastic constants and dynamics in nematic liquid crystals

NASA Astrophysics Data System (ADS)

Humpert, Anja; Allen, Michael P.

2015-09-01

In this paper, we present molecular dynamics calculations of the Frank elastic constants, and associated time correlation functions, in nematic liquid crystals. We study two variants of the Gay-Berne potential, and use system sizes of half a million molecules, significantly larger than in previous studies of elastic behaviour. Equilibrium orientational fluctuations in reciprocal (k-) space were calculated, to determine the elastic constants by fitting at low |k|; our results indicate that small system size may be a source of inaccuracy in previous work. Furthermore, the dynamics of the Gay-Berne nematic were studied by calculating time correlation functions of components of the order tensor, together with associated components of the velocity field, for a set of wave vectors k. Confirming our earlier work, we found exponential decay for splay and twist correlations, and oscillatory exponential decay for the bend correlation. In this work, we confirm similar behaviour for the corresponding velocity components. In all cases, the decay rates, and oscillation frequencies, were found to be accurately proportional to k2 for small k, as predicted by the equations of nematodynamics. However, the observation of oscillatory bend fluctuations, and corresponding oscillatory shear flow decay, is in contradiction to the usual assumptions appearing in the literature, and in standard texts. We discuss the advantages and drawbacks of using large systems in these calculations.

On the Identication of Wrinkles of Membrane by Traveling Elastic Wave

NASA Astrophysics Data System (ADS)

Akaike, Yusuke; Yokozeki, Tomhiro

2012-07-01

Wrinkling is one of the critical factors that degrade the performance of space membrane structures. This paper proposes the way to detect the size and the position of wrinkles by observing reflection of the elastic waves at the boundary between the wrinkled section and the flat section. A wrinkle is modeled as a part of an annulus, and the effects of thickness, material properties and curvature of the membrane on the reflection rates of elastic waves are investigated. Finally, the proposed identification method is experimentally demonstrated.

Advantages of formulating an evolution equation directly for elastic distortional deformation in finite deformation plasticity

NASA Astrophysics Data System (ADS)

Rubin, M. B.; Cardiff, P.

2017-11-01

Simo (Comput Methods Appl Mech Eng 66:199-219, 1988) proposed an evolution equation for elastic deformation together with a constitutive equation for inelastic deformation rate in plasticity. The numerical algorithm (Simo in Comput Methods Appl Mech Eng 68:1-31, 1988) for determining elastic distortional deformation was simple. However, the proposed inelastic deformation rate caused plastic compaction. The corrected formulation (Simo in Comput Methods Appl Mech Eng 99:61-112, 1992) preserves isochoric plasticity but the numerical integration algorithm is complicated and needs special methods for calculation of the exponential map of a tensor. Alternatively, an evolution equation for elastic distortional deformation can be proposed directly with a simplified constitutive equation for inelastic distortional deformation rate. This has the advantage that the physics of inelastic distortional deformation is separated from that of dilatation. The example of finite deformation J2 plasticity with linear isotropic hardening is used to demonstrate the simplicity of the numerical algorithm.

Elasticity imaging of speckle-free tissue regions with moving acoustic radiation force and phase-sensitive optical coherence tomography

NASA Astrophysics Data System (ADS)

Hsieh, Bao-Yu; Song, Shaozhen; Nguyen, Thu-Mai; Yoon, Soon Joon; Shen, Tueng; Wang, Ruikang; O'Donnell, Matthew

2016-03-01

Phase-sensitive optical coherence tomography (PhS-OCT) can be utilized for quantitative shear-wave elastography using speckle tracking. However, current approaches cannot directly reconstruct elastic properties in speckle-less or speckle-free regions, for example within the crystalline lens in ophthalmology. Investigating the elasticity of the crystalline lens could improve understanding and help manage presbyopia-related pathologies that change biomechanical properties. We propose to reconstruct the elastic properties in speckle-less regions by sequentially launching shear waves with moving acoustic radiation force (mARF), and then detecting the displacement at a specific speckle-generating position, or limited set of positions, with PhS-OCT. A linear ultrasound array (with a center frequency of 5 MHz) interfaced with a programmable imaging system was designed to launch shear waves by mARF. Acoustic sources were electronically translated to launch shear waves at laterally shifted positions, where displacements were detected by speckle tracking images produced by PhS-OCT operating in M-B mode with a 125-kHz A-line rate. Local displacements were calculated and stitched together sequentially based on the distance between the acoustic source and the detection beam. Shear wave speed, and the associated elasticity map, were then reconstructed based on a time-of-flight algorithm. In this study, moving-source shear wave elasticity imaging (SWEI) can highlight a stiff inclusion within an otherwise homogeneous phantom but with a CNR increased by 3.15 dB compared to a similar image reconstructed with moving-detector SWEI. Partial speckle-free phantoms were also investigated to demonstrate that the moving-source sequence could reconstruct the elastic properties of speckle-free regions. Results show that harder inclusions within the speckle-free region can be detected, suggesting that this imaging method may be able to detect the elastic properties of the crystalline lens.

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.

Minimum film thickness in elliptical contacts for different regimes of fluid-film lubrication

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1978-01-01

The film-parameter equations are provided for four fluid-film lubrication regimes found in elliptical contacts. These regimes are isoviscous-rigid; viscous-rigid; elastohydrodynamic of low-elastic-modulus materials, or isoviscous-elastic; and elastohydrodynamic, or viscous-elastic. The influence or lack of influence of elastic and viscous effects is the factor that distinguishes these regimes. The film-parameter equations for the respective regimes come from earlier theoretical studies by the authors on elastohydrodynamic and hydrodynamic lubrication of elliptical conjunctions. These equations are restated and the results are presented as a map of the lubrication regimes, with film-thickness contours on a log-log grid of the viscosity and elasticity parameters for five values of the ellipticity parameter. The results present a complete theoretical film-parameter solution for elliptical contacts in the four lubrication regimes.

Equations of motion of slung load systems with results for dual lift

NASA Technical Reports Server (NTRS)

Cicolani, Luigi S.; Kanning, Gerd

1990-01-01

General simulation equations are derived for the rigid body motion of slung load systems. These systems are viewed as consisting of several rigid bodies connected by straight-line cables or links. The suspension can be assumed to be elastic or inelastic, both cases being of interest in simulation and control studies. Equations for the general system are obtained via D'Alembert's principle and the introduction of generalized velocity coordinates. Three forms are obtained. Two of these generalize previous case-specific results for single helicopter systems with elastic or inelastic suspensions. The third is a new formulation for inelastic suspensions. It is derived from the elastic suspension equations by choosing the generalized coordinates so as to separate motion due to cable stretching from motion with invariant cable lengths. The result is computationally more efficient than the conventional formulation, and is readily integrated with the elastic suspension formulation and readily applied to the complex dual lift and multilift systems. Equations are derived for dual lift systems. Three proposed suspension arrangements can be integrated in a single equation set. The equations are given in terms of the natural vectors and matrices of three-dimensional rigid body mechanics and are tractable for both analysis and programming.

Modeling the effect of orientation on the shock response of a damageable composite material

NASA Astrophysics Data System (ADS)

Lukyanov, Alexander A.

2012-10-01

A carbon fiber-epoxy composite (CFEC) shock response in the through thickness orientation and in one of the fiber directions is significantly different. The hydrostatic pressure inside anisotropic materials depends on deviatoric strain components as well as volumetric strain. Non-linear effects, such as shock effects, can be incorporated through the volumetric straining in the material. Thus, a new basis is required to couple the anisotropic material stiffness and strength with anisotropic shock effects, associated energy dependence, and damage softening process. This article presents these constitutive equations for shock wave modeling of a damageable carbon fiber-epoxy composite. Modeling the effect of fiber orientation on the shock response of a CFEC has been performed using a generalized decomposition of the stress tensor [A. A. Lukyanov, Int. J. Plast. 24, 140 (2008)] and Mie-Grüneisen's extrapolation of high-pressure shock Hugoniot states to other thermodynamics states for shocked CFEC materials. The three-wave structure (non-linear anisotropic, fracture, and isotropic elastic waves) that accompanies damage softening process is also proposed in this work for describing CFEC behavior under shock loading which allows to remove any discontinuities observed in the linear case for relation between shock velocities and particle velocities [A. A. Lukyanov, Eur. Phys. J. B 74, 35 (2010)]. Different Hugoniot stress levels are obtained when the material is impacted in different directions; their good agreement with the experiment demonstrates that the anisotropic equation of state, strength, and damage model are adequate for the simulation of shock wave propagation within damageable CFEC material. Remarkably, in the through thickness orientation, the material behaves similar to a simple polymer whereas in the fiber direction, the proposed in this paper model explains an initial ramp, before at sufficiently high stresses, and a much faster rising shock above it. The numerical results for shock wave modeling using proposed constitutive equations are presented, discussed, and future studies are outlined.

Wave propagation in magneto-electro-elastic multilayered plates with nonlocal effect

NASA Astrophysics Data System (ADS)

Chen, Jiangyi; Guo, Junhong; Pan, Ernian

2017-07-01

In this paper, analytical solutions for propagation of time-harmonic waves in three-dimensional, transversely isotropic, magnetoelectroelastic and multilayered plates with nonlocal effect are derived. We first convert the time-harmonic wave problem into a linear eigenvalue system, from which we obtain the general solutions of the extended displacements and stresses. The solutions are then employed to derive the propagator matrix which connects the field variables at the upper and lower interfaces of each layer. Making use of the continuity conditions of the physical quantities across the interface, the global propagator relation is assembled by propagating the solutions in each layer from the bottom to the top of the layered plate. From the global propagator matrix, the dispersion equation is obtained by imposing the traction-free boundary conditions on both the top and bottom surfaces of the layered plate. Dispersion curves and mode shapes in layered plates made of piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials are presented to show the influence of the nonlocal parameter, stacking sequence, as well as the orientation of incident wave on the time-harmonic field response.

Interaction of wave with a body submerged below an ice sheet with multiple arbitrarily spaced cracks

NASA Astrophysics Data System (ADS)

Li, Z. F.; Wu, G. X.; Ji, C. Y.

2018-05-01

The problem of wave interaction with a body submerged below an ice sheet with multiple arbitrarily spaced cracks is considered, based on the linearized velocity potential theory together with the boundary element method. The ice sheet is modeled as a thin elastic plate with uniform properties, and zero bending moment and shear force conditions are enforced at the cracks. The Green function satisfying all the boundary conditions including those at cracks, apart from that on the body surface, is derived and is expressed in an explicit integral form. The boundary integral equation for the velocity potential is constructed with an unknown source distribution over the body surface only. The wave/crack interaction problem without the body is first solved directly without the need for source. The convergence and comparison studies are undertaken to show the accuracy and reliability of the solution procedure. Detailed numerical results through the hydrodynamic coefficients and wave exciting forces are provided for a body submerged below double cracks and an array of cracks. Some unique features are observed, and their mechanisms are analyzed.

Should tsunami simulations include a nonzero initial horizontal velocity?

NASA Astrophysics Data System (ADS)

Lotto, Gabriel C.; Nava, Gabriel; Dunham, Eric M.

2017-08-01

Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require initial conditions on sea surface height and depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a "full-physics" integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). Full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor confirm that substantial horizontal momentum is imparted to the ocean. However, almost all of that initial momentum is carried away by ocean acoustic waves, with negligible momentum imparted to the tsunami. We also compare tsunami propagation in each simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial velocity. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves from ocean acoustic and seismic waves at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity.[Figure not available: see fulltext.

Should tsunami models use a nonzero initial condition for horizontal velocity?

NASA Astrophysics Data System (ADS)

Nava, G.; Lotto, G. C.; Dunham, E. M.

2017-12-01

Tsunami propagation in the open ocean is most commonly modeled by solving the shallow water wave equations. These equations require two initial conditions: one on sea surface height and another on depth-averaged horizontal particle velocity or, equivalently, horizontal momentum. While most modelers assume that initial velocity is zero, Y.T. Song and collaborators have argued for nonzero initial velocity, claiming that horizontal displacement of a sloping seafloor imparts significant horizontal momentum to the ocean. They show examples in which this effect increases the resulting tsunami height by a factor of two or more relative to models in which initial velocity is zero. We test this claim with a "full-physics" integrated dynamic rupture and tsunami model that couples the elastic response of the Earth to the linearized acoustic-gravitational response of a compressible ocean with gravity; the model self-consistently accounts for seismic waves in the solid Earth, acoustic waves in the ocean, and tsunamis (with dispersion at short wavelengths). We run several full-physics simulations of subduction zone megathrust ruptures and tsunamis in geometries with a sloping seafloor, using both idealized structures and a more realistic Tohoku structure. Substantial horizontal momentum is imparted to the ocean, but almost all momentum is carried away in the form of ocean acoustic waves. We compare tsunami propagation in each full-physics simulation to that predicted by an equivalent shallow water wave simulation with varying assumptions regarding initial conditions. We find that the initial horizontal velocity conditions proposed by Song and collaborators consistently overestimate the tsunami amplitude and predict an inconsistent wave profile. Finally, we determine tsunami initial conditions that are rigorously consistent with our full-physics simulations by isolating the tsunami waves (from ocean acoustic and seismic waves) at some final time, and backpropagating the tsunami waves to their initial state by solving the adjoint problem. The resulting initial conditions have negligible horizontal velocity.

Computer program for investigating effects of nonlinear suspension-system elastic properties on parachute inflation loads and motions

NASA Technical Reports Server (NTRS)

Poole, L. R.

1972-01-01

A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.

Quantitative modeling of coupled piezo-elastodynamic behavior of piezoelectric actuators bonded to an elastic medium for structural health monitoring: a review.

PubMed

Huang, Guoliang; Song, Fei; Wang, Xiaodong

2010-01-01

Elastic waves, especially guided waves, generated by a piezoelectric actuator/sensor network, have shown great potential for on-line health monitoring of advanced aerospace, nuclear, and automotive structures in recent decades. Piezoelectric materials can function as both actuators and sensors in these applications due to wide bandwidth, quick response and low costs. One of the most fundamental issues surrounding the effective use of piezoelectric actuators is the quantitative evaluation of the resulting elastic wave propagation by considering the coupled piezo-elastodynamic behavior between the actuator and the host medium. Accurate characterization of the local interfacial stress distribution between the actuator and the host medium is the key issue for the problem. This paper presents a review of the development of analytical, numerical and hybrid approaches for modeling of the coupled piezo-elastodynamic behavior. The resulting elastic wave propagation for structural health monitoring is also summarized.

High strain rate deformation and fracture of the magnesium alloy Ma2-1 under shock wave loading

NASA Astrophysics Data System (ADS)

Garkushin, G. V.; Kanel', G. I.; Razorenov, S. V.

2012-05-01

This paper presents the results of measurements of the dynamic elastic limit and spall strength under shock wave loading of specimens of the magnesium alloy Ma2-1 with a thickness ranging from 0.25 to 10 mm at normal and elevated (to 550°C) temperatures. From the results of measurements of the decay of the elastic precursor of a shock compression wave, it has been found that the plastic strain rate behind the front of the elastic precursor decreases from 2 × 105 s-1 at a distance of 0.25 mm to 103 s-1 at a distance of 10 mm. The plastic strain rate in a shock wave is one order of magnitude higher than that in the elastic precursor at the same value of the shear stress. The spall strength of the alloy decreases as the solidus temperature is approached.