Exact solutions for the static bending of Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model

NASA Astrophysics Data System (ADS)

Wang, Y. B.; Zhu, X. W.; Dai, H. H.

2016-08-01

Though widely used in modelling nano- and micro- structures, Eringen's differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings are considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.

Free vibration analysis of microtubules based on the molecular mechanics and continuum beam theory.

PubMed

Zhang, Jin; Wang, Chengyuan

2016-10-01

A molecular structural mechanics (MSM) method has been implemented to investigate the free vibration of microtubules (MTs). The emphasis is placed on the effects of the configuration and the imperfect boundaries of MTs. It is shown that the influence of protofilament number on the fundamental frequency is strong, while the effect of helix-start number is almost negligible. The fundamental frequency is also found to decrease as the number of the blocked filaments at boundaries decreases. Subsequently, the Euler-Bernoulli beam theory is employed to reveal the physics behind the simulation results. Fitting the Euler-Bernoulli beam into the MSM data leads to an explicit formula for the fundamental frequency of MTs with various configurations and identifies a possible correlation between the imperfect boundary conditions and the length-dependent bending stiffness of MTs reported in experiments.

Symmetries and integrability of a fourth-order Euler-Bernoulli beam equation

NASA Astrophysics Data System (ADS)

Bokhari, Ashfaque H.; Mahomed, F. M.; Zaman, F. D.

2010-05-01

The complete symmetry group classification of the fourth-order Euler-Bernoulli ordinary differential equation, where the elastic modulus and the area moment of inertia are constants and the applied load is a function of the normal displacement, is obtained. We perform the Lie and Noether symmetry analysis of this problem. In the Lie analysis, the principal Lie algebra which is one dimensional extends in four cases, viz. the linear, exponential, general power law, and a negative fractional power law. It is further shown that two cases arise in the Noether classification with respect to the standard Lagrangian. That is, the linear case for which the Noether algebra dimension is one less than the Lie algebra dimension as well as the negative fractional power law. In the latter case the Noether algebra is three dimensional and is isomorphic to the Lie algebra which is sl(2,R). This exceptional case, although admitting the nonsolvable algebra sl(2,R), remarkably allows for a two-parameter family of exact solutions via the Noether integrals. The Lie reduction gives a second-order ordinary differential equation which has nonlocal symmetry.

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.

Dynamics of 3D Timoshenko gyroelastic beams with large attitude changes for the gyros

NASA Astrophysics Data System (ADS)

Hassanpour, Soroosh; Heppler, G. R.

2016-01-01

This work is concerned with the theoretical development of dynamic equations for undamped gyroelastic beams which are dynamic systems with continuous inertia, elasticity, and gyricity. Assuming unrestricted or large attitude changes for the axes of the gyros and utilizing generalized Hooke's law, Duleau torsion theory, and Timoshenko bending theory, the energy expressions and equations of motion for the gyroelastic beams in three-dimensional space are derived. The so-obtained comprehensive gyroelastic beam model is compared against earlier gyroelastic beam models developed using Euler-Bernoulli beam models and is used to study the dynamics of gyroelastic beams through numerical examples. It is shown that there are significant differences between the developed unrestricted Timoshenko gyroelastic beam model and the previously derived zero-order restricted Euler-Bernoulli gyroelastic beam models. These differences are more pronounced in the short beam and transverse gyricity cases.

A Revelation: Quantum-Statistics and Classical-Statistics are Analytic-Geometry Conic-Sections and Numbers/Functions: Euler, Riemann, Bernoulli Generating-Functions: Conics to Numbers/Functions Deep Subtle Connections

NASA Astrophysics Data System (ADS)

Descartes, R.; Rota, G.-C.; Euler, L.; Bernoulli, J. D.; Siegel, Edward Carl-Ludwig

2011-03-01

Quantum-statistics Dichotomy: Fermi-Dirac(FDQS) Versus Bose-Einstein(BEQS), respectively with contact-repulsion/non-condensation(FDCR) versus attraction/ condensationBEC are manifestly-demonstrated by Taylor-expansion ONLY of their denominator exponential, identified BOTH as Descartes analytic-geometry conic-sections, FDQS as Elllipse (homotopy to rectangle FDQS distribution-function), VIA Maxwell-Boltzmann classical-statistics(MBCS) to Parabola MORPHISM, VS. BEQS to Hyperbola, Archimedes' HYPERBOLICITY INEVITABILITY, and as well generating-functions[Abramowitz-Stegun, Handbook Math.-Functions--p. 804!!!], respectively of Euler-numbers/functions, (via Riemann zeta-function(domination of quantum-statistics: [Pathria, Statistical-Mechanics; Huang, Statistical-Mechanics]) VS. Bernoulli-numbers/ functions. Much can be learned about statistical-physics from Euler-numbers/functions via Riemann zeta-function(s) VS. Bernoulli-numbers/functions [Conway-Guy, Book of Numbers] and about Euler-numbers/functions, via Riemann zeta-function(s) MORPHISM, VS. Bernoulli-numbers/ functions, visa versa!!! Ex.: Riemann-hypothesis PHYSICS proof PARTLY as BEQS BEC/BEA!!!

Design and Analyze a New Measuring Lift Device for Fin Stabilizers Using Stiffness Matrix of Euler-Bernoulli Beam

PubMed Central

Liang, Lihua; Sun, Mingxiao; Shi, Hongyu; Luan, Tiantian

2017-01-01

Fin-angle feedback control is usually used in conventional fin stabilizers, and its actual anti-rolling effect is difficult to reach theoretical design requirements. Primarily, lift of control torque is a theoretical value calculated by static hydrodynamic characteristics of fin. However, hydrodynamic characteristics of fin are dynamic while fin is moving in waves. As a result, there is a large deviation between actual value and theoretical value of lift. Firstly, the reasons of deviation are analyzed theoretically, which could avoid a variety of interference factors and complex theoretical derivations. Secondly, a new device is designed for direct measurement of actual lift, which is composed of fin-shaft combined mechanism and sensors. This new device can make fin-shaft not only be the basic function of rotating fin, but also detect actual lift. Through analysis using stiffness matrix of Euler-Bernoulli beam, displacement of shaft-core end is measured instead of lift which is difficult to measure. Then quantitative relationship between lift and displacement is defined. Three main factors are analyzed with quantitative relationship. What is more, two installation modes of sensors and a removable shaft-end cover are proposed according to hydrodynamic characteristics of fin. Thus the new device contributes to maintenance and measurement. Lastly, the effectiveness and accuracy of device are verified by contrasting calculation and simulation on the basis of actual design parameters. And the new measuring lift method can be proved to be effective through experiments. The new device is achieved from conventional fin stabilizers. Accordingly, the reliability of original equipment is inherited. The alteration of fin stabilizers is minor, which is suitable for engineering application. In addition, the flexural properties of fin-shaft are digitized with analysis of stiffness matrix. This method provides theoretical support for engineering application by carrying out finite

Dynamic response of a viscoelastic Timoshenko beam

NASA Technical Reports Server (NTRS)

Kalyanasundaram, S.; Allen, D. H.; Schapery, R. A.

1987-01-01

The analysis presented in this study deals with the vibratory response of viscoelastic Timoshenko (1955) beams under the assumption of small material loss tangents. The appropriate method of analysis employed here may be applied to more complex structures. This study compares the damping ratios obtained from the Timoshenko and Euler-Bernoulli theories for a given viscoelastic material system. From this study the effect of shear deformation and rotary inertia on damping ratios can be identified.

Identification of unknown spatial load distributions in a vibrating Euler-Bernoulli beam from limited measured data

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Kawano, Alexandre

2016-05-01

Two types of inverse source problems of identifying asynchronously distributed spatial loads governed by the Euler-Bernoulli beam equation ρ (x){w}{tt}+μ (x){w}t+{({EI}(x){w}{xx})}{xx}-{T}r{u}{xx}={\\sum }m=1M{g}m(t){f}m(x), (x,t)\\in {{{Ω }}}T := (0,l)× (0,T), with hinged-clamped ends (w(0,t)={w}{xx}(0,t)=0,w(l,t) = {w}x(l,t)=0,t\\in (0,T)), are studied. Here {g}m(t) are linearly independent functions, describing an asynchronous temporal loading, and {f}m(x) are the spatial load distributions. In the first identification problem the values {ν }k(t),k=\\bar{1,K}, of the deflection w(x,t), are assumed to be known, as measured output data, in a neighbourhood of the finite set of points P:= \\{{x}k\\in (0,l),k=\\bar{1,K}\\}\\subset (0,l), corresponding to the internal points of a continuous beam, for all t\\in ]0,T[. In the second identification problem the values {θ }k(t),k=\\bar{1,K}, of the slope {w}x(x,t), are assumed to be known, as measured output data in a neighbourhood of the same set of points P for all t\\in ]0,T[. These inverse source problems will be defined subsequently as the problems ISP1 and ISP2. The general purpose of this study is to develop mathematical concepts and tools that are capable of providing effective numerical algorithms for the numerical solution of the considered class of inverse problems. Note that both measured output data {ν }k(t) and {θ }k(t) contain random noise. In the first part of the study we prove that each measured output data {ν }k(t) and {θ }k(t),k=\\bar{1,K} can uniquely determine the unknown functions {f}m\\in {H}-1(]0,l[),m=\\bar{1,M}. In the second part of the study we will introduce the input-output operators {{ K }}d :{L}2(0,T)\\mapsto {L}2(0,T),({{ K }}df)(t):= w(x,t;f),x\\in P, f(x) := ({f}1(x),\\ldots ,{f}M(x)), and {{ K }}s :{L}2(0,T)\\mapsto {L}2(0,T), ({{ K }}sf)(t):= {w}x(x,t;f), x\\in P , corresponding to the problems ISP1 and ISP2, and then reformulate these problems as the operator equations: {{ K

Accuracy of AFM force distance curves via direct solution of the Euler-Bernoulli equation

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

Eppell, Steven J., E-mail: steven.eppell@case.edu; Liu, Yehe; Zypman, Fredy R.

2016-03-15

In an effort to improve the accuracy of force-separation curves obtained from atomic force microscope data, we compare force-separation curves computed using two methods to solve the Euler-Bernoulli equation. A recently introduced method using a direct sequential forward solution, Causal Time-Domain Analysis, is compared against a previously introduced Tikhonov Regularization method. Using the direct solution as a benchmark, it is found that the regularization technique is unable to reproduce accurate curve shapes. Using L-curve analysis and adjusting the regularization parameter, λ, to match either the depth or the full width at half maximum of the force curves, the two techniquesmore » are contrasted. Matched depths result in full width at half maxima that are off by an average of 27% and matched full width at half maxima produce depths that are off by an average of 109%.« less

DichotomY IdentitY: Euler-Bernoulli Numbers, Sets-Multisets, FD-BE Quantum-Statistics, 1 /f0 - 1 /f1 Power-Spectra, Ellipse-Hyperbola Conic-Sections, Local-Global Extent: ``Category-Semantics''

NASA Astrophysics Data System (ADS)

Rota, G.-C.; Siegel, Edward Carl-Ludwig

2011-03-01

Seminal Apostol[Math.Mag.81,3,178(08);Am.Math.Month.115,9,795(08)]-Rota[Intro.Prob. Thy.(95)-p.50-55] DichotomY equivalence-class: set-theory: sets V multisets; closed V open; to Abromowitz-Stegun[Hdbk.Math.Fns.(64)]-ch.23,p.803!]: numbers/polynomials generating-functions: Euler V Bernoulli; to Siegel[Schrodinger Cent.Symp.(87); Symp.Fractals, MRS Fall Mtg.,(1989)-5-papers!] power-spectrum: 1/ f {0}-White V 1/ f {1}-Zipf/Pink (Archimedes) HYPERBOLICITY INEVITABILITY; to analytic-geometry Conic-Sections: Ellipse V (via Parabola) V Hyperbola; to Extent/Scale/Radius: Locality V Globality, Root-Causes/Ultimate-Origins: Dimensionality: odd-Z V (via fractal) V even-Z, to Symmetries/(Noether's-theorem connected)/Conservation-Laws Dichotomy: restored/conservation/convergence=0- V broken/non-conservation/divergence=/=0: with asymptotic-limit antipodes morphisms/ crossovers: Eureka!!!; "FUZZYICS"=''CATEGORYICS''!!! Connection to Kummer(1850) Bernoulli-numbers proof of FLT is via Siegel(CCNY;1964) < (1994)[AMS Joint Mtg. (2002)-Abs.973-60-124] short succinct physics proof: FLT = Least-Action Principle!!!

Euler polynomials and identities for non-commutative operators

NASA Astrophysics Data System (ADS)

De Angelis, Valerio; Vignat, Christophe

2015-12-01

Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt [Phys. Rev. D 54(12), 7710-7723 (1996)], expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, by Pain [J. Phys. A: Math. Theor. 46, 035304 (2013)], links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Figuieira de Morisson and Fring [J. Phys. A: Math. Gen. 39, 9269 (2006)] in the context of non-Hermitian Hamiltonian systems. In each case, we provide several proofs and extensions of these identities that highlight the role of Euler and Bernoulli polynomials.

The Modelling of Axially Translating Flexible Beams

NASA Astrophysics Data System (ADS)

Theodore, R. J.; Arakeri, J. H.; Ghosal, A.

1996-04-01

The axially translating flexible beam with a prismatic joint can be modelled by using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, a non-dimensional form of the Euler Bernoulli beam equation is presented, obtained by using the concept of group velocity, and also the conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions leads to a time-dependent frequency equation for the translating flexible beam. A novel method is presented for solving this time dependent frequency equation by using a differential form of the frequency equation. The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. It is shown by using Lyapunov's first method that the dynamic responses of flexural modal variables become unstable during retraction of the flexible beam, which the dynamic response during extension of the beam is stable. Numerical simulation results are presented for the uniform axial motion induced transverse vibration for a typical flexible beam.

Bending of Euler-Bernoulli nanobeams based on the strain-driven and stress-driven nonlocal integral models: a numerical approach

NASA Astrophysics Data System (ADS)

Oskouie, M. Faraji; Ansari, R.; Rouhi, H.

2018-04-01

Eringen's nonlocal elasticity theory is extensively employed for the analysis of nanostructures because it is able to capture nanoscale effects. Previous studies have revealed that using the differential form of the strain-driven version of this theory leads to paradoxical results in some cases, such as bending analysis of cantilevers, and recourse must be made to the integral version. In this article, a novel numerical approach is developed for the bending analysis of Euler-Bernoulli nanobeams in the context of strain- and stress-driven integral nonlocal models. This numerical approach is proposed for the direct solution to bypass the difficulties related to converting the integral governing equation into a differential equation. First, the governing equation is derived based on both strain-driven and stress-driven nonlocal models by means of the minimum total potential energy. Also, in each case, the governing equation is obtained in both strong and weak forms. To solve numerically the derived equations, matrix differential and integral operators are constructed based upon the finite difference technique and trapezoidal integration rule. It is shown that the proposed numerical approach can be efficiently applied to the strain-driven nonlocal model with the aim of resolving the mentioned paradoxes. Also, it is able to solve the problem based on the strain-driven model without inconsistencies of the application of this model that are reported in the literature.

An investigation of stress wave propagation in a shear deformable nanobeam based on modified couple stress theory

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, Majid; Shariati, Mahmoud

2016-04-01

This paper presents a new investigation for propagation of stress wave in a nanobeam based on modified couple stress theory. Using Euler-Bernoulli beam theory, Timoshenko beam theory, and Reddy beam theory, the effect of shear deformation is investigated. This nonclassical model contains a material length scale parameter to capture the size effect and the Poisson effect is incorporated in the current model. Governing equations of motion are obtained by Hamilton's principle and solved explicitly. This solution leads to obtain two phase velocities for shear deformable beams in different directions. Effects of shear deformation, material length scale parameter, and Poisson's ratio on the behavior of these phase velocities are investigated and discussed. The results also show a dual behavior for phase velocities against Poisson's ratio.

Theoretical Limits of Damping Attainable by Smart Beams with Rate Feedback

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1997-01-01

Using a generally accepted model we present a comprehensive analysis (within the page limitation) of an Euler- Bernoulli beam with PZT sensor-actuator and pure rate feedback. The emphasis is on the root locus - the dependence of the attainable damping on the feedback gain. There is a critical value of the gain beyond which the damping decreases to zero. We construct the time-domain response using semigroup theory, and show that the eigenfunctions form a Riesz basis, leading to a 'modal' expansion.

Three dimensional steady subsonic Euler flows in bounded nozzles

NASA Astrophysics Data System (ADS)

Chen, Chao; Xie, Chunjing

The existence and uniqueness of three dimensional steady subsonic Euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the entrance are both zero, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. As the magnitude of the normal component of the momentum approaches the critical number, the associated flows converge to a subsonic-sonic flow. Furthermore, when the normal component of vorticity and the variation of Bernoulli function are both small, the existence and uniqueness of subsonic Euler flows with non-zero vorticity are established. The proof of these results is based on a new formulation for the Euler system, a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions, detailed study for a linear div-curl system, and delicate estimate for the transport equations.

Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models

NASA Astrophysics Data System (ADS)

Ansari, R.; Sahmani, S.

2012-04-01

The free vibration response of single-walled carbon nanotubes (SWCNTs) is investigated in this work using various nonlocal beam theories. To this end, the nonlocal elasticity equations of Eringen are incorporated into the various classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Reddy beam theory (RBT) to consider the size-effects on the vibration analysis of SWCNTs. The generalized differential quadrature (GDQ) method is employed to discretize the governing differential equations of each nonlocal beam theory corresponding to four commonly used boundary conditions. Then molecular dynamics (MD) simulation is implemented to obtain fundamental frequencies of nanotubes with different chiralities and values of aspect ratio to compare them with the results obtained by the nonlocal beam models. Through the fitting of the two series of numerical results, appropriate values of nonlocal parameter are derived relevant to each type of chirality, nonlocal beam model, and boundary conditions. It is found that in contrast to the chirality, the type of nonlocal beam model and boundary conditions make difference between the calibrated values of nonlocal parameter corresponding to each one.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

Complete mechanical behavior analysis of FG Nano Beam under non-uniform loading using non-local theory

NASA Astrophysics Data System (ADS)

Ghaffari, I.; Parhizkar Yaghoobi, M.; Ghannad, M.

2018-01-01

The purpose of this study is to offer a complete solution to analyze the mechanical behavior (bending, buckling and vibration) of Nano-beam under non-uniform loading. Furthermore, the effects of size (nonlocal parameters), non-homogeneity constants, and different boundary conditions are investigated by using this method. The exact solution presented here reduces costs incurred by experiments. In this research, the displacement field obeys the kinematics of the Euler-Bernoulli beam theory and non-local elasticity theory has been used. The governing equations and general boundary conditions are derived for a beam by using energy method. The presented solution enables us to analyze any kind of loading profile and boundary conditions with no limitations. Furthermore, this solution, unlike previous studies, is not a series-solution; hence, there is no limitation prior to existing with the series-solution, nor does it need to check convergence. Based on the developed analytical solution, the influence of size, non-homogeneity and non-uniform loads on bending, buckling and vibration behaviors is discussed. Also, the obtained result is highly accurate and in good agreement with previous research. In theoretical method, the allowable range for non-local parameters can be determined so as to make a major contribution to the reduction of the cost of experiments determining the value of non-local parameters.

Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect

NASA Astrophysics Data System (ADS)

Georgiev, V. B.; Cuenca, J.; Gautier, F.; Simon, L.; Krylov, V. V.

2011-05-01

Flexural waves in beams and plates slow down if their thickness decreases. Such property was used in the past for establishing the theory of acoustic black holes (ABH). The aim of the present paper is to establish reliable numerical and experimental approaches for designing, modelling and manufacturing an effective passive vibration damper using the ABH effect. The effectiveness of such vibration absorbers increases with frequency. Initially, the dynamic behaviour of an Euler-Bernoulli beam is expressed using the Impedance Method, which in turn leads to a Riccati equation for the beam impedance. This equation is numerically integrated using an adaptive Runge-Kutta-Fehlberg method, yielding the frequency- and spatially-dependent impedance matrix of the beam, from which the reflection matrix is obtained. Moreover, the mathematical model can be extended to incorporate an absorbing film that assists for reducing reflected waves from the truncated edge. Therefore, the influence of the geometrical and material characteristics of the absorbing film is then studied and an optimal configuration of these parameters is proposed. An experiment consisting of an elliptical plate with a pit of power-law profile placed in one of its foci is presented. The elliptical shape of the plate induces a complete focalisation of the waves towards ABH in case they are generated in the other focus. Consequently, the derived 1-D method for an Euler-Bernoulli beam can be used as a phenomenological model assisting for better understanding the complex processes in 2-D elliptical structure. Finally, both, numerical simulations and experimental measurements show significant reduction of vibration levels.

Vibrations of beams and rods carrying a moving mass

NASA Astrophysics Data System (ADS)

Zhao, X. W.; van der Heijden, G. H. M.; Hu, Z. D.

2016-05-01

We study the vibration of slender one-dimensional elastic structures (beams, cables, wires, rods) under the effect of a moving mass or load. We first consider the classical small- deflection (Euler-Bernoulli) beam case, where we look at tip vibrations of a cantilever as a model for a barreled launch system. Then we develop a theory for large deformations based on Cosserat rod theory. We illustrate the effect of moving loads on large-deformation structures with a few cable and arch problems. Large deformations are found to have a resonance detuning effect on the cable. For the arch we find different failure modes depending on its depth: a shallow arch fails by in-plane collapse, while a deep arch fails by sideways flopping. In both cases the speed of the traversing load is found to have a stabilising effect on the structure, with failure suppressed entirely at sufficiently high speed.

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

Bending analysis of agglomerated carbon nanotube-reinforced beam resting on two parameters modified Vlasov model foundation

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Zamani, M. H.

2018-06-01

The present work deals with bending behavior of nanocomposite beam resting on two parameters modified Vlasov model foundation (MVMF), with consideration of agglomeration and distribution of carbon nanotubes (CNTs) in beam matrix. Equivalent fiber based on Eshelby-Mori-Tanaka approach is employed to determine influence of CNTs aggregation on elastic properties of CNT-reinforced beam. The governing equations are deduced using the principle of minimum potential energy under assumption of the Euler-Bernoulli beam theory. The MVMF required the estimation of γ parameter; to this purpose, unique iterative technique based on variational principles is utilized to compute value of the γ and subsequently fourth-order differential equation is solved analytically. Eventually, the transverse displacements and bending stresses are obtained and compared for different agglomeration parameters, various boundary conditions simultaneously and variant elastic foundation without requirement to instate values for foundation parameters.

Influence of foundation mass and surface roughness on dynamic response of beam on dynamic foundation subjected to the moving load

NASA Astrophysics Data System (ADS)

Tran Quoc, Tinh; Khong Trong, Toan; Luong Van, Hai

2018-04-01

In this paper, Improved Moving Element Method (IMEM) is used to analyze the dynamic response of Euler-Bernoulli beam structures on the dynamic foundation model subjected to the moving load. The effects of characteristic foundation model parameters such as Winkler stiffness, shear layer based on the Pasternak model, viscoelastic dashpot and characteristic parameter of mass on foundation. Beams are modeled by moving elements while the load is fixed. Based on the principle of the publicly virtual balancing and the theory of moving element method, the motion differential equation of the system is established and solved by means of the numerical integration based on the Newmark algorithm. The influence of mass on foundation and the roughness of the beam surface on the dynamic response of beam are examined in details.

Vibration based algorithm for crack detection in cantilever beam containing two different types of cracks

NASA Astrophysics Data System (ADS)

Behzad, Mehdi; Ghadami, Amin; Maghsoodi, Ameneh; Michael Hale, Jack

2013-11-01

In this paper, a simple method for detection of multiple edge cracks in Euler-Bernoulli beams having two different types of cracks is presented based on energy equations. Each crack is modeled as a massless rotational spring using Linear Elastic Fracture Mechanics (LEFM) theory, and a relationship among natural frequencies, crack locations and stiffness of equivalent springs is demonstrated. In the procedure, for detection of m cracks in a beam, 3m equations and natural frequencies of healthy and cracked beam in two different directions are needed as input to the algorithm. The main accomplishment of the presented algorithm is the capability to detect the location, severity and type of each crack in a multi-cracked beam. Concise and simple calculations along with accuracy are other advantages of this method. A number of numerical examples for cantilever beams including one and two cracks are presented to validate the method.

Modeling and Control of Intelligent Flexible Structures

DTIC Science & Technology

1994-03-26

can be approximated as a simply supported beam in transverse vibration. Assuming that the Euler- Bernoulli beam assumptions hold, linear equations of...The assumptions made during the derivation are that the element can be modeled as an Euler- Bernoulli beam, that the cross-section is symmetric, and...parametes A,. and ,%. andc input maces 3,,. The closed loop system. ecuation (7), is stable when the 3.. 8 and output gain mantices H1., H., H. for

Study of the bending vibration characteristic of phononic crystals beam-foundation structures by Timoshenko beam theory

NASA Astrophysics Data System (ADS)

Zhang, Yan; Ni, Zhi-Qiang; Jiang, Lin-Hua; Han, Lin; Kang, Xue-Wei

2015-07-01

Vibration problems wildly exist in beam-foundation structures. In this paper, finite periodic composites inspired by the concept of ideal phononic crystals (PCs), as well as Timoshenko beam theory (TBT), are proposed to the beam anchored on Winkler foundation. The bending vibration band structure of the PCs Timoshenko beam-foundation structure is derived from the modified transfer matrix method (MTMM) and Bloch's theorem. Then, the frequency response of the finite periodic composite Timoshenko beam-foundation structure by the finite element method (FEM) is performed to verify the above theoretical deduction. Study shows that the Timoshenko beam-foundation structure with periodic composites has wider attenuation zones compared with homogeneous ones. It is concluded that TBT is more available than Euler beam theory (EBT) in the study of the bending vibration characteristic of PCs beam-foundation structures with different length-to-height ratios.

Alternate Solution to Generalized Bernoulli Equations via an Integrating Factor: An Exact Differential Equation Approach

ERIC Educational Resources Information Center

Tisdell, C. C.

2017-01-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem…

Numerical modeling of guided ultrasonic waves generated and received by piezoelectric wafer in a Delaminated composite beam

NASA Astrophysics Data System (ADS)

Xu, G. D.; Xu, B. Q.; Xu, C. G.; Luo, Y.

2017-05-01

A spectral finite element method (SFEM) is developed to analyze guided ultrasonic waves in a delaminated composite beam excited and received by a pair of surface-bonded piezoelectric wafers. The displacements of the composite beam and the piezoelectric wafer are represented by Timoshenko beam and Euler Bernoulli theory respectively. The linear piezoelectricity is used to model the electrical-mechanical coupling between the piezoelectric wafer and the beam. The coupled governing equations and the boundary conditions in time domain are obtained by using the Hamilton's principle, and then the SFEM are formulated by transforming the coupled governing equations into frequency domain via the discrete Fourier transform. The guided waves are analyzed while the interaction of waves with delamination is also discussed. The elements needed in SFEM is far fewer than those for finite element method (FEM), which result in a much faster solution speed in this study. The high accuracy of the present SFEM is verified by comparing with the finite element results.

Optimal positions and parameters of translational and rotational mass dampers in beams subjected to random excitation

NASA Astrophysics Data System (ADS)

Łatas, Waldemar

2018-01-01

The problem of vibrations of the beam with the attached system of translational and rotational dynamic mass dampers subjected to random excitations with peaked power spectral densities, is presented in the hereby paper. The Euler-Bernoulli beam model is applied, while for solving the equation of motion the Galerkin method and the Laplace time transform are used. The obtained transfer functions allow to determine power spectral densities of the beam deflection and other dependent variables. Numerical examples present simple optimization problems of mass dampers parameters for local and global objective functions.

Baseline Experiments on Coulomb Damping due to Rotational Slip

DTIC Science & Technology

1992-12-01

by Griffe121 . As expected Equation (2-39) matches the result given by Griffel . 2.2.2. Euler-Bernoulli Beam versus Timeshenko Beam. Omitted from Euler...McGraw-Hill, Inc., 1983. 20. Clark, S. K., Dynamics of Continuous Elements, New Jersey, Prentice-Hall, Inc., 1972. 21. Griffel , W., Beam Formulas

The effect of rotatory inertia on the natural frequencies of composite beams

NASA Astrophysics Data System (ADS)

Auclair, Samuel C.; Sorelli, Luca; Salenikovich, Alexander; Fafard, Mario

2016-03-01

This paper focuses on the dynamic behaviour of two-layer composite beams, which is an important aspect of performance of structures, such as a concrete slab on a girder in residential floors or bridges. After briefly reviewing the composite beam theory based on Euler-Bernoulli hypothesis, the dynamic formulation is extended by including the effect of the relative longitudinal motion of the layers in the rotatory inertia, which can be particularly important for timber-concrete composite beams. The governing equation and the finite element model are derived in detail and validated by comparing the natural frequency predictions against other methods. A parametric analysis shows the key factors, which affect the rotatory inertia and its influence on the frequency of a single-span composite beam with different boundary conditions. The effect of the rotatory inertia on the first natural frequency of the composite beam appears below 5 percent; however, the effect on the higher natural frequencies becomes more important and not negligible in a full dynamics analysis. Finally, a simplified equation is proposed to account for the effect of the rotatory inertia on the calculation of the frequency of a composite beam for design purpose.

Control theory based airfoil design using the Euler equations

NASA Technical Reports Server (NTRS)

Jameson, Antony; Reuther, James

1994-01-01

This paper describes the implementation of optimization techniques based on control theory for airfoil design. In our previous work it was shown that control theory could be employed to devise effective optimization procedures for two-dimensional profiles by using the potential flow equation with either a conformal mapping or a general coordinate system. The goal of our present work is to extend the development to treat the Euler equations in two-dimensions by procedures that can readily be generalized to treat complex shapes in three-dimensions. Therefore, we have developed methods which can address airfoil design through either an analytic mapping or an arbitrary grid perturbation method applied to a finite volume discretization of the Euler equations. Here the control law serves to provide computationally inexpensive gradient information to a standard numerical optimization method. Results are presented for both the inverse problem and drag minimization problem.

Mechanical and Thermal Analysis of Classical Functionally Graded Coated Beam

NASA Astrophysics Data System (ADS)

Toudehdehghan, Abdolreza; Mujibur Rahman, Md.; Tarlochan, Faris

2018-03-01

The governing equation of a classical rectangular coated beam made of two layers subjected to thermal and uniformly distributed mechanical loads are derived by using the principle of virtual displacements and based on Euler-Bernoulli deformation beam theory (EBT). The aim of this paper was to analyze the static behavior of clamped-clamped thin coated beam under thermo-mechanical load using MATLAB. Two models were considered for composite coated. The first model was consisting of ceramic layer as a coated and substrate which was metal (HC model). The second model was consisting of Functionally Graded Material (FGM) as a coated layer and metal substrate (FGC model). From the result it was apparent that the superiority of the FGC composite against conventional coated composite has been demonstrated. From the analysis, the stress level throughout the thickness at the interface of the coated beam for the FGC was reduced. Yet, the deflection in return was observed to increase. Therefore, this could cater to various new engineering applications where warrant the utilization of material that has properties that are well-beyond the capabilities of the conventional or yesteryears materials.

The influence of inertia on the efflux velocity: From Daniel Bernoulli to a contemporary theory

NASA Astrophysics Data System (ADS)

Malcherek, Andreas

2015-11-01

In 1644 Evangelista Torricelli claimed that the outflow velocity from a vessel is equal to the terminal speed of a body falling freely from the filling level h, i.e. v =√{ 2 gh } . Therefore the largest velocities are predicted when the height in a vessel is at the highest position. As a consequence the efflux would start with the highest velocity directly from the initiation of motion which contradicts the inertia principle. In 1738 Daniel Bernoulli derived a much more sophisticated and instationary outflow theory basing on the conservation of potential and kinetic energy. As a special case Torricelli's law is obtained, when inertia is neglected and the cross section of the opening is small compared to the vessel's cross section. To the Authors knowledge, this theory was never applied or even mentioned in text books although it is superior to the Torricelli theory in many aspects. In this paper Bernoulli's forgotten theory will be presented. Deriving this theory using the state of the arts hydrodynamics results in a new formula v =√{ gh } . Although this formula contradicts Torricelli's principle, it is confirmed by all kind of experiments stating that a discharge coefficient of about β = 0 . 7 is needed in Torricelli's formula v = β√{ 2 gh } .

THE BERNOULLI EQUATION AND COMPRESSIBLE FLOW THEORIES

EPA Science Inventory

The incompressible Bernoulli equation is an analytical relationship between pressure, kinetic energy, and potential energy. As perhaps the simplest and most useful statement for describing laminar flow, it buttresses numerous incompressible flow models that have been developed ...

Bernoulli's Principle

ERIC Educational Resources Information Center

Hewitt, Paul G.

2004-01-01

Some teachers have difficulty understanding Bernoulli's principle particularly when the principle is applied to the aerodynamic lift. Some teachers favor using Newton's laws instead of Bernoulli's principle to explain the physics behind lift. Some also consider Bernoulli's principle too difficult to explain to students and avoid teaching it…

Vertical dynamics of a single-span beam subjected to moving mass-suspended payload system with variable speeds

NASA Astrophysics Data System (ADS)

He, Wei

2018-03-01

This paper presents the vertical dynamics of a simply supported Euler-Bernoulli beam subjected to a moving mass-suspended payload system of variable velocities. A planar theoretical model of the moving mass-suspended payload system of variable speeds is developed based on several assumptions: the rope is massless and rigid, and its length keeps constant; the stiffness of the gantry beam is much greater than the supporting beam, and the gantry beam can be treated as a mass particle traveling along the supporting beam; the supporting beam is assumed as a simply supported Bernoulli-Euler beam. The model can be degenerated to consider two classical cases-the moving mass case and the moving payload case. The proposed model is verified using both numerical and experimental methods. To further investigate the effect of possible influential factors, numerical examples are conducted covering a range of parameters, such as variable speeds (acceleration or deceleration), mass ratios of the payload to the total moving load, and the pendulum lengths. The effect of beam flexibility on swing response of the payload is also investigated. It is shown that the effect of a variable speed is significant for the deflections of the beam. The accelerating movement tends to induce larger beam deflections, while the decelerating movement smaller ones. For accelerating or decelerating movements, the moving mass model may underestimate the deflections of the beam compared with the presented model; while for uniform motion, both the moving mass model and the moving mass-payload model lead to same beam responses. Furthermore, it is observed that the swing response of the payload is not sensitive to the stiffness of the beam for operational cases of a moving crane, thus a simple moving payload model can be employed in the swing control of the payload.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

NASA Astrophysics Data System (ADS)

Jiang, Fang

functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

NASA Astrophysics Data System (ADS)

Aureli, M.; Basaran, M. E.; Porfiri, M.

2012-03-01

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler-Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.

Inverse problems in the modeling of vibrations of flexible beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Powers, R. K.; Rosen, I. G.

1987-01-01

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

A derivation of the beam equation

NASA Astrophysics Data System (ADS)

Duque, Daniel

2016-01-01

The Euler-Bernoulli equation describing the deflection of a beam is a vital tool in structural and mechanical engineering. However, its derivation usually entails a number of intermediate steps that may confuse engineering or science students at the beginnig of their undergraduate studies. We explain how this equation may be deduced, beginning with an approximate expression for the energy, from which the forces and finally the equation itself may be obtained. The description is begun at the level of small ‘particles’, and the continuum level is taken later on. However, when a computational solution is sought, the description turns back to the discrete level again. We first consider the easier case of a string under tension, and then focus on the beam. Numerical solutions for several loads are obtained.

Nonlinear dynamics of contact interaction of a size-dependent plate supported by a size-dependent beam

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, V. A.; Yakovleva, T. V.; Pavlov, S. P.; Krysko, V. A.

2018-05-01

A mathematical model of complex vibrations exhibited by contact dynamics of size-dependent beam-plate constructions was derived by taking the account of constraints between these structural members. The governing equations were yielded by variational principles based on the moment theory of elasticity. The centre of the investigated plate was supported by a beam. The plate and the beam satisfied the Kirchhoff/Euler-Bernoulli hypotheses. The derived partial differential equations (PDEs) were reduced to the Cauchy problems by the Faedo-Galerkin method in higher approximations, whereas the Cauchy problem was solved using a few Runge-Kutta methods. Reliability of results was validated by comparing the solutions obtained by qualitatively different methods. Complex vibrations were investigated with the help of methods of nonlinear dynamics such as vibration signals, phase portraits, Fourier power spectra, wavelet analysis, and estimation of the largest Lyapunov exponents based on the Rosenstein, Kantz, and Wolf methods. The effect of size-dependent parameters of the beam and plate on their contact interaction was investigated. It was detected and illustrated that the first contact between the size-dependent structural members implies chaotic vibrations. In addition, problems of chaotic synchronization between a nanoplate and a nanobeam were addressed.

Propulsion at low Reynolds number via beam extrusion

NASA Astrophysics Data System (ADS)

Gosselin, Frederick; Neetzow, Paul

2014-03-01

We present experimental and theoretical results on the extrusion of a slender beam in a viscous fluid. We are particularly interested in the force necessary to extrude the beam as it buckles with large amplitude due to viscous friction. The problem is inspired by the propulsion of Paramecium via trichocyst extrusion. Self-propulsion in micro-organisms is mostly achieved through the beating of flagella or cilia. However, to avoid a severe aggression, unicellular Paramecium has been observed to extrude trichocysts in the direction of the aggression to burst away. These trichocysts are rod-like organelles which, upon activation, grow to about 40 μm in length in 3 milliseconds before detaching from the animal. The drag force created by these extruding rods pushing against the viscous fluid generates thrust in the opposite direction. We developed an experimental setup to measure the force required to push a steel piano wire into an aquarium filled with corn syrup. This setup offers a near-zero Reynolds number, and allows studying deployments for a range of constant extrusion speeds. The experimental results are reproduced with a numerical model coupling a large amplitude Euler-Bernoulli beam theory with a fluid load model proportional to the local beam velocity. This study was funded in part by the The Natural Sciences and Engineering Research Council of Canada.

Electrostatically frequency tunable micro-beam-based piezoelectric fluid flow energy harvester

NASA Astrophysics Data System (ADS)

Rezaee, Mousa; Sharafkhani, Naser

2017-07-01

This research investigates the dynamic behavior of a sandwich micro-beam based piezoelectric energy harvester with electrostatically adjustable resonance frequency. The system consists of a cantilever micro-beam immersed in a fluid domain and is subjected to the simultaneous action of cross fluid flow and nonlinear electrostatic force. Two parallel piezoelectric laminates are extended along the length of the micro-beam and connected to an external electric circuit which generates an output power as a result of the micro-beam oscillations. The fluid-coupled structure is modeled using Euler-Bernoulli beam theory and the equivalent force terms for the fluid flow. Fluid induced forces comprise the added inertia force which is evaluated using equivalent added mass and the drag and lift forces which are evaluated using relative velocity and Van der Pol equation. In addition to flow velocity and fluid density, the influence of several design parameters such as external electrical resistance, piezo layer position, and dc voltage on the generated power are investigated by using Galerkin and step by step linearization method. It is shown that for given flowing fluid parameters, i.e., density and velocity, one can adjust the applied dc voltage to tune resonance frequency so that the lock-in phenomenon with steady large amplitude oscillations happens, also by adjusting the harvester parameters including the mechanical and electrical ones, the maximal output power of the harvester becomes possible.

Creep rupture analysis of a beam resting on high temperature foundation

NASA Technical Reports Server (NTRS)

Gu, Randy J.; Cozzarelli, Francis A.

1988-01-01

A simplified uniaxial strain controlled creep damage law is deduced with the use of experimental observation from a more complex strain dependent law. This creep damage law correlates the creep damage, which is interpreted as the density variation in the material, directly with the accumulated creep strain. Based on the deduced uniaxial strain controlled creep damage law, a continuum mechanical creep rupture analysis is carried out for a beam resting on a high temperature elastic (Winkler) foundation. The analysis includes the determination of the nondimensional time for initial rupture, the propagation of the rupture front with the associated thinning of the beam, and the influence of creep damage on the deflection of the beam. Creep damage starts accumulating in the beam as soon as the load is applied, and a creep rupture front develops at and propagates from the point at which the creep damage first reaches its critical value. By introducing a series of fundamental assumptions within the framework of technical Euler-Bernoulli type beam theory, a governing set of integro-differential equations is derived in terms of the nondimensional bending moment and the deflection. These governing equations are subjected to a set of interface conditions at the propagating rupture front. A numerical technique is developed to solve the governing equations together with the interface equations, and the computed results are presented and discussed in detail.

A design procedure for active control of beam vibrations

NASA Technical Reports Server (NTRS)

Dickerson, S. L.; Jarocki, G.

1983-01-01

The transverse vibrations of beams is discussed and a methodology for the design of an active damping device is given. The Bernoulli-Euler equation is used to derive a transcendental transfer function, which relates a torque applied at one end of the beam to the rotational position and velocity at that point. The active damping device consists of a wire, a linear actuator and a short torque arm attached to one end of the beam. The action of the actuator varies a tension in the wire and creates a torque which opposes the rotation of the beam and thus damps vibration. A design procedure for such an active damper is given. This procedure shows the relationships and trade-offs between the actuator stroke, power required, stress levels in the wire and beam and the geometry of the beam and wire. It is shown that by consideration of the frequency response at the beam natural frequencies, the aforementioned relationships can be greatly simplified. Similarly, a simple way of estimating the effective damping ratios and eigenvalue locations of actively controlled beams is presented.

Beyond Bernoulli

PubMed Central

Donati, Fabrizio; Myerson, Saul; Bissell, Malenka M.; Smith, Nicolas P.; Neubauer, Stefan; Monaghan, Mark J.; Nordsletten, David A.

2017-01-01

Background— Transvalvular peak pressure drops are routinely assessed noninvasively by echocardiography using the Bernoulli principle. However, the Bernoulli principle relies on several approximations that may not be appropriate, including that the majority of the pressure drop is because of the spatial acceleration of the blood flow, and the ejection jet is a single streamline (single peak velocity value). Methods and Results— We assessed the accuracy of the Bernoulli principle to estimate the peak pressure drop at the aortic valve using 3-dimensional cardiovascular magnetic resonance flow data in 32 subjects. Reference pressure drops were computed from the flow field, accounting for the principles of physics (ie, the Navier–Stokes equations). Analysis of the pressure components confirmed that the spatial acceleration of the blood jet through the valve is most significant (accounting for 99% of the total drop in stenotic subjects). However, the Bernoulli formulation demonstrated a consistent overestimation of the transvalvular pressure (average of 54%, range 5%–136%) resulting from the use of a single peak velocity value, which neglects the velocity distribution across the aortic valve plane. This assumption was a source of uncontrolled variability. Conclusions— The application of the Bernoulli formulation results in a clinically significant overestimation of peak pressure drops because of approximation of blood flow as a single streamline. A corrected formulation that accounts for the cross-sectional profile of the blood flow is proposed and adapted to both cardiovascular magnetic resonance and echocardiographic data. PMID:28093412

Proceedings of the Annual Symposium on Frequency Control (33rd) Held in Atlantic City, New Jersey on 30 May-1 June 1979

DTIC Science & Technology

1979-01-01

from the Bernoullis was Daniel Bernoulli’s n’est pas la meme dans tous les sens", Exercices addition of the acceleration term to the beam e- de Math...frequencies). improved during 1811-1816 by Germain and Lagrange and, finally, the correct derivation was produced 1852 G. Lame, "Leqons sur la ...de la re- tropic membranes and plates (low frequencies) sistance des solides et des solides d’egale by Euler, Jacques Bernoulli, Germin, Lagrange

Transverse vibration of Bernoulli Euler beams carrying point masses and taking into account their rotatory inertia: Exact solution

NASA Astrophysics Data System (ADS)

Maiz, Santiago; Bambill, Diana V.; Rossit, Carlos A.; Laura, P. A. A.

2007-06-01

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of the machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. An exact solution for the title problem is obtained in closed-form fashion, considering general boundary conditions by means of translational and rotatory springs at both ends. The model allows to analyze the influence of the masses and their rotatory inertia on the dynamic behavior of beams with all the classic boundary conditions, and also, as particular cases, to determine the frequencies of continuous beams.

Application of nonlocal models to nano beams. Part II: Thickness length scale effect.

PubMed

Kim, Jun-Sik

2014-10-01

Applicability of nonlocal models to nano-beams is discussed in terms of the Eringen's nonlocal Euler-Bernoulli (EB) beam model. In literature, most work has taken the axial coordinate derivative in the Laplacian operator presented in nonlocal elasticity. This causes that the non-locality always makes the beam soften as compared to the local counterpart. In this paper, the thickness scale effect is solely considered to investigate if the nonlocal model can simulate stiffening effect. Taking the thickness derivative in the Laplacian operator leads to the presence of a surface stress state. The governing equation derived is compared to that of the EB model with the surface stress. The results obtained reveal that the nonlocality tends to decrease the bending moment stiffness whereas to increase the bending rigidity in the governing equation. This tendency also depends on the surface conditions.

Planar reorientation of a free-free beam in space using embedded electromechanical actuators

NASA Technical Reports Server (NTRS)

Kolmanovsky, Ilya V.; Mcclamroch, N. Harris

1993-01-01

It is demonstrated that the planar reorientation of a free-free beam in zero gravity space can be accomplished by periodically changing the shape of the beam using embedded electromechanical actuators. The dynamics which determine the shape of the free-free beam is assumed to be characterized by the Euler-Bernoulli equation, including material damping, with appropriate boundary conditions. The coupling between the rigid body motion and the flexible motion is explained using the angular momentum expression which includes rotatory inertia and kinematically exact effects. A control scheme is proposed where the embedded actuators excite the flexible motion of the beam so that it rotates in the desired sense with respect to a fixed inertial reference. Relations are derived which relate the average rotation rate to the amplitudes and the frequencies of the periodic actuation signal and the properties of the beam. These reorientation maneuvers can be implemented by using feedback control.

Interpretation of Bernoulli's Equation.

ERIC Educational Resources Information Center

Bauman, Robert P.; Schwaneberg, Rolf

1994-01-01

Discusses Bernoulli's equation with regards to: horizontal flow of incompressible fluids, change of height of incompressible fluids, gases, liquids and gases, and viscous fluids. Provides an interpretation, properties, terminology, and applications of Bernoulli's equation. (MVL)

Conformal field theory as microscopic dynamics of incompressible Euler and Navier-Stokes equations.

PubMed

Fouxon, Itzhak; Oz, Yaron

2008-12-31

We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the nonrelativistic incompressible Euler equation. For viscous hydrodynamics we show that the limit of slow motions leads to the nonrelativistic incompressible Navier-Stokes equation. We explain the physical reasons for the reduction and discuss the implications. We propose that conformal field theories provide a fundamental microscopic viewpoint of the equations and the dynamics governed by them.

Analysis of thermoelastic damping in laminated composite micromechanical beam resonators

NASA Astrophysics Data System (ADS)

Vengallatore, Srikar

2005-12-01

Minimization of structural damping is an essential requirement in the design of multifunctional composite micromachined resonators used for sensing and communications applications. Here, we study thermoelastic damping in symmetric, three-layered, laminated, micromechanical Euler-Bernoulli beams using an analytical framework developed by Bishop and Kinra in 1997. The frequency dependence of damping in two representative sets of structures—metallized ceramic beams and ceramic/ceramic laminates—is investigated in detail. The effects of material properties and relative volume fractions are numerically evaluated. The results indicate that metallization of Si and SiC beams using Al, Cu, Ag or Au leads to a considerable increase in damping over a broad frequency range. Similarly, coating silicon with SiC leads to a monotonic increase of the peak damping value as a function of the volume fraction of silicon carbide but, remarkably, there exists a range of frequencies at which the damping in the composite is less than that of bare silicon. Implications for the design of metallized ceramic beams, and for the simultaneous optimization of natural frequency and damping, are discussed.

Polynomial elimination theory and non-linear stability analysis for the Euler equations

NASA Technical Reports Server (NTRS)

Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

1986-01-01

Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

Structure-property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study.

PubMed

Li, Si; Wang, Chengyuan; Nithiarasu, Perumal

2018-04-01

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure-property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the 'more accurate' beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body.

Biomechanics of hair cell kinocilia: experimental measurement of kinocilium shaft stiffness and base rotational stiffness with Euler–Bernoulli and Timoshenko beam analysis

PubMed Central

Spoon, Corrie; Grant, Wally

2011-01-01

Vestibular hair cell bundles in the inner ear contain a single kinocilium composed of a 9+2 microtubule structure. Kinocilia play a crucial role in transmitting movement of the overlying mass, otoconial membrane or cupula to the mechanotransducing portion of the hair cell bundle. Little is known regarding the mechanical deformation properties of the kinocilium. Using a force-deflection technique, we measured two important mechanical properties of kinocilia in the utricle of a turtle, Trachemys (Pseudemys) scripta elegans. First, we measured the stiffness of kinocilia with different heights. These kinocilia were assumed to be homogenous cylindrical rods and were modeled as both isotropic Euler–Bernoulli beams and transversely isotropic Timoshenko beams. Two mechanical properties of the kinocilia were derived from the beam analysis: flexural rigidity (EI) and shear rigidity (kGA). The Timoshenko model produced a better fit to the experimental data, predicting EI=10,400 pN μm2 and kGA=247 pN. Assuming a homogenous rod, the shear modulus (G=1.9 kPa) was four orders of magnitude less than Young's modulus (E=14.1 MPa), indicating that significant shear deformation occurs within deflected kinocilia. When analyzed as an Euler–Bernoulli beam, which neglects translational shear, EI increased linearly with kinocilium height, giving underestimates of EI for shorter kinocilia. Second, we measured the rotational stiffness of the kinocilium insertion (κ) into the hair cell's apical surface. Following BAPTA treatment to break the kinocilial links, the kinocilia remained upright, and κ was measured as 177±47 pN μm rad–1. The mechanical parameters we quantified are important for understanding how forces arising from head movement are transduced and encoded by hair cells. PMID:21307074

A Brief Historical Introduction to Euler's Formula for Polyhedra, Topology, Graph Theory and Networks

ERIC Educational Resources Information Center

Debnath, Lokenath

2010-01-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Konigsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real…

A method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems

NASA Technical Reports Server (NTRS)

Tzes, Anthony P.; Yurkovich, Stephen; Langer, F. Dieter

1989-01-01

An efficient numerical method for solving the partial differential equation (PDE) governing the flexible manipulator control dynamics is presented. A finite-dimensional model of the equation is obtained through discretization in both time and space coordinates by using finite-difference approximations to the PDE. An expert program written in the Macsyma symbolic language is utilized in order to embed the boundary conditions into the program, accounting for a mass carried at the tip of the manipulator. The advantages of the proposed algorithm are many, including the ability to (1) include any distributed actuation term in the partial differential equation, (2) provide distributed sensing of the beam displacement, (3) easily modify the boundary conditions through an expert program, and (4) modify the structure for running under a multiprocessor environment.

A brief historical introduction to Euler's formula for polyhedra, topology, graph theory and networks

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2010-09-01

This article is essentially devoted to a brief historical introduction to Euler's formula for polyhedra, topology, theory of graphs and networks with many examples from the real-world. Celebrated Königsberg seven-bridge problem and some of the basic properties of graphs and networks for some understanding of the macroscopic behaviour of real physical systems are included. We also mention some important and modern applications of graph theory or network problems from transportation to telecommunications. Graphs or networks are effectively used as powerful tools in industrial, electrical and civil engineering, communication networks in the planning of business and industry. Graph theory and combinatorics can be used to understand the changes that occur in many large and complex scientific, technical and medical systems. With the advent of fast large computers and the ubiquitous Internet consisting of a very large network of computers, large-scale complex optimization problems can be modelled in terms of graphs or networks and then solved by algorithms available in graph theory. Many large and more complex combinatorial problems dealing with the possible arrangements of situations of various kinds, and computing the number and properties of such arrangements can be formulated in terms of networks. The Knight's tour problem, Hamilton's tour problem, problem of magic squares, the Euler Graeco-Latin squares problem and their modern developments in the twentieth century are also included.

Thin film flow along a periodically-stretched elastic beam

NASA Astrophysics Data System (ADS)

Boamah Mensah, Chris; Chini, Greg; Jensen, Oliver

2017-11-01

Motivated by an application to pulmonary alveolar micro-mechanics, a system of partial differential equations is derived that governs the motion of a thin liquid film lining both sides of an inertia-less elastic substrate. The evolution of the film mass distribution is described by invoking the usual lubrication approximation while the displacement of the substrate is determined by employing a kinematically nonlinear Euler-Bernoulli beam formulation. In the parameter regime of interest, the axial strain can be readily shown to be a linear function of arc-length specified completely by the motion of ends of the substrate. In contrast, the normal force balance on the beam yields an equation for the substrate curvature that is fully coupled to the time-dependent lubrication equation. Linear analyses of both a stationary and periodically-stretched flat substrate confirm the potential for buckling instabilities and reveal an upper bound on the dimensionless axial stiffness for which the coupled thin-film/inertial-less-beam model is well-posed. Numerical simulations of the coupled system are used to explore the nonlinear development of the buckling instabilities.

Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Wang, Jing; Shen, Huoming; Zhang, Bo; Liu, Juan; Zhang, Yingrong

2018-07-01

We investigate the transverse free vibration behaviour of axially moving nanobeams based on the nonlocal strain gradient theory. Considering the geometrical nonlinearity, which takes the form of von Kármán strains, the coupled plane motion equations and related boundary conditions of a new size-dependent beam model of Euler-Bernoulli type are developed using the generalized Hamilton principle. Using the simply supported axially moving nanobeams as an example, the complex modal analysis method is adopted to solve the governing equation; then, the effect of the order of modal truncation on the natural frequencies is discussed. Subsequently, the roles of the nonlocal parameter, material characteristic parameter, axial speed, stiffness and axial support rigidity parameter on the free vibration are comprehensively addressed. The material characteristic parameter induces the stiffness hardening of nanobeams, while the nonlocal parameter induces stiffness softening. In addition, the roles of small-scale parameters on the flutter critical velocity and stability are explained.

Wave propagation in fluid-conveying viscoelastic carbon nanotubes under longitudinal magnetic field with thermal and surface effect via nonlocal strain gradient theory

NASA Astrophysics Data System (ADS)

Zhen, Yaxin; Zhou, Lin

2017-03-01

Based on nonlocal strain gradient theory, wave propagation in fluid-conveying viscoelastic single-walled carbon nanotubes (SWCNTs) is studied in this paper. With consideration of thermal effect and surface effect, wave equation is derived for fluid-conveying viscoelastic SWCNTs under longitudinal magnetic field utilizing Euler-Bernoulli beam theory. The closed-form expressions are derived for the frequency and phase velocity of the wave motion. The influences of fluid flow velocity, structural damping coefficient, temperature change, magnetic flux and surface effect are discussed in detail. SWCNTs’ viscoelasticity reduces the wave frequency of the system and the influence gets remarkable with the increase of wave number. The fluid in SWCNTs decreases the frequency of wave propagation to a certain extent. The frequency (phase velocity) gets larger due to the existence of surface effect, especially when the diameters of SWCNTs and the wave number decrease. The wave frequency increases with the increase of the longitudinal magnetic field, while decreases with the increase of the temperature change. The results may be helpful for better understanding the potential applications of SWCNTs in nanotechnology.

Analysis of axial compressive loaded beam under random support excitations

NASA Astrophysics Data System (ADS)

Xiao, Wensheng; Wang, Fengde; Liu, Jian

2017-12-01

An analytical procedure to investigate the response spectrum of a uniform Bernoulli-Euler beam with axial compressive load subjected to random support excitations is implemented based on the Mindlin-Goodman method and the mode superposition method in the frequency domain. The random response spectrum of the simply supported beam subjected to white noise excitation and to Pierson-Moskowitz spectrum excitation is investigated, and the characteristics of the response spectrum are further explored. Moreover, the effect of axial compressive load is studied and a method to determine the axial load is proposed. The research results show that the response spectrum mainly consists of the beam's additional displacement response spectrum when the excitation is white noise; however, the quasi-static displacement response spectrum is the main component when the excitation is the Pierson-Moskowitz spectrum. Under white noise excitation, the amplitude of the power spectral density function decreased as the axial compressive load increased, while the frequency band of the vibration response spectrum increased with the increase of axial compressive load.

Finite element formulation of viscoelastic sandwich beams using fractional derivative operators

NASA Astrophysics Data System (ADS)

Galucio, A. C.; Deü, J.-F.; Ohayon, R.

This paper presents a finite element formulation for transient dynamic analysis of sandwich beams with embedded viscoelastic material using fractional derivative constitutive equations. The sandwich configuration is composed of a viscoelastic core (based on Timoshenko theory) sandwiched between elastic faces (based on Euler-Bernoulli assumptions). The viscoelastic model used to describe the behavior of the core is a four-parameter fractional derivative model. Concerning the parameter identification, a strategy to estimate the fractional order of the time derivative and the relaxation time is outlined. Curve-fitting aspects are focused, showing a good agreement with experimental data. In order to implement the viscoelastic model into the finite element formulation, the Grünwald definition of the fractional operator is employed. To solve the equation of motion, a direct time integration method based on the implicit Newmark scheme is used. One of the particularities of the proposed algorithm lies in the storage of displacement history only, reducing considerably the numerical efforts related to the non-locality of fractional operators. After validations, numerical applications are presented in order to analyze truncation effects (fading memory phenomena) and solution convergence aspects.

On the dynamic stability of shear deformable beams under a tensile load

NASA Astrophysics Data System (ADS)

Caddemi, S.; Caliò, I.; Cannizzaro, F.

2016-07-01

Loss of stability of beams in a linear static context due to the action of tensile loads has been disclosed only recently in the scientific literature. However, tensile instability in the dynamic regime has been only marginally covered. Several aspects concerning the role of shear deformation on the tensile dynamic instability on continuous and discontinuous beams are still to be addressed. It may appear as a paradox, but also for the case of the universally studied Timoshenko beam model, despite its old origin, frequency-axial load diagrams in the range of negative values of the load (i.e. tensile load) has never been brought to light. In this paper, for the first time, the influence of a conservative tensile axial loads on the dynamic behaviour of the Timoshenko model, according to the Haringx theory, is assessed. It is shown that, under increasing tensile loads, regions of positive/negative fundamental frequency variations can be distinguished. In addition, the beam undergoes eigen-mode changes, from symmetric to anti-symmetric shapes, until tensile instability of divergence type is reached. As a further original contribution on the subject, taking advantage of a new closed form solution, it is shown that the same peculiarities are recovered for an axially loaded Euler-Bernoulli vibrating beam with multiple elastic sliders. This latter model can be considered as the discrete counterpart of the Timoshenko beam-column in which the internal sliders concentrate the shear deformation that in the Timoshenko model is continuously distributed. Original aspects regarding the evolution of the vibration frequencies and the relevant mode shapes with the tensile load value are highlighted.

Characteristics of steady vibration in a rotating hub-beam system

NASA Astrophysics Data System (ADS)

Zhao, Zhen; Liu, Caishan; Ma, Wei

2016-02-01

A rotating beam features a puzzling character in which its frequencies and modal shapes may vary with the hub's inertia and its rotating speed. To highlight the essential nature behind the vibration phenomena, we analyze the steady vibration of a rotating Euler-Bernoulli beam with a quasi-steady-state stretch. Newton's law is used to derive the equations governing the beam's elastic motion and the hub's rotation. A combination of these equations results in a nonlinear partial differential equation (PDE) that fully reflects the mutual interaction between the two kinds of motion. Via the Fourier series expansion within a finite interval of time, we reduce the PDE into an infinite system of a nonlinear ordinary differential equation (ODE) in spatial domain. We further nondimensionalize the ODE and discretize it via a difference method. The frequencies and modal shapes of a general rotating beam are then determined numerically. For a low-speed beam where the ignorance of geometric stiffening is feasible, the beam's vibration characteristics are solved analytically. We validate our numerical method and the analytical solutions by comparing with either the past experiments or the past numerical findings reported in existing literature. Finally, systematic simulations are performed to demonstrate how the beam's eigenfrequencies vary with the hub's inertia and rotating speed.

On the use of a roving body with rotary inertia to locate cracks in beams

NASA Astrophysics Data System (ADS)

Cannizzaro, F.; De Los Rios, J.; Caddemi, S.; Caliò, I.; Ilanko, S.

2018-07-01

Identifying cracks and damages in structures using measured vibrational characteristics has received considerable attention in the past few decades. The possibility of using frequency changes due to the application of a mass appended to the structure has also been considered. In this paper an analytical proof to show that the natural frequencies of a cracked beam with a roving body possessing mass and rotary inertia will generally change abruptly as the body passes over a crack, provided that the crack permits differential flexural rotations, is presented. A novel explicit closed form solution of the governing equation of an Euler-Bernoulli beam with a roving body possessing mass and rotary inertia, in the presence of multiple cracks is also proposed. The presented exact solution is used to conduct a parametric analysis of cracked beams. Numerical results for natural frequencies are provided and a procedure to exploit the occurrence of frequency shifts to detect and locate each crack, without having to perform any additional calculation, is described.

Methods for the identification of material parameters in distributed models for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Crowley, J. M.; Rosen, I. G.

1986-01-01

Theoretical and numerical results are presented for inverse problems involving estimation of spatially varying parameters such as stiffness and damping in distributed models for elastic structures such as Euler-Bernoulli beams. An outline of algorithms used and a summary of computational experiences are presented.

Computational methods for the identification of spatially varying stiffness and damping in beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1986-01-01

A numerical approximation scheme for the estimation of functional parameters in Euler-Bernoulli models for the transverse vibration of flexible beams with tip bodies is developed. The method permits the identification of spatially varying flexural stiffness and Voigt-Kelvin viscoelastic damping coefficients which appear in the hybrid system of ordinary and partial differential equations and boundary conditions describing the dynamics of such structures. An inverse problem is formulated as a least squares fit to data subject to constraints in the form of a vector system of abstract first order evolution equations. Spline-based finite element approximations are used to finite dimensionalize the problem. Theoretical convergence results are given and numerical studies carried out on both conventional (serial) and vector computers are discussed.

An experiment for determining the Euler load by direct computation

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.; Stein, Peter A.

1986-01-01

A direct algorithm is presented for computing the Euler load of a column from experimental data. The method is based on exact inextensional theory for imperfect columns, which predicts two distinct deflected shapes at loads near the Euler load. The bending stiffness of the column appears in the expression for the Euler load along with the column length, therefore the experimental data allows a direct computation of bending stiffness. Experiments on graphite-epoxy columns of rectangular cross-section are reported in the paper. The bending stiffness of each composite column computed from experiment is compared with predictions from laminated plate theory.

Physical Modeling of Microtubules Network

NASA Astrophysics Data System (ADS)

Allain, Pierre; Kervrann, Charles

2014-10-01

Microtubules (MT) are highly dynamic tubulin polymers that are involved in many cellular processes such as mitosis, intracellular cell organization and vesicular transport. Nevertheless, the modeling of cytoskeleton and MT dynamics based on physical properties is difficult to achieve. Using the Euler-Bernoulli beam theory, we propose to model the rigidity of microtubules on a physical basis using forces, mass and acceleration. In addition, we link microtubules growth and shrinkage to the presence of molecules (e.g. GTP-tubulin) in the cytosol. The overall model enables linking cytosol to microtubules dynamics in a constant state space thus allowing usage of data assimilation techniques.

A fully Sinc-Galerkin method for Euler-Bernoulli beam models

NASA Technical Reports Server (NTRS)

Smith, R. C.; Bowers, K. L.; Lund, J.

1990-01-01

A fully Sinc-Galerkin method in both space and time is presented for fourth-order time-dependent partial differential equations with fixed and cantilever boundary conditions. The Sinc discretizations for the second-order temporal problem and the fourth-order spatial problems are presented. Alternate formulations for variable parameter fourth-order problems are given which prove to be especially useful when applying the forward techniques to parameter recovery problems. The discrete system which corresponds to the time-dependent partial differential equations of interest are then formulated. Computational issues are discussed and a robust and efficient algorithm for solving the resulting matrix system is outlined. Numerical results which highlight the method are given for problems with both analytic and singular solutions as well as fixed and cantilever boundary conditions.

Transverse Vibration of Tapered Single-Walled Carbon Nanotubes Embedded in Viscoelastic Medium

NASA Astrophysics Data System (ADS)

Lei, Y. J.; Zhang, D. P.; Shen, Z. B.

2017-12-01

Based on the nonlocal theory, Euler-Bernoulli beam theory and Kelvin viscoelastic foundation model, free transverse vibration is studied for a tapered viscoelastic single-walled carbon nanotube (visco-SWCNT) embedded in a viscoelastic medium. Firstly, the governing equations for vibration analysis are established. And then, we derive the natural frequencies in closed form for SWCNTs with arbitrary boundary conditions by applying transfer function method and perturbation method. Numerical results are also presented to discuss the effects of nonlocal parameter, relaxation time and taper parameter of SWCNTs, and material property parameters of the medium. This study demonstrates that the proposed model is available for vibration analysis of the tapered SWCNTs-viscoelastic medium coupling system.

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2004-01-01

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam

PubMed Central

Thomsen, Jon Juel

2016-01-01

The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation. PMID:27118899

Structural Influence of Dynamics of Bottom Loads

DTIC Science & Technology

2014-02-10

using the Numerette research craft, are underway. Early analytic research on slamming was done by von Karman [5] using a momentum approach, and by...pressure q{x,t) as two constant pressures, qi and qj, traveling at a constant speed c. Using the Euler- Bernoulli beam assumptions the governing

Backstepping boundary control: an application to the suppression of flexible beam vibration

NASA Astrophysics Data System (ADS)

Boonkumkrong, Nipon; Asadamongkon, Pichai; Chinvorarat, Sinchai

2018-01-01

This paper presents a backstepping boundary control for vibration suppression of flexible beam. The applications are such as industrial robotic arms, space structures, etc. Most slender beams can be modelled using a shear beam. The shear beam is more complex than the conventional Euler-Bernoulli beam in that a shear deformation is additionally taken into account. At present, the application of this method in industry is rather limited, because the application of controllers to the beam is difficult. In this research, we use the shear beam with moving base as a model. The beam is cantilever type. This design method allows us to deal directly with the beam’s partial differential equations (PDEs) without resorting to approximations. An observer is used to estimate the deflections along the beam. Gain kernel of the system is calculated and then used in the control law design. The control setup is anti-collocation, i.e. a sensor is placed at the beam tip and an actuator is placed at the beam moving base. Finite difference equations are used to solve the PDEs and the partial integro-differential equations (PIDEs). Control parameters are varied to see their influences that affect the control performance. The results of the control are presented via computer simulation to verify that the control scheme is effective.

Closed-form solution for static pull-in voltage of electrostatically actuated clamped-clamped micro/nano beams under the effect of fringing field and van der Waals force

NASA Astrophysics Data System (ADS)

Bhojawala, V. M.; Vakharia, D. P.

2017-12-01

This investigation provides an accurate prediction of static pull-in voltage for clamped-clamped micro/nano beams based on distributed model. The Euler-Bernoulli beam theory is used adapting geometric non-linearity of beam, internal (residual) stress, van der Waals force, distributed electrostatic force and fringing field effects for deriving governing differential equation. The Galerkin discretisation method is used to make reduced-order model of the governing differential equation. A regime plot is presented in the current work for determining the number of modes required in reduced-order model to obtain completely converged pull-in voltage for micro/nano beams. A closed-form relation is developed based on the relationship obtained from curve fitting of pull-in instability plots and subsequent non-linear regression for the proposed relation. The output of regression analysis provides Chi-square (χ 2) tolerance value equals to 1  ×  10-9, adjusted R-square value equals to 0.999 29 and P-value equals to zero, these statistical parameters indicate the convergence of non-linear fit, accuracy of fitted data and significance of the proposed model respectively. The closed-form equation is validated using available data of experimental and numerical results. The relative maximum error of 4.08% in comparison to several available experimental and numerical data proves the reliability of the proposed closed-form equation.

Nonlinear Acoustic Metamaterials for Sound Attenuation Applications

DTIC Science & Technology

2011-03-16

elastic guides, which are discretized into Bernoulli -Euler beam elements [29]. We first describe the equations of particles’ motion in the DE model...to 613 N in the curved one [see Fig. 15(b)]. Overall, the area under the force-time curve, which corresponds to the amount of momentum transferred

Stability analysis of internally damped rotating composite shafts using a finite element formulation

NASA Astrophysics Data System (ADS)

Ben Arab, Safa; Rodrigues, José Dias; Bouaziz, Slim; Haddar, Mohamed

2018-04-01

This paper deals with the stability analysis of internally damped rotating composite shafts. An Euler-Bernoulli shaft finite element formulation based on Equivalent Single Layer Theory (ESLT), including the hysteretic internal damping of composite material and transverse shear effects, is introduced and then used to evaluate the influence of various parameters: stacking sequences, fiber orientations and bearing properties on natural frequencies, critical speeds, and instability thresholds. The obtained results are compared with those available in the literature using different theories. The agreement in the obtained results show that the developed Euler-Bernoulli finite element based on ESLT including hysteretic internal damping and shear transverse effects can be effectively used for the stability analysis of internally damped rotating composite shafts. Furthermore, the results revealed that rotor stability is sensitive to the laminate parameters and to the properties of the bearings.

Thinking About Bernoulli

NASA Astrophysics Data System (ADS)

Kamela, Martin

2007-09-01

One of the most fun demonstrations in a freshman mechanics class is the levitation of a ball in a steady air stream even when the jet is directed at an angle. This and other demonstrations are often used to argue for the validity of Bernoulli's principle. As cautioned by some authors,2-4 however, it is important to avoid making sweeping statements such as "high speed implies lower pressure" with respect to interpreting the popular demonstrations. In this paper I present a demonstration that can be used in conjunction with the discussion of Bernoulli's principle to encourage students to consider assumptions carefully. Specifically, it shows that a correlation of high speed with lower fluid pressure is not true in general.

Buckling and postbuckling of size-dependent cracked microbeams based on a modified couple stress theory

NASA Astrophysics Data System (ADS)

Akbarzadeh Khorshidi, M.; Shariati, M.

2017-07-01

The elastic buckling analysis and the static postbuckling response of the Euler-Bernoulli microbeams containing an open edge crack are studied based on a modified couple stress theory. The cracked section is modeled by a massless elastic rotational spring. This model contains a material length scale parameter and can capture the size effect. The von Kármán nonlinearity is applied to display the postbuckling behavior. Analytical solutions of a critical buckling load and the postbuckling response are presented for simply supported cracked microbeams. This parametric study indicates the effects of the crack location, crack severity, and length scale parameter on the buckling and postbuckling behaviors of cracked microbeams.

A Refined Zigzag Beam Theory for Composite and Sandwich Beams

NASA Technical Reports Server (NTRS)

Tessler, Alexander; Sciuva, Marco Di; Gherlone, Marco

2009-01-01

A new refined theory for laminated composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse-shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. Exact solutions for simply supported and cantilevered beams subjected to static loads are derived and the improved modelling capability of the new zigzag beam theory is demonstrated. In particular, extensive results for thick beams with highly heterogeneous material lay-ups are discussed and compared with corresponding results obtained from elasticity solutions, two other zigzag theories, and high-fidelity finite element analyses. Comparisons with the baseline Timoshenko Beam Theory are also presented. The comparisons clearly show the improved accuracy of the new, refined zigzag theory presented herein over similar existing theories. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining relatively low-cost, accurate estimates of structural response needed to design an important class of high-performance aerospace structures.

Refined gradient theory of scale-dependent superthin rods

NASA Astrophysics Data System (ADS)

Lurie, S. A.; Kuznetsova, E. L.; Rabinskii, L. N.; Popova, E. I.

2015-03-01

A version of the refined nonclassical theory of thin beams whose thickness is comparable with the scale characteristic of the material structure is constructed on the basis of the gradient theory of elasticity which, in contrast to the classical theory, contains some additional physical characteristics depending on the structure scale parameters and is therefore most appropriate for modeling the strains of scale-dependent systems. The fundamental conditions for the well-posedness of the gradient theories are obtained for the first time, and it is shown that some of the known applied gradient theories do not generally satisfy the well-posedness criterion. A version of the well-posed gradient strain theory which satisfies the symmetry condition is proposed. The well-posed gradient theory is then used to implement the method of kinematic hypotheses for constructing a refined theory of scale-dependent beams. The equilibrium equations of the refined theory of scale-dependent Timoshenko and Bernoulli beams are obtained. It is shown that the scale effects are localized near the beam ends, and therefore, taking the scale effects into account does not give any correction to the bending rigidity of long beams as noted in the previously published papers dealing with the scale-dependent beams.

Free vibration investigation of nano mass sensor using differential transformation method

NASA Astrophysics Data System (ADS)

Zarepour, Misagh; Hosseini, S. Amirhosein; Ghadiri, Majid

2017-03-01

In the present study, transverse vibration of nano-cantilever beam with attached mass and two rotational and transverse springs at its end is studied. Resonance frequency of vibrating system is influenced by changing mass particle and stiffness coefficients. Euler-Bernoulli beam theory, nonlocal constitutive equations of Eringen, and Hamilton's principle are used to develop equations of motion. Differential transformation method (DTM) is applied to solve the governing equations of the nanobeam with attached mass particle. Accurate results with minimum mathematical calculation are the advantages of DTM. A detailed parametric study is conducted to investigate the influences of nonlocal parameter. The results can be used in designing of nanoelectromechanical systems. To verify the results, some comparisons are presented between differential transform method results and open literature to show the accuracy of this new approach.

The Legacy of Leonhard Euler--A Tricentennial Tribute

ERIC Educational Resources Information Center

Debnath, Lokenath

2009-01-01

This tricentennial tribute commemorates Euler's major contributions to mathematical and physical sciences. A brief biographical sketch is presented with his major contributions to certain selected areas of number theory, differential and integral calculus, differential equations, solid and fluid mechanics, topology and graph theory, infinite…

Alternate solution to generalized Bernoulli equations via an integrating factor: an exact differential equation approach

NASA Astrophysics Data System (ADS)

Tisdell, C. C.

2017-08-01

Solution methods to exact differential equations via integrating factors have a rich history dating back to Euler (1740) and the ideas enjoy applications to thermodynamics and electromagnetism. Recently, Azevedo and Valentino presented an analysis of the generalized Bernoulli equation, constructing a general solution by linearizing the problem through a substitution. The purpose of this note is to present an alternative approach using 'exact methods', illustrating that a substitution and linearization of the problem is unnecessary. The ideas may be seen as forming a complimentary and arguably simpler approach to Azevedo and Valentino that have the potential to be assimilated and adapted to pedagogical needs of those learning and teaching exact differential equations in schools, colleges, universities and polytechnics. We illustrate how to apply the ideas through an analysis of the Gompertz equation, which is of interest in biomathematical models of tumour growth.

Poly-Frobenius-Euler polynomials

NASA Astrophysics Data System (ADS)

Kurt, Burak

2017-07-01

Hamahata [3] defined poly-Euler polynomials and the generalized poly-Euler polynomials. He proved some relations and closed formulas for the poly-Euler polynomials. By this motivation, we define poly-Frobenius-Euler polynomials. We give some relations for this polynomials. Also, we prove the relationships between poly-Frobenius-Euler polynomials and Stirling numbers of the second kind.

Bernoulli's Principle: Science as a Human Endeavor

ERIC Educational Resources Information Center

McCarthy, Deborah

2008-01-01

What do the ideas of Daniel Bernoulli--an 18th-century Swiss mathematician, physicist, natural scientist, and professor--and your students' next landing of the space shuttle via computer simulation have in common? Because of his contribution, referred in physical science as Bernoulli's principle, modern flight is possible. The mini learning-cycle…

Leonhard Euler and the mechanics of rigid bodies

NASA Astrophysics Data System (ADS)

Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J.

2017-01-01

In this work we present the original ideas and the construction of the rigid bodies theory realised by Leonhard Euler between 1738 and 1775. The number of treatises written by Euler on this subject is enormous, including the most notorious Scientia Navalis (1749), Decouverte d’un noveau principe de mecanique (1752), Du mouvement de rotation des corps solides autour d’un axe variable (1765), Theoria motus corporum solidorum seu rigidorum (1765) and Nova methodus motu corporum rigidorum determinandi (1776), in which he developed the ideas of the instantaneous rotation axis, the so-called Euler equations and angles, the components of what is now known as the inertia tensor, the principal axes of inertia, and, finally, the generalisation of the translation and rotation movement equations for any system. Euler, the man who ‘put most of mechanics into its modern form’ (Truesdell 1968 Essays in the History of Mechanics (Berlin: Springer) p 106).

On the application of the partition of unity method for nonlocal response of low-dimensional structures

NASA Astrophysics Data System (ADS)

Natarajan, Sundararajan

2014-12-01

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen's nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

Numerical solutions for Helmholtz equations using Bernoulli polynomials

NASA Astrophysics Data System (ADS)

Bicer, Kubra Erdem; Yalcinbas, Salih

2017-07-01

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations.

Approximation techniques for parameter estimation and feedback control for distributed models of large flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rosen, I. G.

1984-01-01

Approximation ideas are discussed that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems. Focusing on parameter estimation problems, ways by which one can obtain convergence results for cubic spline based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration are outlined. Sample numerical findings are also presented.

Analytical and experimental studies on detection of longitudinal, L and inverted T cracks in isotropic and bi-material beams based on changes in natural frequencies

NASA Astrophysics Data System (ADS)

Ravi, J. T.; Nidhan, S.; Muthu, N.; Maiti, S. K.

2018-02-01

An analytical method for determination of dimensions of longitudinal crack in monolithic beams, based on frequency measurements, has been extended to model L and inverted T cracks. Such cracks including longitudinal crack arise in beams made of layered isotropic or composite materials. A new formulation for modelling cracks in bi-material beams is presented. Longitudinal crack segment sizes, for L and inverted T cracks, varying from 2.7% to 13.6% of length of Euler-Bernoulli beams are considered. Both forward and inverse problems have been examined. In the forward problems, the analytical results are compared with finite element (FE) solutions. In the inverse problems, the accuracy of prediction of crack dimensions is verified using FE results as input for virtual testing. The analytical results show good agreement with the actual crack dimensions. Further, experimental studies have been done to verify the accuracy of the analytical method for prediction of dimensions of three types of crack in isotropic and bi-material beams. The results show that the proposed formulation is reliable and can be employed for crack detection in slender beam like structures in practice.

An analytical method for free vibration analysis of functionally graded beams with edge cracks

NASA Astrophysics Data System (ADS)

Wei, Dong; Liu, Yinghua; Xiang, Zhihai

2012-03-01

In this paper, an analytical method is proposed for solving the free vibration of cracked functionally graded material (FGM) beams with axial loading, rotary inertia and shear deformation. The governing differential equations of motion for an FGM beam are established and the corresponding solutions are found first. The discontinuity of rotation caused by the cracks is simulated by means of the rotational spring model. Based on the transfer matrix method, then the recurrence formula is developed to get the eigenvalue equations of free vibration of FGM beams. The main advantage of the proposed method is that the eigenvalue equation for vibrating beams with an arbitrary number of cracks can be conveniently determined from a third-order determinant. Due to the decrease in the determinant order as compared with previous methods, the developed method is simpler and more convenient to analytically solve the free vibration problem of cracked FGM beams. Moreover, free vibration analyses of the Euler-Bernoulli and Timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method. These advantages of the proposed procedure would be more remarkable as the increase of the number of cracks. A comprehensive analysis is conducted to investigate the influences of the location and total number of cracks, material properties, axial load, inertia and end supports on the natural frequencies and vibration mode shapes of FGM beams. The present work may be useful for the design and control of damaged structures.

A Short History of Probability Theory and Its Applications

ERIC Educational Resources Information Center

Debnath, Lokenath; Basu, Kanadpriya

2015-01-01

This paper deals with a brief history of probability theory and its applications to Jacob Bernoulli's famous law of large numbers and theory of errors in observations or measurements. Included are the major contributions of Jacob Bernoulli and Laplace. It is written to pay the tricentennial tribute to Jacob Bernoulli, since the year 2013…

Thinking about Bernoulli

ERIC Educational Resources Information Center

Kamela, Martin

2007-01-01

One of the most fun demonstrations in a freshman mechanics class is the levitation of a ball in a steady air stream even when the jet is directed at an angle. This and other demonstrations are often used to argue for the validity of Bernoulli's principle. As cautioned by some authors, however, it is important to avoid making sweeping statements…

Analysis of Pull-In Instability of Geometrically Nonlinear Microbeam Using Radial Basis Artificial Neural Network Based on Couple Stress Theory

PubMed Central

Heidari, Mohammad; Heidari, Ali; Homaei, Hadi

2014-01-01

The static pull-in instability of beam-type microelectromechanical systems (MEMS) is theoretically investigated. Two engineering cases including cantilever and double cantilever microbeam are considered. Considering the midplane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent Euler-Bernoulli beam model is used based on a modified couple stress theory, capable of capturing the size effect. By selecting a range of geometric parameters such as beam lengths, width, thickness, gaps, and size effect, we identify the static pull-in instability voltage. A MAPLE package is employed to solve the nonlinear differential governing equations to obtain the static pull-in instability voltage of microbeams. Radial basis function artificial neural network with two functions has been used for modeling the static pull-in instability of microcantilever beam. The network has four inputs of length, width, gap, and the ratio of height to scale parameter of beam as the independent process variables, and the output is static pull-in voltage of microbeam. Numerical data, employed for training the network, and capabilities of the model have been verified in predicting the pull-in instability behavior. The output obtained from neural network model is compared with numerical results, and the amount of relative error has been calculated. Based on this verification error, it is shown that the radial basis function of neural network has the average error of 4.55% in predicting pull-in voltage of cantilever microbeam. Further analysis of pull-in instability of beam under different input conditions has been investigated and comparison results of modeling with numerical considerations shows a good agreement, which also proves the feasibility and effectiveness of the adopted approach. The results reveal significant influences of size effect and geometric parameters on the static pull-in instability voltage of MEMS. PMID:24860602

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.

Quantum Markov semigroups constructed from quantum Bernoulli noises

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

Wang, Caishi; Chen, Jinshu

2016-02-15

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combiningmore » the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.« less

Fracture Analysis of MWCNT/Epoxy Nanocomposite Film Deposited on Aluminum Substrate.

PubMed

Her, Shiuh-Chuan; Chien, Pao-Chu

2017-04-13

Multi-walled carbon nanotube (MWCNT) reinforced epoxy films were deposited on an aluminum substrate by a hot-pressing process. Three-point bending tests were performed to determine the Young's modulus of MWCNT reinforced nanocomposite films. Compared to the neat epoxy film, nanocomposite film with 1 wt % of MWCNT exhibits an increase of 21% in the Young's modulus. Four-point-bending tests were conducted to investigate the fracture toughness of the MWCNT/epoxy nanocomposite film deposited on an aluminum substrate with interfacial cracks. Based on the Euler-Bernoulli beam theory, the strain energy in a film/substrate composite beam is derived. The difference of strain energy before and after the propagation of the interfacial crack are calculated, leading to the determination of the strain energy release rate. Experimental test results show that the fracture toughness of the nanocomposite film deposited on the aluminum substrate increases with the increase in the MWCNT content.

Modeling of capacitor charging dynamics in an energy harvesting system considering accurate electromechanical coupling effects

NASA Astrophysics Data System (ADS)

Bagheri, Shahriar; Wu, Nan; Filizadeh, Shaahin

2018-06-01

This paper presents an iterative numerical method that accurately models an energy harvesting system charging a capacitor with piezoelectric patches. The constitutive relations of piezoelectric materials connected with an external charging circuit with a diode bridge and capacitors lead to the electromechanical coupling effect and the difficulty of deriving accurate transient mechanical response, as well as the charging progress. The proposed model is built upon the Euler-Bernoulli beam theory and takes into account the electromechanical coupling effects as well as the dynamic process of charging an external storage capacitor. The model is validated through experimental tests on a cantilever beam coated with piezoelectric patches. Several parametric studies are performed and the functionality of the model is verified. The efficiency of power harvesting system can be predicted and tuned considering variations in different design parameters. Such a model can be utilized to design robust and optimal energy harvesting system.

In-plane vibration of FG micro/nano-mass sensor based on nonlocal theory under various thermal loading via differential transformation method

NASA Astrophysics Data System (ADS)

Rahmani, O.; Mohammadi Niaei, A.; Hosseini, S. A. H.; Shojaei, M.

2017-01-01

In the present study, free vibration model of a cantilever functionally graded (FG) nanobeam with an attached mass at tip and under various thermal loading and two types of material distribution is introduced. The vibration performance is considered using nonlocal Euler-Bernoulli beam theory. Two types of thermal loading, namely, uniform and nonlinear temperature rises through the thickness direction are considered. Thermo-mechanical properties of FG nano mass sensor are supposed to vary smoothly and continuously throughout the thickness based on power-law and Mori Tanaka distributions of material properties. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. The governing equations of the system with both axial and transverse displacements are derived based on Hamilton's principle and solved utilizing the differential transformation method (DTM) to find the non-dimensional natural frequencies. The results have good agreements with those discussing in the literature. After validation of the present model, the effect of various parameters such as mass and position of the attached nano particle, FG power-law exponent, thermal load type, material distribution type and nonlocal parameter on the frequency of nano sensor are studied. It is shown that the present model produces results of high accuracy, and it can be used as a benchmark in future studies of the free vibration of FG Nano-Mass Sensors.

Computational Methods for Design, Control and Optimization

DTIC Science & Technology

2007-10-01

Krueger Eugene M. Cliff Hoan Nguyen Traian Iliescu John Singler James Vance Eric Vugrin Adam Childers Dan Sutton References [11 J. T. Borggaard, S...Control, 45th IEEE Conference on Decision and Control, accepted. [11] L. C. Berselli, T. Iliescu and W. J. Layton , Mathematics of Large Eddy...Daniel Inman, Eric Ruggiero and John Singler, Finite Element For- mulation for Static Control of a Thin Euler-Bernoulli Beam Using Piezoelectric

A general multiblock Euler code for propulsion integration. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

A general multiblock Euler solver was developed for the analysis of flow fields over geometrically complex configurations either in free air or in a wind tunnel. In this approach, the external space around a complex configuration was divided into a number of topologically simple blocks, so that surface-fitted grids and an efficient flow solution algorithm could be easily applied in each block. The computational grid in each block is generated using a combination of algebraic and elliptic methods. A grid generation/flow solver interface program was developed to facilitate the establishment of block-to-block relations and the boundary conditions for each block. The flow solver utilizes a finite volume formulation and an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. The generality of the method was demonstrated through the analysis of two complex configurations at various flow conditions. Results were compared to available test data. Two accompanying volumes, user manuals for the preparation of multi-block grids (vol. 2) and for the Euler flow solver (vol. 3), provide information on input data format and program execution.

Peeling flexible beams in viscous fluids: Rigidity and extensional compliance

NASA Astrophysics Data System (ADS)

Dhong, Charles; Fréchette, Joëlle

2017-01-01

We describe small angle peeling measurements in completely submerged environments to study the coupling between viscous forces and the mechanical properties of the plates being peeled. During the experiments, the plates resist motion because of lubrication forces while van der Waals forces between the plates and the static surface are negligible. In particular, we study the role played by flexural rigidity in the force-displacement curves and in the energy release rate. We show that the coupling between the viscous forces and the flexural rigidity of the plates dictates the shape and magnitude of the force-displacement curves. We develop simple scaling relationships that combine the lubrication forces with an Euler-Bernoulli beam to extract how the peak force and energy release rates depend on the ratio between rigidity and viscosity, and show good agreement between the predictions and experimental results. We also show that increasing the extensional compliance leads to a decrease in both the force-displacement curve and in the energy release rate. We then demonstrate that this reduction can be interpreted in terms of a stress decay length.

Active-passive vibration absorber of beam-cart-seesaw system with piezoelectric transducers

NASA Astrophysics Data System (ADS)

Lin, J.; Huang, C. J.; Chang, Julian; Wang, S.-W.

2010-09-01

In contrast with fully controllable systems, a super articulated mechanical system (SAMS) is a controlled underactuated mechanical system in which the dimensions of the configuration space exceed the dimensions of the control input space. The objectives of the research are to develop a novel SAMS model which is called beam-cart-seesaw system, and renovate a novel approach for achieving a high performance active-passive piezoelectric vibration absorber for such system. The system consists of two mobile carts, which are coupled via rack and pinion mechanics to two parallel tracks mounted on pneumatic rodless cylinders. One cart carries an elastic beam, and the other cart acts as a counterbalance. One adjustable counterweight mass is also installed underneath the seesaw to serve as a passive damping mechanism to absorb impact and shock energy. The motion and control of a Bernoulli-Euler beam subjected to the modified cart/seesaw system are analyzed first. Moreover, gray relational grade is utilized to investigate the sensitivity of tuning the active proportional-integral-derivative (PID) controller to achieve desired vibration suppression performance. Consequently, it is shown that the active-passive vibration absorber can not only provide passive damping, but can also enhance the active action authority. The proposed software/hardware platform can also be profitable for the standardization of laboratory equipment, as well as for the development of entertainment tools.

3D GIS spatial operation based on extended Euler operators

NASA Astrophysics Data System (ADS)

Xu, Hongbo; Lu, Guonian; Sheng, Yehua; Zhou, Liangchen; Guo, Fei; Shang, Zuoyan; Wang, Jing

2008-10-01

The implementation of 3 dimensions spatial operations, based on certain data structure, has a lack of universality and is not able to treat with non-manifold cases, at present. ISO/DIS 19107 standard just presents the definition of Boolean operators and set operators for topological relationship query, and OGC GeoXACML gives formal definitions for several set functions without implementation detail. Aiming at these problems, based mathematical foundation on cell complex theory, supported by non-manifold data structure and using relevant research in the field of non-manifold geometry modeling for reference, firstly, this paper according to non-manifold Euler-Poincaré formula constructs 6 extended Euler operators and inverse operators to carry out creating, updating and deleting 3D spatial elements, as well as several pairs of supplementary Euler operators to convenient for implementing advanced functions. Secondly, we change topological element operation sequence of Boolean operation and set operation as well as set functions defined in GeoXACML into combination of extended Euler operators, which separates the upper functions and lower data structure. Lastly, we develop underground 3D GIS prototype system, in which practicability and credibility of extended Euler operators faced to 3D GIS presented by this paper are validated.

Analytical solutions to the free vibration of a double-walled carbon nanotube carrying a bacterium at its tip

NASA Astrophysics Data System (ADS)

Storch, Joel A.; Elishakoff, Isaac

2013-11-01

We calculate the natural frequencies and mode shapes of a cantilevered double-walled carbon nanotube carrying a rigid body—representative of a bacterium or virus—at the tip of the outer nanotube. By idealizing the nanotubes as Bernoulli-Euler beams, we are able to obtain exact expressions for both the mode shapes and characteristic frequency equation. Separate analyses are performed for the special case of a concentrated tip mass and the more complicated situation where the tip body also exhibits inertia and mass center offset from the beam tip.

Beltrami–Bernoulli equilibria in plasmas with degenerate electrons

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

Berezhiani, V. I., E-mail: vazhab@yahoo.com; Shatashvili, N. L., E-mail: shatash@ictp.it; Mahajan, S. M., E-mail: mahajan@mail.utexas.edu

2015-02-15

A new class of Double Beltrami–Bernoulli equilibria, sustained by electron degeneracy pressure, is investigated. It is shown that due to electron degeneracy, a nontrivial Beltrami–Bernoulli equilibrium state is possible even for a zero temperature plasma. These states are, conceptually, studied to show the existence of new energy transformation pathways converting, for instance, the degeneracy energy into fluid kinetic energy. Such states may be of relevance to compact astrophysical objects like white dwarfs, neutron stars, etc.

Euler Teaches a Class in Structural Steel Design

ERIC Educational Resources Information Center

Boyajian, David M.

2009-01-01

Even before steel was a topic of formal study for structural engineers, the brilliant eighteenth century Swiss mathematician and physicist, Leonhard Euler (1707-1783), investigated the theory governing the elastic behaviour of columns, the results of which are incorporated into the American Institute of Steel Construction's (AISC's) Bible: the…

The evaluation of shear deformation for contact analysis with large displacement

NASA Astrophysics Data System (ADS)

Nizam, Z. M.; Obiya, H.; Ijima, K.; Azhar, A. T. S.; Hazreek, Z. A. M.; Shaylinda, M. Z. N.

2018-04-01

A common problem encountered in the study of contact problem is the failure to obtain stable and accurate convergence result when the contact node is close to the element edge, which is referred as “critical area”. In previous studies, the modification of the element force equation to apply it to a node-element contact problem using the Euler-Bernoulli beam theory [1]. A simple single-element consists two edges and a contact point was used to simulate contact phenomenon of a plane frame. The modification was proven to be effective by the converge-ability of the unbalanced force at the tip of element edge, which enabled the contact node to “pass-through”, resulting in precise results. However, in another recent study, we discover that, if shear deformation based on Timoshenko beam theory is taken into consideration, a basic simply supported beam coordinate afforded a much simpler and more efficient technique for avoiding the divergence of the unbalanced force in the “critical area”. Using our unique and robust Tangent Stiffness Method, the improved equation can be used to overcome any geometrically nonlinear analyses, including those involving extremely large displacements.

Regularized estimation of Euler pole parameters

NASA Astrophysics Data System (ADS)

Aktuğ, Bahadir; Yildirim, Ömer

2013-07-01

Euler vectors provide a unified framework to quantify the relative or absolute motions of tectonic plates through various geodetic and geophysical observations. With the advent of space geodesy, Euler parameters of several relatively small plates have been determined through the velocities derived from the space geodesy observations. However, the available data are usually insufficient in number and quality to estimate both the Euler vector components and the Euler pole parameters reliably. Since Euler vectors are defined globally in an Earth-centered Cartesian frame, estimation with the limited geographic coverage of the local/regional geodetic networks usually results in highly correlated vector components. In the case of estimating the Euler pole parameters directly, the situation is even worse, and the position of the Euler pole is nearly collinear with the magnitude of the rotation rate. In this study, a new method, which consists of an analytical derivation of the covariance matrix of the Euler vector in an ideal network configuration, is introduced and a regularized estimation method specifically tailored for estimating the Euler vector is presented. The results show that the proposed method outperforms the least squares estimation in terms of the mean squared error.

Refinement of Timoshenko Beam Theory for Composite and Sandwich Beams Using Zigzag Kinematics

NASA Technical Reports Server (NTRS)

Tessler, Alexander; DiSciuva, Marco; Gherlone, Marco

2007-01-01

A new refined theory for laminated-composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining accurate estimates of structural response of laminated composites.

Toward Higher-Order Mass Detection: Influence of an Adsorbate's Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam.

PubMed

Heinrich, Stephen M; Dufour, Isabelle

2015-11-19

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam's length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate's geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate's (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for "higher-order" nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate's mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing.

The small length scale effect for a non-local cantilever beam: a paradox solved.

PubMed

Challamel, N; Wang, C M

2008-08-27

Non-local continuum mechanics allows one to account for the small length scale effect that becomes significant when dealing with microstructures or nanostructures. This paper presents some simplified non-local elastic beam models, for the bending analyses of small scale rods. Integral-type or gradient non-local models abandon the classical assumption of locality, and admit that stress depends not only on the strain value at that point but also on the strain values of all points on the body. There is a paradox still unresolved at this stage: some bending solutions of integral-based non-local elastic beams have been found to be identical to the classical (local) solution, i.e. the small scale effect is not present at all. One example is the Euler-Bernoulli cantilever nanobeam model with a point load which has application in microelectromechanical systems and nanoelectromechanical systems as an actuator. In this paper, it will be shown that this paradox may be overcome with a gradient elastic model as well as an integral non-local elastic model that is based on combining the local and the non-local curvatures in the constitutive elastic relation. The latter model comprises the classical gradient model and Eringen's integral model, and its application produces small length scale terms in the non-local elastic cantilever beam solution.

A precise integration method for solving coupled vehicle-track dynamics with nonlinear wheel-rail contact

NASA Astrophysics Data System (ADS)

Zhang, J.; Gao, Q.; Tan, S. J.; Zhong, W. X.

2012-10-01

A new method is proposed as a solution for the large-scale coupled vehicle-track dynamic model with nonlinear wheel-rail contact. The vehicle is simplified as a multi-rigid-body model, and the track is treated as a three-layer beam model. In the track model, the rail is assumed to be an Euler-Bernoulli beam supported by discrete sleepers. The vehicle model and the track model are coupled using Hertzian nonlinear contact theory, and the contact forces of the vehicle subsystem and the track subsystem are approximated by the Lagrange interpolation polynomial. The response of the large-scale coupled vehicle-track model is calculated using the precise integration method. A more efficient algorithm based on the periodic property of the track is applied to calculate the exponential matrix and certain matrices related to the solution of the track subsystem. Numerical examples demonstrate the computational accuracy and efficiency of the proposed method.

Flutter of wings involving a locally distributed flexible control surface

NASA Astrophysics Data System (ADS)

Mozaffari-Jovin, S.; Firouz-Abadi, R. D.; Roshanian, J.

2015-11-01

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli beam theory, along with the Kelvin-Voigt viscoelastic constitutive law. Meanwhile, the unsteady thin-airfoil and strip theories are the tools of producing the three-dimensional airloads. The origin of aerodynamic instability undergoes analysis in light of the oscillatory loads as well as the loads owing to arbitrary motions. After successful verification of the model, a systematic flutter survey was conducted on the theoretical effects of various control surface parameters. The results obtained demonstrate that the flapping modes and parameters of the control surface can significantly impact the flutter characteristics of the wings, which leads to a series of pertinent conclusions.

Theoretical study on a Miniature Joule-Thomson & Bernoulli Cryocooler

NASA Astrophysics Data System (ADS)

Xiong, L. Y.; Kaiser, G.; Binneberg, A.

2004-11-01

In this paper, a microchannel-based cryocooler consisting of a compressor, a recuperator and a cold heat exchanger has been developed to study the feasibility of cryogenic cooling by the use of Joule-Thomson effect and Bernoulli effect. A set of governing equations including Bernoulli equations and energy equations are introduced and the performance of the cooler is calculated. The influences of some working conditions and structure parameters on the performance of coolers are discussed in details.

Shape optimisation of an underwater Bernoulli gripper

NASA Astrophysics Data System (ADS)

Flint, Tim; Sellier, Mathieu

2015-11-01

In this work, we are interested in maximising the suction produced by an underwater Bernoulli gripper. Bernoulli grippers work by exploiting low pressure regions caused by the acceleration of a working fluid through a narrow channel, between the gripper and a surface, to provide a suction force. This mechanism allows for non-contact adhesion to various surfaces and may be used to hold a robot to the hull of a ship while it inspects welds for example. A Bernoulli type pressure analysis was used to model the system with a Darcy friction factor approximation to include the effects of frictional losses. The analysis involved a constrained optimisation in order to avoid cavitation within the mechanism which would result in decreased performance and damage to surfaces. A sensitivity based method and gradient descent approach was used to find the optimum shape of a discretised surface. The model's accuracy has been quantified against finite volume computational fluid dynamics simulation (ANSYS CFX) using the k- ω SST turbulence model. Preliminary results indicate significant improvement in suction force when compared to a simple geometry by retaining a pressure just above that at which cavitation would occur over as much surface area as possible. Doctoral candidate in the Mechanical Engineering Department of the University of Canterbury, New Zealand.

Testing Bernoulli's Law

ERIC Educational Resources Information Center

Ivanov, Dragia; Nikolov, Stefan; Petrova, Hristina

2014-01-01

In this paper we present three different methods for testing Bernoulli's law that are different from the standard "tube with varying cross-section." They are all applicable to high-school level physics education, with varying levels of theoretical and experimental complexity, depending on students' skills, and may even be…

Generalization of the Bernoulli ODE

ERIC Educational Resources Information Center

Azevedo, Douglas; Valentino, Michele C.

2017-01-01

In this note, we propose a generalization of the famous Bernoulli differential equation by introducing a class of nonlinear first-order ordinary differential equations (ODEs). We provide a family of solutions for this introduced class of ODEs and also we present some examples in order to illustrate the applications of our result.

A Bernoulli Gaussian Watermark for Detecting Integrity Attacks in Control Systems

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

Weerakkody, Sean; Ozel, Omur; Sinopoli, Bruno

We examine the merit of Bernoulli packet drops in actively detecting integrity attacks on control systems. The aim is to detect an adversary who delivers fake sensor measurements to a system operator in order to conceal their effect on the plant. Physical watermarks, or noisy additive Gaussian inputs, have been previously used to detect several classes of integrity attacks in control systems. In this paper, we consider the analysis and design of Gaussian physical watermarks in the presence of packet drops at the control input. On one hand, this enables analysis in a more general network setting. On the othermore » hand, we observe that in certain cases, Bernoulli packet drops can improve detection performance relative to a purely Gaussian watermark. This motivates the joint design of a Bernoulli-Gaussian watermark which incorporates both an additive Gaussian input and a Bernoulli drop process. We characterize the effect of such a watermark on system performance as well as attack detectability in two separate design scenarios. Here, we consider a correlation detector for attack recognition. We then propose efficiently solvable optimization problems to intelligently select parameters of the Gaussian input and the Bernoulli drop process while addressing security and performance trade-offs. Finally, we provide numerical results which illustrate that a watermark with packet drops can indeed outperform a Gaussian watermark.« less

An installed nacelle design code using a multiblock Euler solver. Volume 1: Theory document

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

An efficient multiblock Euler design code was developed for designing a nacelle installed on geometrically complex airplane configurations. This approach employed a design driver based on a direct iterative surface curvature method developed at LaRC. A general multiblock Euler flow solver was used for computing flow around complex geometries. The flow solver used a finite-volume formulation with explicit time-stepping to solve the Euler Equations. It used a multiblock version of the multigrid method to accelerate the convergence of the calculations. The design driver successively updated the surface geometry to reduce the difference between the computed and target pressure distributions. In the flow solver, the change in surface geometry was simulated by applying surface transpiration boundary conditions to avoid repeated grid generation during design iterations. Smoothness of the designed surface was ensured by alternate application of streamwise and circumferential smoothings. The capability and efficiency of the code was demonstrated through the design of both an isolated nacelle and an installed nacelle at various flow conditions. Information on the execution of the computer program is provided in volume 2.

Theory of electronically phased coherent beam combination without a reference beam

NASA Astrophysics Data System (ADS)

Shay, Thomas M.

2006-12-01

The first theory for two novel coherent beam combination architectures that are the first electronic beam combination architectures that completely eliminate the need for a separate reference beam are presented. Detailed theoretical models are developed and presented for the first time.

Modelling of Safety Instrumented Systems by using Bernoulli trials: towards the notion of odds on for SIS failures analysis

NASA Astrophysics Data System (ADS)

Cauffriez, Laurent

2017-01-01

This paper deals with the modeling of a random failures process of a Safety Instrumented System (SIS). It aims to identify the expected number of failures for a SIS during its lifecycle. Indeed, the fact that the SIS is a system being tested periodically gives the idea to apply Bernoulli trials to characterize the random failure process of a SIS and thus to verify if the PFD (Probability of Failing Dangerously) experimentally obtained agrees with the theoretical one. Moreover, the notion of "odds on" found in Bernoulli theory allows engineers and scientists determining easily the ratio between “outcomes with success: failure of SIS” and “outcomes with unsuccess: no failure of SIS” and to confirm that SIS failures occur sporadically. A Stochastic P-temporised Petri net is proposed and serves as a reference model for describing the failure process of a 1oo1 SIS architecture. Simulations of this stochastic Petri net demonstrate that, during its lifecycle, the SIS is rarely in a state in which it cannot perform its mission. Experimental results are compared to Bernoulli trials in order to validate the powerfulness of Bernoulli trials for the modeling of the failures process of a SIS. The determination of the expected number of failures for a SIS during its lifecycle opens interesting research perspectives for engineers and scientists by completing the notion of PFD.

On the dynamics of viscous masonry beams

NASA Astrophysics Data System (ADS)

Lucchesi, M.; Pintucchi, B.; Šilhavý, M.; Zani, N.

2015-05-01

In this paper, we consider the longitudinal and transversal vibrations of the masonry beams and arches. The basic motivation is the seismic vulnerability analysis of masonry structures that can be modeled as monodimensional elements. The Euler-Bernoulli hypothesis is employed for the system of forces in the beam. The axial force and the bending moment are assumed to consist of the elastic and viscous parts. The elastic part is described by the no-tension material, i.e., the material with no resistance to tension and which accounts for the cases of limitless, as well as bounded compressive strength. The adaptation of this material to beams has been developed in Orlandi (Analisi non lineare di strutture ad arco in muratura. Thesis, 1999) and Zani (Eur J Mech A/Solids 23:467-484, 2004). The viscous part amounts to the Kelvin-Voigt damping depending linearly on the time derivatives of the linearized strain and curvature. The dynamical equations are formulated, and a mathematical analysis of them is presented. Specifically, following Gajewski et al. (Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Akademie-Verlag, Berlin, 1974), the theorems of existence, uniqueness and regularity of the solution of the dynamical equations are recapitulated and specialized for our purposes, to support the numerical analysis applied previously in Lucchesi and Pintucchi (Eur J Mech A/Solids 26:88-105, 2007 ). As usual, for that the Galerkin method has been used. As an illustration, two numerical examples (slender masonry tower and masonry arch) are presented in this paper with the applied forces corresponding to the acceleration in the earthquake in Emilia Romagna in May 29, 2012.

Geometrical study of phyllotactic patterns by Bernoulli spiral lattices.

PubMed

Sushida, Takamichi; Yamagishi, Yoshikazu

2017-06-01

Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. van Iterson (Mathematische und mikroskopisch - anatomische Studien über Blattstellungen nebst Betrachtungen über den Schalenbau der Miliolinen, Verlag von Gustav Fischer, Jena, 1907) suggested a centric model representing ideal phyllotactic patterns as disk packings of Bernoulli spiral lattices and presented a phase diagram now called Van Iterson's diagram explaining the bifurcation processes of their combinatorial structures. Geometrical properties on disk packings were shown by Rothen & Koch (J. Phys France, 50(13), 1603-1621, 1989). In contrast, as another centric model, we organized a mathematical framework of Voronoi tilings of Bernoulli spiral lattices and showed mathematically that the phase diagram of a Voronoi tiling is graph-theoretically dual to Van Iterson's diagram. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices. © 2017 Japanese Society of Developmental Biologists.

Linear stochastic Schrödinger equations in terms of quantum Bernoulli noises

NASA Astrophysics Data System (ADS)

Chen, Jinshu; Wang, Caishi

2017-05-01

Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation. In this paper, we study linear stochastic Schrödinger equations (LSSEs) associated with QBN in the space of square integrable complex-valued Bernoulli functionals. We first rigorously prove a formula concerning the number operator N on Bernoulli functionals. And then, by using this formula as well as Mora and Rebolledo's results on a general LSSE [C. M. Mora and R. Rebolledo, Infinite. Dimens. Anal. Quantum Probab. Relat. Top. 10, 237-259 (2007)], we obtain an easily checking condition for a LSSE associated with QBN to have a unique Nr-strong solution of mean square norm conservation for given r ≥0 . Finally, as an application of this condition, we examine a special class of LSSEs associated with QBN and some further results are proven.

Euler-Lagrange formulas for pseudo-Kähler manifolds

NASA Astrophysics Data System (ADS)

Park, JeongHyeong

2016-01-01

Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m > 2 k. Taking the inner product with the Kähler form Ωk gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler-Lagrange equations are a generalized Einstein-Gauss-Bonnet gravity theory; this theory restricts to the canonical formalism if c =c2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting.

Bernoulli in the operating room: from the perspective of a cardiac surgeon.

PubMed

Matt, Peter

2014-12-01

The Bernoullis were one of the most distinguished families in the history of science. It was Daniel Bernoulli who applied mathematical physics to medicine to further his understanding of physiological mechanisms that have an impact even in today's high-end medicine. His masterwork was the analysis of fluid dynamics, which resulted in Bernoulli's law. Most important for cardiac surgery, it describes how a centrifugal pump works within an extracorporeal circulation, lays the basis for measuring a gradient over a stenotic heart valve, and explains how to measure the transit time flow within a bypass graft. Georg Thieme Verlag KG Stuttgart · New York.

Bernoulli? Perhaps, but What about Viscosity?

ERIC Educational Resources Information Center

Eastwell, Peter

2007-01-01

Bernoulli's principle is being misunderstood and consequently misused. This paper clarifies the issues involved, hypothesises as to how this unfortunate situation has arisen, provides sound explanations for many everyday phenomena involving moving air, and makes associated recommendations for teaching the effects of moving fluids.

Colonic transit time and pressure based on Bernoulli's principle.

PubMed

Uno, Yoshiharu

2018-01-01

Variations in the caliber of human large intestinal tract causes changes in pressure and the velocity of its contents, depending on flow volume, gravity, and density, which are all variables of Bernoulli's principle. Therefore, it was hypothesized that constipation and diarrhea can occur due to changes in the colonic transit time (CTT), according to Bernoulli's principle. In addition, it was hypothesized that high amplitude peristaltic contractions (HAPC), which are considered to be involved in defecation in healthy subjects, occur because of cecum pressure based on Bernoulli's principle. A virtual healthy model (VHM), a virtual constipation model and a virtual diarrhea model were set up. For each model, the CTT was decided according to the length of each part of the colon, and then calculating the velocity due to the cecum inflow volume. In the VHM, the pressure change was calculated, then its consistency with HAPC was verified. The CTT changed according to the difference between the cecum inflow volume and the caliber of the intestinal tract, and was inversely proportional to the cecum inflow volume. Compared with VHM, the CTT was prolonged in the virtual constipation model, and shortened in the virtual diarrhea model. The calculated pressure of the VHM and the gradient of the interlocked graph were similar to that of HAPC. The CTT and HAPC can be explained by Bernoulli's principle, and constipation and diarrhea may be fundamentally influenced by flow dynamics.

Deployment of a multi-link flexible structure

NASA Astrophysics Data System (ADS)

Na, Kyung-Su; Kim, Ji-Hwan

2006-06-01

Deployment of a multi-link beam structure undergoing locking is analyzed in the Timoshenko beam theory. In the modeling of the system, dynamic forces are assumed to be torques and restoring forces due to the torsion spring at each joint. Hamilton's principle is used to determine the equations of motion and the finite element method is adopted to analyze the system. Newmark time integration and Newton-Raphson iteration methods are used to solve for the non-linear equations of motion at each time step. The locking at the joints of the multi-link flexible structure is analyzed by the momentum balance method. Numerical results are compared with the previous experimental data. The angles and angular velocities of each joint, tip displacement, and velocity of each link are investigated to study the motions of the links at each time step. To analyze the effect of thickness on the motion of the link, the angle and the tip displacement of each link are compared according to the various slenderness ratios. Additionally, in order to investigate the effect of shear, the tip displacements of a Timoshenko beam are compared with those of an Euler-Bernoulli beam.

Bernoulli Suction Effect on Soap Bubble Blowing?

NASA Astrophysics Data System (ADS)

Davidson, John; Ryu, Sangjin

2015-11-01

As a model system for thin-film bubble with two gas-liquid interfaces, we experimentally investigated the pinch-off of soap bubble blowing. Using the lab-built bubble blower and high-speed videography, we have found that the scaling law exponent of soap bubble pinch-off is 2/3, which is similar to that of soap film bridge. Because air flowed through the decreasing neck of soap film tube, we studied possible Bernoulli suction effect on soap bubble pinch-off by evaluating the Reynolds number of airflow. Image processing was utilized to calculate approximate volume of growing soap film tube and the volume flow rate of the airflow, and the Reynolds number was estimated to be 800-3200. This result suggests that soap bubbling may involve the Bernoulli suction effect.

Design and analysis of a MEMS-based bifurcate-shape piezoelectric energy harvester

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

Luo, Yuan; Gan, Ruyi, E-mail: 2471390146@qq.com; Wan, Shalang

This paper presents a novel piezoelectric energy harvester, which is a MEMS-based device. This piezoelectric energy harvester uses a bifurcate-shape. The derivation of the mathematical modeling is based on the Euler-Bernoulli beam theory, and the main mechanical and electrical parameters of this energy harvester are analyzed and simulated. The experiment result shows that the maximum output voltage can achieve 3.3 V under an acceleration of 1 g at 292.11 Hz of frequency, and the output power can be up to 0.155 mW under the load of 0.4 MΩ. The power density is calculated as 496.79 μWmm{sup −3}. Besides that, itmore » is demonstrated efficiently at output power and voltage and adaptively in practical vibration circumstance. This energy harvester could be used for low-power electronic devices.« less

Hydraulic jump and Bernoulli equation in nonlinear shallow water model

NASA Astrophysics Data System (ADS)

Sun, Wen-Yih

2018-06-01

A shallow water model was applied to study the hydraulic jump and Bernoulli equation across the jump. On a flat terrain, when a supercritical flow plunges into a subcritical flow, discontinuity develops on velocity and Bernoulli function across the jump. The shock generated by the obstacle may propagate downstream and upstream. The latter reflected from the inflow boundary, moves downstream and leaves the domain. Before the reflected wave reaching the obstacle, the short-term integration (i.e., quasi-steady) simulations agree with Houghton and Kasahara's results, which may have unphysical complex solutions. The quasi-steady flow is quickly disturbed by the reflected wave, finally, flow reaches steady and becomes critical without complex solutions. The results also indicate that Bernoulli function is discontinuous but the potential of mass flux remains constant across the jump. The latter can be used to predict velocity/height in a steady flow.

On Bi-Grid Local Mode Analysis of Solution Techniques for 3-D Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Ibraheem, S. O.; Demuren, A. O.

1994-01-01

A procedure is presented for utilizing a bi-grid stability analysis as a practical tool for predicting multigrid performance in a range of numerical methods for solving Euler and Navier-Stokes equations. Model problems based on the convection, diffusion and Burger's equation are used to illustrate the superiority of the bi-grid analysis as a predictive tool for multigrid performance in comparison to the smoothing factor derived from conventional von Neumann analysis. For the Euler equations, bi-grid analysis is presented for three upwind difference based factorizations, namely Spatial, Eigenvalue and Combination splits, and two central difference based factorizations, namely LU and ADI methods. In the former, both the Steger-Warming and van Leer flux-vector splitting methods are considered. For the Navier-Stokes equations, only the Beam-Warming (ADI) central difference scheme is considered. In each case, estimates of multigrid convergence rates from the bi-grid analysis are compared to smoothing factors obtained from single-grid stability analysis. Effects of grid aspect ratio and flow skewness are examined. Both predictions are compared with practical multigrid convergence rates for 2-D Euler and Navier-Stokes solutions based on the Beam-Warming central scheme.

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

NASA Astrophysics Data System (ADS)

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, corresponding to the definition of the tensors mentioned above. The analogy between the classical continuous Euler-Bernoulli model of beams and the present discrete model is developed, leading to the expressions for the equivalent spiral and axial stiffness, in terms of the continuous beam geometrical and mechanical characteristics. Some numerical results are also given, showing the amplitude dependence of the frequencies on the amplitude of vibration, and compared to the backbone curves obtained previously by the continuous nonlinear classical beam theory, presented for example in [3,5,8,15-22]. A convergence study is performed by increasing the number of masses and bars, showing a good convergence to the theoretical values of continuous beams.

Who Solved the Bernoulli Differential Equation and How Did They Do It?

ERIC Educational Resources Information Center

Parker, Adam E.

2013-01-01

The Bernoulli brothers, Jacob and Johann, and Leibniz: Any of these might have been first to solve what is called the Bernoulli differential equation. We explore their ideas and the chronology of their work, finding out, among other things, that variation of parameters was used in 1697, 78 years before 1775, when Lagrange introduced it in general.

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

NASA Astrophysics Data System (ADS)

Liu, J.; Zhu, W. D.; Charalambides, P. G.; Shao, Y. M.; Xu, Y. F.; Fang, X. M.

2016-11-01

As one of major failure modes of mechanical structures subjected to periodic loads, embedded cracks due to fatigue can cause catastrophic failure of machineries. Understanding the dynamic characteristics of a structure with an embedded crack is helpful for early crack detection and diagnosis. In this work, a new three-segment beam model with local flexibilities at crack tips is developed to investigate the vibration of a cantilever beam with a closed, fully embedded horizontal crack, which is assumed to be not located at its clamped or free end or distributed near its top or bottom side. The three-segment beam model is assumed to be a linear elastic system, and it does not account for the nonlinear crack closure effect; the top and bottom segments always stay in contact at their interface during the beam vibration. It can model the effects of local deformations in the vicinity of the crack tips, which cannot be captured by previous methods in the literature. The middle segment of the beam containing the crack is modeled by a mechanically consistent, reduced bending moment. Each beam segment is assumed to be an Euler-Bernoulli beam, and the compliances at the crack tips are analytically determined using a J-integral approach and verified using commercial finite element software. Using compatibility conditions at the crack tips and the transfer matrix method, the nature frequencies and mode shapes of the cracked cantilever beam are obtained. The three-segment beam model is used to investigate the effects of local flexibilities at crack tips on the first three natural frequencies and mode shapes of the cracked cantilever beam. A stationary wavelet transform (SWT) method is used to process the mode shapes of the cracked cantilever beam; jumps in single-level SWT decomposition detail coefficients can be used to identify the length and location of an embedded horizontal crack.

The importance of Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov

NASA Astrophysics Data System (ADS)

Sharkov, N. A.; Sharkova, O. A.

2018-05-01

The paper identifies the importance of the Leonhard Euler's discoveries in the field of shipbuilding for the scientific evolution of academician A. N. Krylov and for the modern knowledge in survivability and safety of ships. The works by Leonard Euler "Marine Science" and "The Moon Motion New Theory" are discussed.

Analytical and experimental comparisons of electromechanical vibration response of a piezoelectric bimorph beam for power harvesting

NASA Astrophysics Data System (ADS)

Lumentut, M. F.; Howard, I. M.

2013-03-01

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical method for modelling an electromechanical piezoelectric bimorph beam with tip mass under two input base transverse and longitudinal excitations. The Euler-Bernoulli beam equations were used to model the piezoelectric bimorph beam. The polarity-electric field of the piezoelectric element is excited by the strain field caused by base input excitation, resulting in electrical charge. The governing electromechanical dynamic equations were derived analytically using the weak form of the Hamiltonian principle to obtain the constitutive equations. Three constitutive electromechanical dynamic equations based on independent coefficients of virtual displacement vectors were formulated and then further modelled using the normalised Ritz eigenfunction series. The electromechanical formulations include both the series and parallel connections of the piezoelectric bimorph. The multi-mode frequency response functions (FRFs) under varying electrical load resistance were formulated using Laplace transformation for the multi-input mechanical vibrations to provide the multi-output dynamic displacement, velocity, voltage, current and power. The experimental and theoretical validations reduced for the single mode system were shown to provide reasonable predictions. The model results from polar base excitation for off-axis input motions were validated with experimental results showing the change to the electrical power frequency response amplitude as a function of excitation angle, with relevance for practical implementation.

Flawed Applications of Bernoulli's Principle

NASA Astrophysics Data System (ADS)

Koumaras, Panagiotis; Primerakis, Georgios

2018-04-01

One of the most popular demonstration experiments pertaining to Bernoulli's principle is the production of a water spray by using a vertical plastic straw immersed in a glass of water and a horizontal straw to blow air towards the top edge of the vertical one. A more general version of this phenomenon, appearing also in school physics problems, is the determination of the rise of the water level h in the straw (see Fig. 1).

Active control of acoustic pressure fields using smart material technologies

NASA Technical Reports Server (NTRS)

Banks, H. T.; Smith, R. C.

1993-01-01

An overview describing the use of piezoceramic patches in reducing noise in a structural acoustics setting is presented. The passive and active contributions due to patches which are bonded to an Euler-Bernoulli beam or thin shell are briefly discussed and the results are incorporated into a 2-D structural acoustics model. In this model, an exterior noise source causes structural vibrations which in turn lead to interior noise as a result of nonlinear fluid/structure coupling mechanism. Interior sound pressure levels are reduced via patches bonded to the flexible boundary (a beam in this case) which generate pure bending moments when an out-of-phase voltage is applied. Well-posedness results for the infinite dimensional system are discussed and a Galerkin scheme for approximating the system dynamics is outlined. Control is implemented by using linear quadratic regulator (LQR) optimal control theory to calculate gains for the linearized system and then feeding these gains back into the nonlinear system of interest. The effectiveness of this strategy for this problem is illustrated in an example.

Dynamic probability control limits for risk-adjusted Bernoulli CUSUM charts.

PubMed

Zhang, Xiang; Woodall, William H

2015-11-10

The risk-adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, the use of a fixed control limit for the chart leads to a quite variable in-control average run length performance for patient populations with different risk score distributions. To overcome this problem, we determine simulation-based dynamic probability control limits (DPCLs) patient-by-patient for the risk-adjusted Bernoulli CUSUM charts. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, our risk-adjusted CUSUM charts with DPCLs have consistent in-control performance at the desired level with approximately geometrically distributed run lengths. Our simulation results demonstrate that our method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk-adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. Copyright © 2015 John Wiley & Sons, Ltd.

Image-Based Multi-Target Tracking through Multi-Bernoulli Filtering with Interactive Likelihoods.

PubMed

Hoak, Anthony; Medeiros, Henry; Povinelli, Richard J

2017-03-03

We develop an interactive likelihood (ILH) for sequential Monte Carlo (SMC) methods for image-based multiple target tracking applications. The purpose of the ILH is to improve tracking accuracy by reducing the need for data association. In addition, we integrate a recently developed deep neural network for pedestrian detection along with the ILH with a multi-Bernoulli filter. We evaluate the performance of the multi-Bernoulli filter with the ILH and the pedestrian detector in a number of publicly available datasets (2003 PETS INMOVE, Australian Rules Football League (AFL) and TUD-Stadtmitte) using standard, well-known multi-target tracking metrics (optimal sub-pattern assignment (OSPA) and classification of events, activities and relationships for multi-object trackers (CLEAR MOT)). In all datasets, the ILH term increases the tracking accuracy of the multi-Bernoulli filter.

Image-Based Multi-Target Tracking through Multi-Bernoulli Filtering with Interactive Likelihoods

PubMed Central

Hoak, Anthony; Medeiros, Henry; Povinelli, Richard J.

2017-01-01

We develop an interactive likelihood (ILH) for sequential Monte Carlo (SMC) methods for image-based multiple target tracking applications. The purpose of the ILH is to improve tracking accuracy by reducing the need for data association. In addition, we integrate a recently developed deep neural network for pedestrian detection along with the ILH with a multi-Bernoulli filter. We evaluate the performance of the multi-Bernoulli filter with the ILH and the pedestrian detector in a number of publicly available datasets (2003 PETS INMOVE, Australian Rules Football League (AFL) and TUD-Stadtmitte) using standard, well-known multi-target tracking metrics (optimal sub-pattern assignment (OSPA) and classification of events, activities and relationships for multi-object trackers (CLEAR MOT)). In all datasets, the ILH term increases the tracking accuracy of the multi-Bernoulli filter. PMID:28273796

A Universal Formula for Extracting the Euler Angles

NASA Technical Reports Server (NTRS)

Shuster, Malcolm D.; Markley, F. Landis

2004-01-01

Recently, the authors completed a study of the Davenport angles, which are a generalization of the Euler angles for which the initial and final Euler axes need not be either mutually parallel or mutually perpendicular or even along the coordinate axes. During the conduct of that study, those authors discovered a relationship which can be used to compute straightforwardly the Euler angles characterizing a proper-orthogonal direction-cosine matrix for an arbitrary Euler-axis set satisfying n(sub 1) x n(sub 2) = 0 and n(sub 3) x n(sub 1) = 0, which is also satisfied by the more usual Euler angles we encounter commonly in the practice of Astronautics. Rather than leave that relationship hidden in an article with very different focus from the present Engineering note, we present it and the universal algorithm derived from it for extracting the Euler angles from the direction-cosine matrix here. We also offer literal "code" for performing the operations, numerical examples, and general considerations about the extraction of Euler angles which are not universally known, particularly, the treatment of statistical error.

Heuristic analogy in Ars Conjectandi: From Archimedes' De Circuli Dimensione to Bernoulli's theorem.

PubMed

Campos, Daniel G

2018-02-01

This article investigates the way in which Jacob Bernoulli proved the main mathematical theorem that undergirds his art of conjecturing-the theorem that founded, historically, the field of mathematical probability. It aims to contribute a perspective into the question of problem-solving methods in mathematics while also contributing to the comprehension of the historical development of mathematical probability. It argues that Bernoulli proved his theorem by a process of mathematical experimentation in which the central heuristic strategy was analogy. In this context, the analogy functioned as an experimental hypothesis. The article expounds, first, Bernoulli's reasoning for proving his theorem, describing it as a process of experimentation in which hypothesis-making is crucial. Next, it investigates the analogy between his reasoning and Archimedes' approximation of the value of π, by clarifying both Archimedes' own experimental approach to the said approximation and its heuristic influence on Bernoulli's problem-solving strategy. The discussion includes some general considerations about analogy as a heuristic technique to make experimental hypotheses in mathematics. Copyright © 2018 Elsevier Ltd. All rights reserved.

Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method

NASA Astrophysics Data System (ADS)

Zhou, Zhenhuan; Li, Yuejie; Fan, Junhai; Rong, Dalun; Sui, Guohao; Xu, Chenghui

2018-05-01

A new Hamiltonian-based approach is presented for finding exact solutions for transverse vibrations of double-nanobeam-systems embedded in an elastic medium. The continuum model is established within the frameworks of the symplectic methodology and the nonlocal Euler-Bernoulli and Timoshenko beam beams. The symplectic eigenfunctions are obtained after expressing the governing equations in a Hamiltonian form. Exact frequency equations, vibration modes and displacement amplitudes are obtained by using symplectic eigenfunctions and end conditions. Comparisons with previously published work are presented to illustrate the accuracy and reliability of the proposed method. The comprehensive results for arbitrary boundary conditions could serve as benchmark results for verifying numerically obtained solutions. In addition, a study on the difference between the nonlocal beam and the nonlocal plate is also included.

A theoretical model for investigating the effect of vacuum fluctuations on the electromechanical stability of nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, A.; Mokhtari, J.; Koochi, A.; Abadyan, M.

2015-06-01

In this paper, the impact of the Casimir attraction on the electromechanical stability of nanowire-fabricated nanotweezers is investigated using a theoretical continuum mechanics model. The Dirichlet mode is considered and an asymptotic solution, based on path integral approach, is applied to consider the effect of vacuum fluctuations in the model. The Euler-Bernoulli beam theory is employed to derive the nonlinear governing equation of the nanotweezers. The governing equations are solved by three different approaches, i.e. the modified variation iteration method, generalized differential quadrature method and using a lumped parameter model. Various perspectives of the problem, including the comparison with the van der Waals force regime, the variation of instability parameters and effects of geometry are addressed in present paper. The proposed approach is beneficial for the precise determination of the electrostatic response of the nanotweezers in the presence of Casimir force.

Effect of Longitudinal Magnetic Field on Vibration Characteristics of Single-Walled Carbon Nanotubes in a Viscoelastic Medium

NASA Astrophysics Data System (ADS)

Zhang, D. P.; Lei, Y.; Shen, Z. B.

2017-12-01

The effect of longitudinal magnetic field on vibration response of a sing-walled carbon nanotube (SWCNT) embedded in viscoelastic medium is investigated. Based on nonlocal Euler-Bernoulli beam theory, Maxwell's relations, and Kelvin viscoelastic foundation model, the governing equations of motion for vibration analysis are established. The complex natural frequencies and corresponding mode shapes in closed form for the embedded SWCNT with arbitrary boundary conditions are obtained using transfer function method (TFM). The new analytical expressions for the complex natural frequencies are also derived for certain typical boundary conditions and Kelvin-Voigt model. Numerical results from the model are presented to show the effects of nonlocal parameter, viscoelastic parameter, boundary conditions, aspect ratio, and strength of the magnetic field on vibration characteristics for the embedded SWCNT in longitudinal magnetic field. The results demonstrate the efficiency of the proposed methods for vibration analysis of embedded SWCNTs under magnetic field.

Static deflection analysis of non prismatic multilayer p-NEMS cantilevers under electrical load

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

Pavithra, M., E-mail: pavithramasi78@gmail.com; Muruganand, S.

2016-04-13

Deflection of Euler-Bernoulli non prismatic multilayer piezoelectric nano electromechanical (p-NEMS) cantilever beams have been studied theoretically for various profiles of p-NEMS cantilevers by applying the electrical load. This problem has been answered by applying the boundary conditions derived by simple polynomials. This method is applied for various profiles like rectangular and trapezoidal by varying the thickness of the piezoelectric layer as well as the material. The obtained results provide the better deflection for trapezoidal profile with ZnO piezo electric layer of suitable nano cantilevers for nano scale applications.

Vehicle - Bridge interaction, comparison of two computing models

NASA Astrophysics Data System (ADS)

Melcer, Jozef; Kuchárová, Daniela

2017-07-01

The paper presents the calculation of the bridge response on the effect of moving vehicle moves along the bridge with various velocities. The multi-body plane computing model of vehicle is adopted. The bridge computing models are created in two variants. One computing model represents the bridge as the Bernoulli-Euler beam with continuously distributed mass and the second one represents the bridge as the lumped mass model with 1 degrees of freedom. The mid-span bridge dynamic deflections are calculated for both computing models. The results are mutually compared and quantitative evaluated.

Nonlinear theory of transverse beam echoes

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

Sen, Tanaji; Li, Yuan Shen

Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough.more » The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.« less

Nonlinear theory of transverse beam echoes

DOE PAGES

Sen, Tanaji; Li, Yuan Shen

2018-02-23

Transverse beam echoes can be excited with a single dipole kick followed by a single quadrupole kick. They have been used to measure diffusion in hadron beams and have other diagnostic capabilities. Here we develop theories of the transverse echo nonlinear in both the dipole and quadrupole kick strengths. The theories predict the maximum echo amplitudes and the optimum strength parameters. We find that the echo amplitude increases with smaller beam emittance and the asymptotic echo amplitude can exceed half the initial dipole kick amplitude. We show that multiple echoes can be observed provided the dipole kick is large enough.more » The spectrum of the echo pulse can be used to determine the nonlinear detuning parameter with small amplitude dipole kicks. Simulations are performed to check the theoretical predictions. In the useful ranges of dipole and quadrupole strengths, they are shown to be in reasonable agreement.« less

Toward Higher-Order Mass Detection: Influence of an Adsorbate’s Rotational Inertia and Eccentricity on the Resonant Response of a Bernoulli-Euler Cantilever Beam

PubMed Central

Heinrich, Stephen M.; Dufour, Isabelle

2015-01-01

In this paper a new theoretical model is derived, the results of which permit a detailed examination of how the resonant characteristics of a cantilever are influenced by a particle (adsorbate) attached at an arbitrary position along the beam’s length. Unlike most previous work, the particle need not be small in mass or dimension relative to the beam, and the adsorbate’s geometric characteristics are incorporated into the model via its rotational inertia and eccentricity relative to the beam axis. For the special case in which the adsorbate’s (translational) mass is indeed small, an analytical solution is obtained for the particle-induced resonant frequency shift of an arbitrary flexural mode, including the effects of rotational inertia and eccentricity. This solution is shown to possess the exact first-order behavior in the normalized particle mass and represents a generalization of analytical solutions derived by others in earlier studies. The results suggest the potential for “higher-order” nanobeam-based mass detection methods by which the multi-mode frequency response reflects not only the adsorbate’s mass but also important geometric data related to its size, shape, or orientation (i.e., the mass distribution), thus resulting in more highly discriminatory techniques for discrete-mass sensing. PMID:26610493

A generalized form of the Bernoulli Trial collision scheme in DSMC: Derivation and evaluation

NASA Astrophysics Data System (ADS)

Roohi, Ehsan; Stefanov, Stefan; Shoja-Sani, Ahmad; Ejraei, Hossein

2018-02-01

The impetus of this research is to present a generalized Bernoulli Trial collision scheme in the context of the direct simulation Monte Carlo (DSMC) method. Previously, a subsequent of several collision schemes have been put forward, which were mathematically based on the Kac stochastic model. These include Bernoulli Trial (BT), Ballot Box (BB), Simplified Bernoulli Trial (SBT) and Intelligent Simplified Bernoulli Trial (ISBT) schemes. The number of considered pairs for a possible collision in the above-mentioned schemes varies between N (l) (N (l) - 1) / 2 in BT, 1 in BB, and (N (l) - 1) in SBT or ISBT, where N (l) is the instantaneous number of particles in the lth cell. Here, we derive a generalized form of the Bernoulli Trial collision scheme (GBT) where the number of selected pairs is any desired value smaller than (N (l) - 1), i.e., Nsel < (N (l) - 1), keeping the same the collision frequency and accuracy of the solution as the original SBT and BT models. We derive two distinct formulas for the GBT scheme, where both formula recover BB and SBT limits if Nsel is set as 1 and N (l) - 1, respectively, and provide accurate solutions for a wide set of test cases. The present generalization further improves the computational efficiency of the BT-based collision models compared to the standard no time counter (NTC) and nearest neighbor (NN) collision models.

Fast Euler solver for transonic airfoils. I - Theory. II - Applications

NASA Technical Reports Server (NTRS)

Dadone, Andrea; Moretti, Gino

1988-01-01

Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.

A Novel Nonlinear Piezoelectric Energy Harvesting System Based on Linear-Element Coupling: Design, Modeling and Dynamic Analysis.

PubMed

Zhou, Shengxi; Yan, Bo; Inman, Daniel J

2018-05-09

This paper presents a novel nonlinear piezoelectric energy harvesting system which consists of linear piezoelectric energy harvesters connected by linear springs. In principle, the presented nonlinear system can improve broadband energy harvesting efficiency where magnets are forbidden. The linear spring inevitably produces the nonlinear spring force on the connected harvesters, because of the geometrical relationship and the time-varying relative displacement between two adjacent harvesters. Therefore, the presented nonlinear system has strong nonlinear characteristics. A theoretical model of the presented nonlinear system is deduced, based on Euler-Bernoulli beam theory, Kirchhoff’s law, piezoelectric theory and the relevant geometrical relationship. The energy harvesting enhancement of the presented nonlinear system (when n = 2, 3) is numerically verified by comparing with its linear counterparts. In the case study, the output power area of the presented nonlinear system with two and three energy harvesters is 268.8% and 339.8% of their linear counterparts, respectively. In addition, the nonlinear dynamic response characteristics are analyzed via bifurcation diagrams, Poincare maps of the phase trajectory, and the spectrum of the output voltage.

Theory of beam plasma discharge

NASA Technical Reports Server (NTRS)

Papadopoulos, K.

1982-01-01

The general theory of beam plasma discharge (BPD) is discussed in relation to space and laboratory beam injection situations. An important concept introduced is that even when beam plasma instabilities are excited, there are two regime of BPD with radically different observational properties. They are described here as BPD with either classical or anomalous energy depositions. For high pressures or low altitudes, the classical is expected to dominate. For high altitudes and laboratory experiments, where the axial system size is less than lambda sub en, no BPD will be triggered unless the unstable waves are near the ambient plasma frequency and their amplitudes at saturation are large enough to create suprathermal tails by collapsing.

Elementary Hemodynamic Principles Based on Modified Bernoulli's Equation.

ERIC Educational Resources Information Center

Badeer, Henry S.

1985-01-01

Develops and expands basic concepts of Bernoulli's equation as it applies to vascular hemodynamics. Simple models are used to illustrate gravitational potential energy, steady nonturbulent flow, pump-driven streamline flow, and other areas. Relationships to the circulatory system are also discussed. (DH)

Linear stiff string vibrations in musical acoustics: Assessment and comparison of models.

PubMed

Ducceschi, Michele; Bilbao, Stefan

2016-10-01

Strings are amongst the most common elements found in musical instruments and an appropriate physical description of string dynamics is essential to modelling, analysis, and simulation. For linear vibration in a single polarisation, the most common model is based on the Euler-Bernoulli beam equation under tension. In spite of its simple form, such a model gives unbounded phase and group velocities at large wavenumbers, and such behaviour may be interpreted as unphysical. The Timoshenko model has, therefore, been employed in more recent works to overcome such shortcoming. This paper presents a third model based on the shear beam equations. The three models are here assessed and compared with regard to the perceptual considerations in musical acoustics.

Determination of in vivo mechanical properties of long bones from their impedance response curves

NASA Technical Reports Server (NTRS)

Borders, S. G.

1981-01-01

A mathematical model consisting of a uniform, linear, visco-elastic, Euler-Bernoulli beam to represent the ulna or tibia of the vibrating forearm or leg system is developed. The skin and tissue compressed between the probe and bone is represented by a spring in series with the beam. The remaining skin and tissue surrounding the bone is represented by a visco-elastic foundation with mass. An extensive parametric study is carried out to determine the effect of each parameter of the mathematical model on its impedance response. A system identification algorithm is developed and programmed on a digital computer to determine the parametric values of the model which best simulate the data obtained from an impedance test.

Weak turbulence theory for beam-plasma interaction

NASA Astrophysics Data System (ADS)

Yoon, Peter H.

2018-01-01

The kinetic theory of weak plasma turbulence, of which Ronald C. Davidson was an important early pioneer [R. C. Davidson, Methods in Nonlinear Plasma Theory, (Academic Press, New York, 1972)], is a venerable and valid theory that may be applicable to a large number of problems in both laboratory and space plasmas. This paper applies the weak turbulence theory to the problem of gentle beam-plasma interaction and Langmuir turbulence. It is shown that the beam-plasma interaction undergoes various stages of physical processes starting from linear instability, to quasilinear saturation, to mode coupling that takes place after the quasilinear stage, followed by a state of quasi-static "turbulent equilibrium." The long term quasi-equilibrium stage is eventually perturbed by binary collisional effects in order to bring the plasma to a thermodynamic equilibrium with increased entropy.

A novel approach to enhance the accuracy of vibration control of Frames

NASA Astrophysics Data System (ADS)

Toloue, Iraj; Shahir Liew, Mohd; Harahap, I. S. H.; Lee, H. E.

2018-03-01

All structures built within known seismically active regions are typically designed to endure earthquake forces. Despite advances in earthquake resistant structures, it can be inferred from hindsight that no structure is entirely immune to damage from earthquakes. Active vibration control systems, unlike the traditional methods which enlarge beams and columns, are highly effective countermeasures to reduce the effects of earthquake loading on a structure. It requires fast computation of nonlinear structural analysis in near time and has historically demanded advanced programming hosted on powerful computers. This research aims to develop a new approach for active vibration control of frames, which is applicable over both elastic and plastic material behavior. In this study, the Force Analogy Method (FAM), which is based on Hook's Law is further extended using the Timoshenko element which considers shear deformations to increase the reliability and accuracy of the controller. The proposed algorithm is applied to a 2D portal frame equipped with linear actuator, which is designed based on full state Linear Quadratic Regulator (LQR). For comparison purposes, the portal frame is analysed by both the Euler Bernoulli and Timoshenko element respectively. The results clearly demonstrate the superiority of the Timoshenko element over Euler Bernoulli for application in nonlinear analysis.

Embedding methods for the steady Euler equations

NASA Technical Reports Server (NTRS)

Chang, S. H.; Johnson, G. M.

1983-01-01

An approach to the numerical solution of the steady Euler equations is to embed the first-order Euler system in a second-order system and then to recapture the original solution by imposing additional boundary conditions. Initial development of this approach and computational experimentation with it were previously based on heuristic physical reasoning. This has led to the construction of a relaxation procedure for the solution of two-dimensional steady flow problems. The theoretical justification for the embedding approach is addressed. It is proven that, with the appropriate choice of embedding operator and additional boundary conditions, the solution to the embedded system is exactly the one to the original Euler equations. Hence, solving the embedded version of the Euler equations will not produce extraneous solutions.

p-Euler equations and p-Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

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

Ghafarian, M.; Ariaei, A., E-mail: ariaei@eng.ui.ac.ir

The free vibration analysis of a multiple rotating nanobeams' system applying the nonlocal Eringen elasticity theory is presented. Multiple nanobeams' systems are of great importance in nano-optomechanical applications. At nanoscale, the nonlocal effects become non-negligible. According to the nonlocal Euler-Bernoulli beam theory, the governing partial differential equations are derived by incorporating the nonlocal scale effects. Assuming a structure of n parallel nanobeams, the vibration of the system is described by a coupled set of n partial differential equations. The method involves a change of variables to uncouple the equations and the differential transform method as an efficient mathematical technique tomore » solve the nonlocal governing differential equations. Then a number of parametric studies are conducted to assess the effect of the nonlocal scaling parameter, rotational speed, boundary conditions, hub radius, and the stiffness coefficients of the elastic interlayer media on the vibration behavior of the coupled rotating multiple-carbon-nanotube-beam system. It is revealed that the bending vibration of the system is significantly influenced by the rotational speed, elastic mediums, and the nonlocal scaling parameters. This model is validated by comparing the results with those available in the literature. The natural frequencies are in a reasonably good agreement with the reported results.« less

Flawed Applications of Bernoulli's Principle

ERIC Educational Resources Information Center

Koumaras, Panagiotis; Primerakis, Georgios

2018-01-01

One of the most popular demonstration experiments pertaining to Bernoulli's principle is the production of a water spray by using a vertical plastic straw immersed in a glass of water and a horizontal straw to blow air towards the top edge of the vertical one. A more general version of this phenomenon, appearing also in school physics problems, is…

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

NASA Technical Reports Server (NTRS)

Wu, R. W.; Witmer, E. A.

1972-01-01

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Space Flight Cable Model Development

NASA Technical Reports Server (NTRS)

Spak, Kaitlin

2013-01-01

This work concentrates the modeling efforts presented in last year's VSGC conference paper, "Model Development for Cable-Harnessed Beams." The focus is narrowed to modeling of space-flight cables only, as a reliable damped cable model is not yet readily available and is necessary to continue modeling cable-harnessed space structures. New experimental data is presented, eliminating the low-frequency noise that plagued the first year's efforts. The distributed transfer function method is applied to a single section of space flight cable for Euler-Bernoulli and shear beams. The work presented here will be developed into a damped cable model that can be incorporated into an interconnected beam-cable system. The overall goal of this work is to accurately predict natural frequencies and modal damping ratios for cabled space structures.

A fourth order Euler/Navier-Stokes prediction method for the aerodynamics and aeroelasticity of hovering rotor blades

NASA Astrophysics Data System (ADS)

Smith, Marilyn Jones

Some of the computational issues relating to the development of a three-dimensional fourth-order compact Euler/Navier-Stokes methodology for rotary wing flows and its coupling with an elastic rotor blade beam structural model have been explored. The compact Euler/NavierStokes method is used to predict the aerodynamic loads on an isolated rotor blade. Because the scheme is fourth-order, fewer grid nodes are necessary to predict loads with the same accuracy as traditional second order methodologies on finer grids. Grid and numerical parameter optimizations were performed to examine the changes in the predictive capabilities of the higher-order scheme. Comparisons were made with experimental data for a rotor using NACA 0012 airfoil sections and a rectangular planform with no twist. Simulations for both lifting and non-lifting configurations at various tip Mach numbers were performed. This Euler/Navier-Stokes methodology can be applied to rotor blades with either rigid-blade or elastic-beam-structural models to determine the steady-state response in hovering flight. The blade is represented by a geometrically nonlinear beam model which accounts for coupled flap bending, lead-lag bending and torsion. Moderately large displacements and rotations due to structural deformations can be simulated. The analysis has been performed for blade configurations having uniform mass and stiffness, no twist, and no chordwise offsets of the elastic and tension axes, as well as the center of mass. The results are compared with a panel method coupled with the same structural dynamics model. Computations have been made to predict the aerodynamic deflections for the rotor in hover. A starting solution using initial deflections predicted by aeroelastic analyses with a two-dimensional aerodynamic model was investigated. The present Euler/Navier-Stokes method using a momentum wake and a contracting vortex wake shows the impact on the aeroelastic deflections of a three-dimensional aerodynamic

Analytical Modeling for the Bending Resonant Frequency of Multilayered Microresonators with Variable Cross-Section

PubMed Central

Herrera-May, Agustín L.; Aguilera-Cortés, Luz A.; Plascencia-Mora, Hector; Rodríguez-Morales, Ángel L.; Lu, Jian

2011-01-01

Multilayered microresonators commonly use sensitive coating or piezoelectric layers for detection of mass and gas. Most of these microresonators have a variable cross-section that complicates the prediction of their fundamental resonant frequency (generally of the bending mode) through conventional analytical models. In this paper, we present an analytical model to estimate the first resonant frequency and deflection curve of single-clamped multilayered microresonators with variable cross-section. The analytical model is obtained using the Rayleigh and Macaulay methods, as well as the Euler-Bernoulli beam theory. Our model is applied to two multilayered microresonators with piezoelectric excitation reported in the literature. Both microresonators are composed by layers of seven different materials. The results of our analytical model agree very well with those obtained from finite element models (FEMs) and experimental data. Our analytical model can be used to determine the suitable dimensions of the microresonator’s layers in order to obtain a microresonator that operates at a resonant frequency necessary for a particular application. PMID:22164071

The Bernoulli Equation in a Moving Reference Frame

ERIC Educational Resources Information Center

Mungan, Carl E.

2011-01-01

Unlike other standard equations in introductory classical mechanics, the Bernoulli equation is not Galilean invariant. The explanation is that, in a reference frame moving with respect to constrictions or obstacles, those surfaces do work on the fluid, constituting an extra term that needs to be included in the work-energy calculation. A…

On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series

PubMed Central

Kushwaha, Jitendra Kumar

2013-01-01

Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler's mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler's means of conjugate of functions belonging to Lip (ξ(t), p) class has been obtained. Lipα and Lip (α, p) classes are the particular cases of Lip (ξ(t), p) class. The main result of this paper generalizes some well-known results in this direction. PMID:24379744

Classic Bernoulli's Principle Derivation and Its Working Hypotheses

ERIC Educational Resources Information Center

Marciotto, Edson R.

2016-01-01

The Bernoulli's principle states that the quantity p+ pgz + pv[superscript 2]/2 must be conserved in a streamtube if some conditions are matched, namely: steady and irrotational flow of an inviscid and incompressible fluid. In most physics textbooks this result is demonstrated invoking the energy conservation of a fluid material volume at two…

Size-dependent resonance frequencies of cantilevered and bridged nanosensors

NASA Astrophysics Data System (ADS)

Shi, W.; Zou, J.; Lee, K. Y.; Li, X. F.

2018-03-01

This paper studies transverse vibration of nanoscale cantilevered and bridged sensors carrying a nanoparticle. The nanoscale sensors are modelled as Euler-Bernoulli beams with surface effect and nanoparticle as a concentrated mass. Frequency equations of cantilevered and bridged beam-mass system are derived and exact resonance frequencies are calculated. An alternative Fredholm integral equation method is used to obtain an approximate explicit expression for the fundamental frequency for both cases. A comparison between the approximate and analytical results is made and the approximation accuracy is satisfactory. The influences of the residual surface stress, surface elasticity, and attached mass on the resonance frequencies and mode shapes are discussed. These results are useful to illustrate the surface phenomena and are helpful to design micro-/nano-mechanical sensors.

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.

Entropy Analysis of Kinetic Flux Vector Splitting Schemes for the Compressible Euler Equations

NASA Technical Reports Server (NTRS)

Shiuhong, Lui; Xu, Jun

1999-01-01

Flux Vector Splitting (FVS) scheme is one group of approximate Riemann solvers for the compressible Euler equations. In this paper, the discretized entropy condition of the Kinetic Flux Vector Splitting (KFVS) scheme based on the gas-kinetic theory is proved. The proof of the entropy condition involves the entropy definition difference between the distinguishable and indistinguishable particles.

An Illustration of the Bernoulli Effect With a Rubber Tube

ERIC Educational Resources Information Center

Hanson, M. J.

1973-01-01

Describes a simple method of demonstrating the Bernoulli effect, by spinning a length of rubber tubing around one's head. A manometer attached to the stationary end of the tube indicates a reduction in pressure. (JR)

Development of Euler's ideas at the Moscow State Regional University

NASA Astrophysics Data System (ADS)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

ASTROP2-LE: A Mistuned Aeroelastic Analysis System Based on a Two Dimensional Linearized Euler Solver

NASA Technical Reports Server (NTRS)

Reddy, T. S. R.; Srivastava, R.; Mehmed, Oral

2002-01-01

An aeroelastic analysis system for flutter and forced response analysis of turbomachines based on a two-dimensional linearized unsteady Euler solver has been developed. The ASTROP2 code, an aeroelastic stability analysis program for turbomachinery, was used as a basis for this development. The ASTROP2 code uses strip theory to couple a two dimensional aerodynamic model with a three dimensional structural model. The code was modified to include forced response capability. The formulation was also modified to include aeroelastic analysis with mistuning. A linearized unsteady Euler solver, LINFLX2D is added to model the unsteady aerodynamics in ASTROP2. By calculating the unsteady aerodynamic loads using LINFLX2D, it is possible to include the effects of transonic flow on flutter and forced response in the analysis. The stability is inferred from an eigenvalue analysis. The revised code, ASTROP2-LE for ASTROP2 code using Linearized Euler aerodynamics, is validated by comparing the predictions with those obtained using linear unsteady aerodynamic solutions.

A study on the use of Gumbel approximation with the Bernoulli spatial scan statistic.

PubMed

Read, S; Bath, P A; Willett, P; Maheswaran, R

2013-08-30

The Bernoulli version of the spatial scan statistic is a well established method of detecting localised spatial clusters in binary labelled point data, a typical application being the epidemiological case-control study. A recent study suggests the inferential accuracy of several versions of the spatial scan statistic (principally the Poisson version) can be improved, at little computational cost, by using the Gumbel distribution, a method now available in SaTScan(TM) (www.satscan.org). We study in detail the effect of this technique when applied to the Bernoulli version and demonstrate that it is highly effective, albeit with some increase in false alarm rates at certain significance thresholds. We explain how this increase is due to the discrete nature of the Bernoulli spatial scan statistic and demonstrate that it can affect even small p-values. Despite this, we argue that the Gumbel method is actually preferable for very small p-values. Furthermore, we extend previous research by running benchmark trials on 12 000 synthetic datasets, thus demonstrating that the overall detection capability of the Bernoulli version (i.e. ratio of power to false alarm rate) is not noticeably affected by the use of the Gumbel method. We also provide an example application of the Gumbel method using data on hospital admissions for chronic obstructive pulmonary disease. Copyright © 2013 John Wiley & Sons, Ltd.

Improved implementation of the risk-adjusted Bernoulli CUSUM chart to monitor surgical outcome quality.

PubMed

Keefe, Matthew J; Loda, Justin B; Elhabashy, Ahmad E; Woodall, William H

2017-06-01

The traditional implementation of the risk-adjusted Bernoulli cumulative sum (CUSUM) chart for monitoring surgical outcome quality requires waiting a pre-specified period of time after surgery before incorporating patient outcome information. We propose a simple but powerful implementation of the risk-adjusted Bernoulli CUSUM chart that incorporates outcome information as soon as it is available, rather than waiting a pre-specified period of time after surgery. A simulation study is presented that compares the performance of the traditional implementation of the risk-adjusted Bernoulli CUSUM chart to our improved implementation. We show that incorporating patient outcome information as soon as it is available leads to quicker detection of process deterioration. Deterioration of surgical performance could be detected much sooner using our proposed implementation, which could lead to the earlier identification of problems. © The Author 2017. Published by Oxford University Press in association with the International Society for Quality in Health Care. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

Localization of quantum Bernoulli noises

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

Wang, Caishi; Zhang, Jihong

2013-10-15

The family (∂{sub k},∂{sub k}{sup *}){sub k≥0} of annihilation and creation operators acting on square integrable functionals of a Bernoulli process Z= (Z{sub k}){sub k⩾0} can be interpreted as quantum Bernoulli noises. In this note we consider the operator family (ℓ{sub k},ℓ{sub k}{sup *}){sub k≥0}, where ℓ{sub k}=∂{sub k}E{sub k} with E{sub k} being the conditional expectation (operator) given σ-field σ(Z{sub j}; 0 ⩽j⩽k). We show that ℓ{sub k} (resp. ℓ{sub k}{sup *}) is essentially a kind of localization of the annihilation operator ∂{sub k} (resp. creation operator ∂{sub k}{sup *}). We examine properties of the family (ℓ{sub k},ℓ{sub k}{supmore » *}){sub k≥0} and prove, among other things, that ℓ{sub k} and ℓ{sub k}{sup *} satisfy a local canonical anti-communication relation and (ℓ{sub k}{sup *}){sub k≥0} forms a mutually orthogonal operator sequence although each ℓ{sub k} is not a projection operator. We find that the operator series Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}Xℓ{sub k} converges in the strong operator topology for each bounded operator X acting on square integrable functionals of Z. In particular we get an explicit sum of the operator series Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}ℓ{sub k}. A useful norm estimate on Σ{sub k=0}{sup ∞}ℓ{sub k}{sup *}Xℓ{sub k} is also obtained. Finally we show applications of our main results to quantum dynamical semigroups and quantum probability.« less

Analytical Solution for the Aeroelastic Response of a Two-Dimensional Elastic Plate in Axial Flow

NASA Astrophysics Data System (ADS)

Medina, Cory; Kang, Chang-Kwon

2017-11-01

The aeroelastic response of an elastic plate in an unsteady flow describes many engineering problems from bio-locomotion, deforming airfoils, to energy harvesting. However, the analysis is challenging because the shape of the plate is a priori unknown. This study presents an analytical model that can predict the two-way tightly coupled aeroelastic response of a two-dimensional elastic plate including the effects of plate curvature along the flow direction. The plate deforms due to the dynamic balance of wing inertia, elastic restoring force, and aerodynamic force. The coupled model utilizes the linearized Euler-Bernoulli beam theory for the structural model and thin airfoil theory as presented by Theodorsen, which assumes incompressible potential flow, for the aerodynamic model. The coupled equations of motion are solved via Galerkin's method, where closed form solutions for the plate deformation are obtained by deriving the unsteady aerodynamic pressure with respect to the plate normal functions, expressed in a Chebyshev polynomial expansion. Stability analysis is performed for a range of mass ratios obtaining the flutter velocities and corresponding frequencies and the results agree well with the results reported in the literature.

Flutter and divergence instability of supported piezoelectric nanotubes conveying fluid

NASA Astrophysics Data System (ADS)

Bahaadini, Reza; Hosseini, Mohammad; Jamali, Behnam

2018-01-01

In this paper, divergence and flutter instabilities of supported piezoelectric nanotubes containing flowing fluid are investigated. To take the size effects into account, the nonlocal elasticity theory is implemented in conjunction with the Euler-Bernoulli beam theory incorporating surface stress effects. The Knudsen number is applied to investigate the slip boundary conditions between the flow and wall of nanotube. The nonlocal governing equations of nanotube are obtained using Newtonian method, including the influence of piezoelectric voltage, surface effects, Knudsen number and nonlocal parameter. Applying Galerkin approach to transform resulting equations into a set of eigenvalue equations under the simple-simple (S-S) and clamped-clamped (C-C) boundary conditions. The effects of the piezoelectric voltage, surface effects, Knudsen number, nonlocal parameter and boundary conditions on the divergence and flutter boundaries of nanotubes are discussed. It is observed that the fluid-conveying nanotubes with both ends supported lose their stability by divergence first and then by flutter with increase in fluid velocity. Results indicate the importance of using piezoelectric voltage, nonlocal parameter and Knudsen number in decrease of critical flow velocities of system. Moreover, the surface effects have a significant role on the eigenfrequencies and critical fluid velocity.

A new beam theory using first-order warping functions

NASA Technical Reports Server (NTRS)

Ie, C. A.; Kosmatka, J. B.

1990-01-01

Due to a certain type of loading and geometrical boundary conditions, each beam will respond differently depending on its geometrical form of the cross section and its material definition. As an example, consider an isotropic rectangular beam under pure bending. Plane sections perpendicular to the longitudinal axis of the beam will remain plane and perpendicular to the deformed axis after deformation. However, due to the Poisson effect, particles in the planes will move relative to each other resulting in a form of anticlastic deformation. In other words, even in pure bending of an isotropic beam, each cross section will deform in the plane. If the material of the beam above is replaced by a generally anisotropic material, then the cross sections will not only deform in the plane, but also out of plane. Hence, in general, both in-plane deformation and out-of-plane warping will exist and depend on the geometrical form and material definition of the cross sections and also on the loadings. For the purpose of explanation, an analogy is made. The geometrical forms of the bodies of each individual are unique. Hence, different sizes of clothes are needed. Finding the sizes of clothes for individuals is like determining the warping functions in beams. A new beam theory using first-order warping functions is introduced. Numerical examples will be presented for an isotropic beam with rectangular cross section. The theory can be extended for composite beams.

Long-term stable time integration scheme for dynamic analysis of planar geometrically exact Timoshenko beams

NASA Astrophysics Data System (ADS)

Nguyen, Tien Long; Sansour, Carlo; Hjiaj, Mohammed

2017-05-01

In this paper, an energy-momentum method for geometrically exact Timoshenko-type beam is proposed. The classical time integration schemes in dynamics are known to exhibit instability in the non-linear regime. The so-called Timoshenko-type beam with the use of rotational degree of freedom leads to simpler strain relations and simpler expressions of the inertial terms as compared to the well known Bernoulli-type model. The treatment of the Bernoulli-model has been recently addressed by the authors. In this present work, we extend our approach of using the strain rates to define the strain fields to in-plane geometrically exact Timoshenko-type beams. The large rotational degrees of freedom are exactly computed. The well-known enhanced strain method is used to avoid locking phenomena. Conservation of energy, momentum and angular momentum is proved formally and numerically. The excellent performance of the formulation will be demonstrated through a range of examples.

On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations

NASA Technical Reports Server (NTRS)

Deshpande, S. M.

1986-01-01

The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.

Voidage correction algorithm for unresolved Euler-Lagrange simulations

NASA Astrophysics Data System (ADS)

Askarishahi, Maryam; Salehi, Mohammad-Sadegh; Radl, Stefan

2018-04-01

The effect of grid coarsening on the predicted total drag force and heat exchange rate in dense gas-particle flows is investigated using Euler-Lagrange (EL) approach. We demonstrate that grid coarsening may reduce the predicted total drag force and exchange rate. Surprisingly, exchange coefficients predicted by the EL approach deviate more significantly from the exact value compared to results of Euler-Euler (EE)-based calculations. The voidage gradient is identified as the root cause of this peculiar behavior. Consequently, we propose a correction algorithm based on a sigmoidal function to predict the voidage experienced by individual particles. Our correction algorithm can significantly improve the prediction of exchange coefficients in EL models, which is tested for simulations involving Euler grid cell sizes between 2d_p and 12d_p . It is most relevant in simulations of dense polydisperse particle suspensions featuring steep voidage profiles. For these suspensions, classical approaches may result in an error of the total exchange rate of up to 30%.

On the Use of Linearized Euler Equations in the Prediction of Jet Noise

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.; Hixon, R.; Shih, S.-H.; Povinelli, L. A.

1995-01-01

Linearized Euler equations are used to simulate supersonic jet noise generation and propagation. Special attention is given to boundary treatment. The resulting solution is stable and nearly free from boundary reflections without the need for artificial dissipation, filtering, or a sponge layer. The computed solution is in good agreement with theory and observation and is much less CPU-intensive as compared to large-eddy simulations.

Leonhard Euler and his contributions to fluid mechanics

NASA Technical Reports Server (NTRS)

Salas, M. D.

1988-01-01

The career of Leonhard Euler, one of the world's most gifted scientists, is reviewed. The paper focuses on Euler's contributions to fluid mechanics and gives a perspective of how this science was born. A bibliography is included to provide the history enthusiast with a starting point for further study.

Remarks on Heisenberg-Euler-type electrodynamics

NASA Astrophysics Data System (ADS)

Kruglov, S. I.

2017-05-01

We consider Heisenberg-Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg-Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at r →∞ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at r →∞. Corrections to the Reissner-Nordström solution are obtained.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli's principle: An application to vocal folds vibration.

PubMed

Zhang, Lucy T; Yang, Jubiao

2016-12-01

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.

Development of a magnetic catheter with rotating multi-magnets to achieve unclogging motions with enhanced steering capability

NASA Astrophysics Data System (ADS)

Kim, N.; Lee, S.; Lee, W.; Jang, G.

2018-05-01

We developed a novel magnetic catheter structure that can selectively generate steering and unclogging motions. The proposed magnetic catheter is composed of a flexible tube and two modules with ring magnets that can axially rotate in a way that enables the catheter to independently steer and unclog blood clots by controlling external magnetic fields. We mathematically modeled the deflection of the catheter using the large deflection Euler-Bernoulli beam model and developed a design method to determine the optimal distance between magnets in order to maximize steering performance. Finally, we prototyped the proposed magnetic catheter and conducted several experiments to verify the theoretical model and assess its steering and unclogging capabilities.

A new solution of measuring thermal response of prestressed concrete bridge girders for structural health monitoring

NASA Astrophysics Data System (ADS)

Jiao, Pengcheng; Borchani, Wassim; Hasni, Hassene; Lajnef, Nizar

2017-08-01

This study develops a novel buckling-based mechanism to measure the thermal response of prestressed concrete bridge girders under continuous temperature changes for structural health monitoring. The measuring device consists of a bilaterally constrained beam and a piezoelectric polyvinylidene fluoride transducer that is attached to the beam. Under thermally induced displacement, the slender beam is buckled. The post-buckling events are deployed to convert the low-rate and low-frequency excitations into localized high-rate motions and, therefore, the attached piezoelectric transducer is triggered to generate electrical signals. Attaching the measuring device to concrete bridge girders, the electrical signals are used to detect the thermal response of concrete bridges. Finite element simulations are conducted to obtain the displacement of prestressed concrete girders under thermal loads. Using the thermal-induced displacement as input, experiments are carried out on a 3D printed measuring device to investigate the buckling response and corresponding electrical signals. A theoretical model is developed based on the nonlinear Euler-Bernoulli beam theory and large deformation assumptions to predict the buckling mode transitions of the beam. Based on the presented theoretical model, the geometry properties of the measuring device can be designed such that its buckling response is effectively controlled. Consequently, the thermally induced displacement can be designed as limit states to detect excessive thermal loads on concrete bridge girders. The proposed solution sufficiently measures the thermal response of concrete bridges.

Bridging the Gap Between Stationary Homogeneous Isotropic Turbulence and Quantum Mechanics

NASA Astrophysics Data System (ADS)

Sohrab, Siavash

A statistical theory of stationary isotropic turbulence is presented with eddies possessing Gaussian velocity distribution, Maxwell-Boltzmann speed distribution in harmony with perceptions of Heisenberg, and Planck energy distribution in harmony with perceptions of Chandrasekhar and in agreement with experimental observations of Van Atta and Chen. Defining the action S = - mΦ in terms of velocity potential of atomic motion, scale-invariant Schrödinger equation is derivedfrom invariant Bernoulli equation. Thus, the gap between the problems of turbulence and quantum mechanics is closed through connections between Cauchy-Euler-Bernoulli equations of hydrodynamics, Hamilton-Jacobi equation of classical mechanics, and finally Schrödinger equation of quantum mechanics. Transitions of particle (molecular cluster cji) from a small rapidly-oscillating eddy ej (high-energy level-j) to a large slowly-oscillating eddy ei (low energy-level-i) leads to emission of a sub-particle (molecule mji) that carries away the excess energy ɛji = h (νj -νi) in harmony with Bohr theory of atomic spectra. ∖ ∖ NASA Grant No. NAG3-1863.

A randomised approach for NARX model identification based on a multivariate Bernoulli distribution

NASA Astrophysics Data System (ADS)

Bianchi, F.; Falsone, A.; Prandini, M.; Piroddi, L.

2017-04-01

The identification of polynomial NARX models is typically performed by incremental model building techniques. These methods assess the importance of each regressor based on the evaluation of partial individual models, which may ultimately lead to erroneous model selections. A more robust assessment of the significance of a specific model term can be obtained by considering ensembles of models, as done by the RaMSS algorithm. In that context, the identification task is formulated in a probabilistic fashion and a Bernoulli distribution is employed to represent the probability that a regressor belongs to the target model. Then, samples of the model distribution are collected to gather reliable information to update it, until convergence to a specific model. The basic RaMSS algorithm employs multiple independent univariate Bernoulli distributions associated to the different candidate model terms, thus overlooking the correlations between different terms, which are typically important in the selection process. Here, a multivariate Bernoulli distribution is employed, in which the sampling of a given term is conditioned by the sampling of the others. The added complexity inherent in considering the regressor correlation properties is more than compensated by the achievable improvements in terms of accuracy of the model selection process.

Determination of regional Euler pole parameters for Eastern Austria

NASA Astrophysics Data System (ADS)

Umnig, Elke; Weber, Robert; Schartner, Matthias; Brueckl, Ewald

2017-04-01

The horizontal motion of lithospheric plates can be described as rotations around a rotation axes through the Earth's center. The two possible points where this axes intersects the surface of the Earth are called Euler poles. The rotation is expressed by the Euler parameters in terms of angular velocities together with the latitude and longitude of the Euler pole. Euler parameters were calculated from GPS data for a study area in Eastern Austria. The observation network is located along the Mur-Mürz Valley and the Vienna Basin. This zone is part of the Vienna Transfer Fault, which is the major fault system between the Eastern Alps and the Carpathians. The project ALPAACT (seismological and geodetic monitoring of ALpine-PAnnonian ACtive Tectonics) investigated intra plate tectonic movements within the Austrian part in order to estimate the seismic hazard. Precise site coordinate time series established from processing 5 years of GPS observations are available for the regional network spanning the years from 2010.0 to 2015.0. Station velocities with respect to the global reference frame ITRF2008 have been computed for 23 sites. The common Euler vector was estimated on base of a subset of reliable site velocities, for stations directly located within the area of interest. In a further step a geokinematic interpretation shall be carried out. Therefore site motions with respect to the Eurasian Plate are requested. To obtain this motion field different variants are conceivable. In a simple approach the mean ITRF2008 velocity of IGS site GRAZ can be adopted as Eurasian rotational velocity. An improved alternative is to calculate site-specific velocity differences between the Euler rotation and the individual site velocities. In this poster presentation the Euler parameters, the residual motion field as well as first geokinematic interpretation results are presented.

Model Reduction in Biomechanics

NASA Astrophysics Data System (ADS)

Feng, Yan

The mechanical characteristic of the cell is primarily performed by the cytoskeleton. Microtubules, actin, and intermediate filaments are the three main cytoskeletal polymers. Of these, microtubules are the stiffest and have multiple functions within a cell that include: providing tracks for intracellular transport, transmitting the mechanical force necessary for cell division during mitosis, and providing sufficient stiffness for propulsion in flagella and cilia. Microtubule mechanics has been studied by a variety of methods: detailed molecular dynamics (MD), coarse-grained models, engineering type models, and elastic continuum models. In principle, atomistic MD simulations should be able to predict all desired mechanical properties of a single molecule, however, in practice the large computational resources are required to carry out a simulation of larger biomolecular system. Due to the limited accessibility using even the most ambitious all-atom models and the demand for the multiscale molecular modeling and simulation, the emergence of the reduced models is critically important to provide the capability for investigating the biomolecular dynamics that are critical to many biological processes. Then the coarse-grained models, such as elastic network models and anisotropic network models, have been shown to bequite accurate in predicting microtubule mechanical response, but still requires significant computational resources. On the other hand, the microtubule is treated as comprising materials with certain continuum material properties. Such continuum models, especially Euler-Bernoulli beam models, are often used to extract mechanical parameters from experimental results. The microtubule is treated as comprising materials with certain continuum material properties. Such continuum models, especially Euler-Bernoulli beam models in which the biomolecular system is assumed as homogeneous isotropic materials with solid cross-sections, are often used to extract

Bernoulli's Principle Applied to Brain Fluids: Intracranial Pressure Does Not Drive Cerebral Perfusion or CSF Flow.

PubMed

Schmidt, Eric; Ros, Maxime; Moyse, Emmanuel; Lorthois, Sylvie; Swider, Pascal

2016-01-01

In line with the first law of thermodynamics, Bernoulli's principle states that the total energy in a fluid is the same at all points. We applied Bernoulli's principle to understand the relationship between intracranial pressure (ICP) and intracranial fluids. We analyzed simple fluid physics along a tube to describe the interplay between pressure and velocity. Bernoulli's equation demonstrates that a fluid does not flow along a gradient of pressure or velocity; a fluid flows along a gradient of energy from a high-energy region to a low-energy region. A fluid can even flow against a pressure gradient or a velocity gradient. Pressure and velocity represent part of the total energy. Cerebral blood perfusion is not driven by pressure but by energy: the blood flows from high-energy to lower-energy regions. Hydrocephalus is related to increased cerebrospinal fluid (CSF) resistance (i.e., energy transfer) at various points. Identification of the energy transfer within the CSF circuit is important in understanding and treating CSF-related disorders. Bernoulli's principle is not an abstract concept far from clinical practice. We should be aware that pressure is easy to measure, but it does not induce resumption of fluid flow. Even at the bedside, energy is the key to understanding ICP and fluid dynamics.

Novel theory for propagation of tilted Gaussian beam through aligned optical system

NASA Astrophysics Data System (ADS)

Xia, Lei; Gao, Yunguo; Han, Xudong

2017-03-01

A novel theory for tilted beam propagation is established in this paper. By setting the propagation direction of the tilted beam as the new optical axis, we establish a virtual optical system that is aligned with the new optical axis. Within the first order approximation of the tilt and off-axis, the propagation of the tilted beam is studied in the virtual system instead of the actual system. To achieve more accurate optical field distributions of tilted Gaussian beams, a complete diffraction integral for a misaligned optical system is derived by using the matrix theory with angular momentums. The theory demonstrates that a tilted TEM00 Gaussian beam passing through an aligned optical element transforms into a decentered Gaussian beam along the propagation direction. The deviations between the peak intensity axis of the decentered Gaussian beam and the new optical axis have linear relationships with the misalignments in the virtual system. ZEMAX simulation of a tilted beam through a thick lens exposed to air shows that the errors between the simulation results and theoretical calculations of the position deviations are less than 2‰ when the misalignments εx, εy, εx', εy' are in the range of [-0.5, 0.5] mm and [-0.5, 0.5]°.

Bernoulli-Langevin Wind Speed Model for Simulation of Storm Events

NASA Astrophysics Data System (ADS)

Fürstenau, Norbert; Mittendorf, Monika

2016-12-01

We present a simple nonlinear dynamics Langevin model for predicting the instationary wind speed profile during storm events typically accompanying extreme low-pressure situations. It is based on a second-degree Bernoulli equation with δ-correlated Gaussian noise and may complement stationary stochastic wind models. Transition between increasing and decreasing wind speed and (quasi) stationary normal wind and storm states are induced by the sign change of the controlling time-dependent rate parameter k(t). This approach corresponds to the simplified nonlinear laser dynamics for the incoherent to coherent transition of light emission that can be understood by a phase transition analogy within equilibrium thermodynamics [H. Haken, Synergetics, 3rd ed., Springer, Berlin, Heidelberg, New York 1983/2004.]. Evidence for the nonlinear dynamics two-state approach is generated by fitting of two historical wind speed profiles (low-pressure situations "Xaver" and "Christian", 2013) taken from Meteorological Terminal Air Report weather data, with a logistic approximation (i.e. constant rate coefficients k) to the solution of our dynamical model using a sum of sigmoid functions. The analytical solution of our dynamical two-state Bernoulli equation as obtained with a sinusoidal rate ansatz k(t) of period T (=storm duration) exhibits reasonable agreement with the logistic fit to the empirical data. Noise parameter estimates of speed fluctuations are derived from empirical fit residuals and by means of a stationary solution of the corresponding Fokker-Planck equation. Numerical simulations with the Bernoulli-Langevin equation demonstrate the potential for stochastic wind speed profile modeling and predictive filtering under extreme storm events that is suggested for applications in anticipative air traffic management.

The second-order theory of electromagnetic hot ion beam instabilities. [in interplanetary magnetic field

NASA Technical Reports Server (NTRS)

Gary, S. P.; Tokar, R. L.

1985-01-01

The present investigation is concerned with the application of a second-order theory for electromagnetic instabilities in a collisionless plasma to two modes which resonate with hot ion beams. The application of the theory is strictly limited to the linear growth phase. However, the application of the theory may be extended to obtain a description of the beam at postsaturation if the wave-beam resonance is sufficiently broad in velocity space. Under the considered limitations, it is shown that, as in the cold beam case, the fluctuating fields do not gain appreciable momentum and that the primary exchange of momentum is between the beam and main component.

On Euler's Theorem for Homogeneous Functions and Proofs Thereof.

ERIC Educational Resources Information Center

Tykodi, R. J.

1982-01-01

Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)

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

Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

NASA Technical Reports Server (NTRS)

Peterson, D.

1979-01-01

Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.

[Work, momentum and fatigue in the work of Daniel Bernoulli: toward the optimization of biological fact].

PubMed

Fonteneau, Yannick; Viard, Jérôme

The concept of mechanical work is inherited from the concepts of potentia absoluta and men's work, both implemented in the section IX of Daniel Bernoulli's Hydrodynamica in 1738. Nonetheless, Bernoulli did not confuse these two entities: he defined a link from gender to species between the former, which is general, and the latter, which is organic. In addition, Bernoulli clearly distinguished between vis viva and potentia absoluta (or work). Their reciprocal conversions are rarely mentioned explicitly in this book, except once, in the section X of his work, from vis viva to work, and subordinated to the mediation of a machine, in a driving forces substitution problem. His attitude evolved significantly in a text in 1753, in which work and vis viva were unambiguously connected, while the concept of potentia absoluta was reduced to that of human work, and the expression itself was abandoned. It was then accepted that work can be converted into vis viva, but the opposite is true in only one case, the intra-organic one. It is the concept of fatigue, seen as an expenditure of animal spirits themselves conceived of as little tensed springs releasing vis viva, that allowed the conversion, never quantified and listed simply as a model, from vis viva to work. Thus, work may have ultimately appeared as a transitional state between two kinds of vis viva, of which the first is non-quantifiable. At the same time, the natural elements were discredited from any hint of profitable production. Only men and animals were able to work in the strict sense of the word. Nature, left to itself, does not work, according to Bernoulli. In spite of his wish to bring together rational mechanics and practical mechanics, one perceived in the work of Bernoulli the subsistence of a rarely crossed disjunction between practical and theoretical fields.

Postbuckling behaviors of nanorods including the effects of nonlocal elasticity theory and surface stress

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

Thongyothee, Chawis, E-mail: chawist@hotmail.com; Chucheepsakul, Somchai

2013-12-28

This paper is concerned with postbuckling behaviors of nanorods subjected to an end concentrated load. One end of the nanorod is clamped while the other end is fixed to a support that can slide in the slot. The governing equation is developed from static equilibrium and geometrical conditions by using the exact curvature corresponding to the elastica theory. The nonlocal elasticity, the effect of surface stress, and their combined effects are taken into account in Euler–Bernoulli beam theory. Differential equations in this problem can be solved numerically by using the shooting-optimization technique for the postbuckling loads and the buckled configurations.more » The results show that nanorods with the nonlocal elasticity effect undergo increasingly large deformation while the effect of surface stress in combination with nonlocal elasticity decreases the deflection of nanorods under the same postbuckling load.« less

Enhanced Acoustic Black Hole effect in beams with a modified thickness profile and extended platform

NASA Astrophysics Data System (ADS)

Tang, Liling; Cheng, Li

2017-03-01

The phenomenon of Acoustics Black Hole (ABH) benefits from the bending wave propagating properties inside a thin-walled structure with power-law thickness variation to achieve zero reflection when the structural thickness approaches zero in the ideal scenario. However, manufacturing an ideally tailored power-law profile of a structure with embedded ABH feature can hardly be achieved in practice. Past research showed that the inevitable truncation at the wedge tip of the structure can significantly weaken the expected ABH effect by creating wave reflections. On the premise of the minimum achievable truncation thickness by the current manufacturing technology, exploring ways to ensure and achieve better ABH effect becomes important. In this paper, we investigate this issue by using a previously developed wavelet-decomposed semi-analytical model on an Euler-Bernoulli beam with a modified power-law profile and an extended platform of constant thickness. Through comparisons with the conventional ABH profile in terms of system loss factor and energy distribution, numerical results show that the modified thickness profile brings about a systematic increase in the ABH effect at mid-to-high frequencies, especially when the truncation thickness is small and the profile parameter m is large. The use of an extended platform further increases the ABH effect to broader the frequency band whilst providing rooms for catering particular low frequency applications.

Design and modeling of magnetically driven electric-field sensor for non-contact DC voltage measurement in electric power systems.

PubMed

Wang, Decai; Li, Ping; Wen, Yumei

2016-10-01

In this paper, the design and modeling of a magnetically driven electric-field sensor for non-contact DC voltage measurement are presented. The magnetic drive structure of the sensor is composed of a small solenoid and a cantilever beam with a cylindrical magnet mounted on it. The interaction of the magnet and the solenoid provides the magnetic driving force for the sensor. Employing magnetic drive structure brings the benefits of low driving voltage and large vibrating displacement, which consequently results in less interference from the drive signal. In the theoretical analyses, the capacitance calculation model between the wire and the sensing electrode is built. The expression of the magnetic driving force is derived by the method of linear fitting. The dynamical model of the magnetic-driven cantilever beam actuator is built by using Euler-Bernoulli theory and distributed parameter method. Taking advantage of the theoretical model, the output voltage of proposed sensor can be predicted. The experimental results are in good agreement with the theoretical results. The proposed sensor shows a favorable linear response characteristic. The proposed sensor has a measuring sensitivity of 9.87 μV/(V/m) at an excitation current of 37.5 mA. The electric field intensity resolution can reach 10.13 V/m.

A Simplified Model for the Optical Force exerted on a Vertically Oriented Cilium by an Optical Trap and the Resulting Deformation

NASA Astrophysics Data System (ADS)

Lofgren, Ian; Resnick, Andrew

2014-03-01

Eukaryotic cilia are essentially whiplike structures extending from the cell body. Although their existence has been long known, their mechanical and functional properties are poorly understood. Optical traps are a non-contact method of applying a localized force to microscopic objects and an ideal tool for the study of ciliary mechanics. Starting with the discrete dipole approximation, a common means of calculating the optical force on an object that is not spherical, we tackle the problem of the optical force on a cilium. Treating the cilium as a homogeneous nonmagnetic cylinder and the electric field of the laser beam as linearly polarized results in a force applied in the direction of polarization. The force density in the polarization direction is derived from the force on an individual dipole within the cilium, which can be integrated over the volume of the cilium in order to find the total force. Utilizing Euler-Bernoulli beam theory, we integrate the force density over a cross section of the cilium and numerically solve a fourth order differential equation to obtain the final deformation of the cilium. This prediction will later be compared with experimental results to infer the mechanical stiffness of the cilium. Support from the National Institutes of Health, 1R15DK092716 is gratefully acknowledged.

Effects of mean flow on transmission loss of orthogonally rib-stiffened aeroelastic plates.

PubMed

Xin, F X; Lu, T J

2013-06-01

This paper investigates the sound transmission loss (STL) of aeroelastic plates reinforced by two sets of orthogonal rib-stiffeners in the presence of external mean flow. Built upon the periodicity of the structure, a comprehensive theoretical model is developed by considering the convection effect of mean flow. The rib-stiffeners are modeled by employing the Bernoulli-Euler beam theory and the torsional wave equation. While the solution for the transmission loss of the structure based on plate displacement and acoustic pressures is given in the form of space-harmonic series, the corresponding coefficients are obtained from the solution of a system of linear equations derived from the plate-beam coupling vibration governing equation and Helmholtz equation. The model predictions are validated by comparing with existing theoretical and experimental results in the absence of mean flow. A parametric study is subsequently performed to quantify the effects of mean flow as well as structure geometrical parameters upon the transmission loss. It is demonstrated that the transmission loss of periodically rib-stiffened structure is increased significantly with increasing Mach number of mean flow over a wide frequency range. The STL value for the case of sound wave incident downstream is pronouncedly larger than that associated with sound wave incident upstream.

A {3,2}-Order Bending Theory for Laminated Composite and Sandwich Beams

NASA Technical Reports Server (NTRS)

Cook, Geoffrey M.; Tessler, Alexander

1998-01-01

A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effect without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.

3-D conditional hyperbolic method of moments for high-fidelity Euler-Euler simulations of particle-laden flows

NASA Astrophysics Data System (ADS)

Patel, Ravi; Kong, Bo; Capecelatro, Jesse; Fox, Rodney; Desjardins, Olivier

2017-11-01

Particle-laden turbulent flows are important features of many environmental and industrial processes. Euler-Euler (EE) simulations of these flows are more computationally efficient than Euler-Lagrange (EL) simulations. However, traditional EE methods, such as the two-fluid model, cannot faithfully capture dilute regions of flow with finite Stokes number particles. For this purpose, the multi-valued nature of the particle velocity field must be treated with a polykinetic description. Various quadrature-based moment methods (QBMM) can be used to approximate the full kinetic description by solving for a set of moments of the particle velocity distribution function (VDF) and providing closures for the higher-order moments. Early QBMM fail to maintain the strict hyperbolicity of the kinetic equations, producing unphysical delta shocks (i.e., mass accumulation at a point). In previous work, a 2-D conditional hyperbolic quadrature method of moments (CHyQMOM) was proposed as a fourth-order QBMM closure that maintains strict hyperbolicity. Here, we present the 3-D extension of CHyQMOM. We compare results from CHyQMOM to other QBMM and EL in the context of particle trajectory crossing, cluster-induced turbulence, and particle-laden channel flow. NSF CBET-1437903.

Improving performance of DS-CDMA systems using chaotic complex Bernoulli spreading codes

NASA Astrophysics Data System (ADS)

Farzan Sabahi, Mohammad; Dehghanfard, Ali

2014-12-01

The most important goal of spreading spectrum communication system is to protect communication signals against interference and exploitation of information by unintended listeners. In fact, low probability of detection and low probability of intercept are two important parameters to increase the performance of the system. In Direct Sequence Code Division Multiple Access (DS-CDMA) systems, these properties are achieved by multiplying the data information in spreading sequences. Chaotic sequences, with their particular properties, have numerous applications in constructing spreading codes. Using one-dimensional Bernoulli chaotic sequence as spreading code is proposed in literature previously. The main feature of this sequence is its negative auto-correlation at lag of 1, which with proper design, leads to increase in efficiency of the communication system based on these codes. On the other hand, employing the complex chaotic sequences as spreading sequence also has been discussed in several papers. In this paper, use of two-dimensional Bernoulli chaotic sequences is proposed as spreading codes. The performance of a multi-user synchronous and asynchronous DS-CDMA system will be evaluated by applying these sequences under Additive White Gaussian Noise (AWGN) and fading channel. Simulation results indicate improvement of the performance in comparison with conventional spreading codes like Gold codes as well as similar complex chaotic spreading sequences. Similar to one-dimensional Bernoulli chaotic sequences, the proposed sequences also have negative auto-correlation. Besides, construction of complex sequences with lower average cross-correlation is possible with the proposed method.

Transverse vibrations of shear-deformable beams using a general higher order theory

NASA Technical Reports Server (NTRS)

Kosmatka, J. B.

1993-01-01

A general higher order theory is developed to study the static and vibrational behavior of beam structures having an arbitrary cross section that utilizes both out-of-plane shear-dependent warping and in-plane (anticlastic) deformations. The equations of motion are derived via Hamilton's principle, where the full 3D constitutive relations are used. A simplified version of the general higher-order theory is also presented for beams having an arbitrary cross section that includes out-of-plane shear deformation but assumes that stresses within the cross section and in-plane deformations are negligible. This simplified model, which is accurate for long to moderately short wavelengths, offers substantial improvements over existing higher order theories that are limited to beams with thin rectangular cross sections. The current approach will be very useful in the study of thin-wall closed-cell beams such as airfoil-type sections where the magnitude of shear-related cross-sectional warping is significant.

Comparison between Euler and quaternion parametrization in UAV dynamics

NASA Astrophysics Data System (ADS)

Alaimo, A.; Artale, V.; Milazzo, C.; Ricciardello, A.

2013-10-01

The main topic addressed in this paper is a comparison between Euler parametrization and Quaternion one in the description of the dynamics of a Unmanned Aerial Vehicle assumed as a rigid body. In details Newton Euler equations are re-written in terms of quaternions due to the singularities that the Euler angles lead. This formulation not only avoids the gimbal lock but also allows a better performance in numerical implementation thanks to the linearity of quaternion algebra. This kind of analysis, proved by some numerical results presented, has a great importance due to the applicability of quaternion to drone control. Indeed, this latter requires a time response as quick as possible, in order to be reliable.

Vibration suppression and slewing control of a flexible structure

NASA Technical Reports Server (NTRS)

Inman, Daniel J.; Garcia, Ephrahim; Pokines, Brett

1991-01-01

Examined here are the effects of motor dynamics and secondary piezoceramic actuators on vibration suppression during the slewing of flexible structures. The approach focuses on the interaction between the structure, the actuators, and the choice of control law. The results presented here are all simulated, but are based on experimentally determined parameters for the motor, structure, piezoceramic actuators, and piezofilm sensors. The simulation results clearly illustrate that the choice of motor inertia relative to beam inertia makes a critical difference in the performance of the system. In addition, the use of secondary piezoelectric actuators reduces the load requirements on the motor and also reduces the overshoot of the tip deflection. The structures considered here are a beam and a frame. The majority of results are based on a Euler Bernoulli beam model. The slewing frame introduces substantial torsional modes and a more realistic model. The slewing frame results are incomplete and represent work in progress.

Nonlinear finite amplitude torsional vibrations of cantilevers in viscous fluids

NASA Astrophysics Data System (ADS)

Aureli, Matteo; Pagano, Christopher; Porfiri, Maurizio

2012-06-01

In this paper, we study torsional vibrations of cantilever beams undergoing moderately large oscillations within a quiescent viscous fluid. The structure is modeled as an Euler-Bernoulli beam, with thin rectangular cross section, under base excitation. The distributed hydrodynamic loading experienced by the vibrating structure is described through a complex-valued hydrodynamic function which incorporates added mass and fluid damping elicited by moderately large rotations. We conduct a parametric study on the two dimensional computational fluid dynamics of a pitching rigid lamina, representative of a generic beam cross section, to investigate the dependence of the hydrodynamic function on the governing flow parameters. As the frequency and amplitude of the oscillation increase, vortex shedding and convection phenomena increase, thus resulting into nonlinear hydrodynamic damping. We derive a handleable nonlinear correction to the classical hydrodynamic function developed for small amplitude torsional vibrations for use in a reduced order nonlinear modal model and we validate theoretical results against experimental findings.

Euler solutions for an unbladed jet engine configuration

NASA Technical Reports Server (NTRS)

Stewart, Mark E. M.

1991-01-01

A Euler solution for an axisymmetric jet engine configuration without blade effects is presented. The Euler equations are solved on a multiblock grid which covers a domain including the inlet, bypass duct, core passage, nozzle, and the far field surrounding the engine. The simulation is verified by considering five theoretical properties of the solution. The solution demonstrates both multiblock grid generation techniques and a foundation for a full jet engine throughflow calculation.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

NASA Astrophysics Data System (ADS)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Accurate electrostatic and van der Waals pull-in prediction for fully clamped nano/micro-beams using linear universal graphs of pull-in instability

NASA Astrophysics Data System (ADS)

Tahani, Masoud; Askari, Amir R.

2014-09-01

In spite of the fact that pull-in instability of electrically actuated nano/micro-beams has been investigated by many researchers to date, no explicit formula has been presented yet which can predict pull-in voltage based on a geometrically non-linear and distributed parameter model. The objective of present paper is to introduce a simple and accurate formula to predict this value for a fully clamped electrostatically actuated nano/micro-beam. To this end, a non-linear Euler-Bernoulli beam model is employed, which accounts for the axial residual stress, geometric non-linearity of mid-plane stretching, distributed electrostatic force and the van der Waals (vdW) attraction. The non-linear boundary value governing equation of equilibrium is non-dimensionalized and solved iteratively through single-term Galerkin based reduced order model (ROM). The solutions are validated thorough direct comparison with experimental and other existing results reported in previous studies. Pull-in instability under electrical and vdW loads are also investigated using universal graphs. Based on the results of these graphs, non-dimensional pull-in and vdW parameters, which are defined in the text, vary linearly versus the other dimensionless parameters of the problem. Using this fact, some linear equations are presented to predict pull-in voltage, the maximum allowable length, the so-called detachment length, and the minimum allowable gap for a nano/micro-system. These linear equations are also reduced to a couple of universal pull-in formulas for systems with small initial gap. The accuracy of the universal pull-in formulas are also validated by comparing its results with available experimental and some previous geometric linear and closed-form findings published in the literature.

The Scaling Group of the 1-D Invisicid Euler Equations

NASA Astrophysics Data System (ADS)

Schmidt, Emma; Ramsey, Scott; Boyd, Zachary; Baty, Roy

2017-11-01

The one dimensional (1-D) compressible Euler equations in non-ideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1-D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials.

A High Order Finite Difference Scheme with Sharp Shock Resolution for the Euler Equations

NASA Technical Reports Server (NTRS)

Gerritsen, Margot; Olsson, Pelle

1996-01-01

We derive a high-order finite difference scheme for the Euler equations that satisfies a semi-discrete energy estimate, and present an efficient strategy for the treatment of discontinuities that leads to sharp shock resolution. The formulation of the semi-discrete energy estimate is based on a symmetrization of the Euler equations that preserves the homogeneity of the flux vector, a canonical splitting of the flux derivative vector, and the use of difference operators that satisfy a discrete analogue to the integration by parts procedure used in the continuous energy estimate. Around discontinuities or sharp gradients, refined grids are created on which the discrete equations are solved after adding a newly constructed artificial viscosity. The positioning of the sub-grids and computation of the viscosity are aided by a detection algorithm which is based on a multi-scale wavelet analysis of the pressure grid function. The wavelet theory provides easy to implement mathematical criteria to detect discontinuities, sharp gradients and spurious oscillations quickly and efficiently.

Interlaminar Stresses by Refined Beam Theories and the Sinc Method Based on Interpolation of Highest Derivative

NASA Technical Reports Server (NTRS)

Slemp, Wesley C. H.; Kapania, Rakesh K.; Tessler, Alexander

2010-01-01

Computation of interlaminar stresses from the higher-order shear and normal deformable beam theory and the refined zigzag theory was performed using the Sinc method based on Interpolation of Highest Derivative. The Sinc method based on Interpolation of Highest Derivative was proposed as an efficient method for determining through-the-thickness variations of interlaminar stresses from one- and two-dimensional analysis by integration of the equilibrium equations of three-dimensional elasticity. However, the use of traditional equivalent single layer theories often results in inaccuracies near the boundaries and when the lamina have extremely large differences in material properties. Interlaminar stresses in symmetric cross-ply laminated beams were obtained by solving the higher-order shear and normal deformable beam theory and the refined zigzag theory with the Sinc method based on Interpolation of Highest Derivative. Interlaminar stresses and bending stresses from the present approach were compared with a detailed finite element solution obtained by ABAQUS/Standard. The results illustrate the ease with which the Sinc method based on Interpolation of Highest Derivative can be used to obtain the through-the-thickness distributions of interlaminar stresses from the beam theories. Moreover, the results indicate that the refined zigzag theory is a substantial improvement over the Timoshenko beam theory due to the piecewise continuous displacement field which more accurately represents interlaminar discontinuities in the strain field. The higher-order shear and normal deformable beam theory more accurately captures the interlaminar stresses at the ends of the beam because it allows transverse normal strain. However, the continuous nature of the displacement field requires a large number of monomial terms before the interlaminar stresses are computed as accurately as the refined zigzag theory.

Congruences between modular forms: raising the level and dropping Euler factors.

PubMed

Diamond, F

1997-10-14

We discuss the relationship among certain generalizations of results of Hida, Ribet, and Wiles on congruences between modular forms. Hida's result accounts for congruences in terms of the value of an L-function, and Ribet's result is related to the behavior of the period that appears there. Wiles' theory leads to a class number formula relating the value of the L-function to the size of a Galois cohomology group. The behavior of the period is used to deduce that a formula at "nonminimal level" is obtained from one at "minimal level" by dropping Euler factors from the L-function.

Modeling the influence of the Casimir force on the pull-in instability of nanowire-fabricated nanotweezers

NASA Astrophysics Data System (ADS)

Farrokhabadi, Amin; Mokhtari, Javad; Rach, Randolph; Abadyan, Mohamadreza

2015-09-01

The Casimir force can strongly interfere with the pull-in performance of ultra-small structures. The strength of the Casimir force is significantly affected by the geometries of interacting bodies. Previous investigators have exclusively studied the effect of the Casimir force on the electromechanical instability of nanostructures with planar geometries. However no work has yet considered this effect on the pull-in instability of systems with cylindrical geometries such as nanotweezers fabricated from nanotube/nanowires. In our present work, the influence of the Casimir attraction on the electrostatic response and pull-in instability of nanotweezers fabricated from cylindrical conductive nanowires/nanotubes is theoretically investigated. An asymptotic solution, based on scattering theory, is applied to consider the effect of vacuum fluctuations in the theoretical model. The Euler-Bernoulli beam model is employed, in conjunction with the size-dependent modified couple stress continuum theory, to derive the governing equation of the nanotweezers. The governing nonlinear equations are solved by two different approaches, i.e., the modified Adomian-Padé method (MAD-Padé) and a numerical solution. Various aspects of the problem, i.e., the variation of pull-in parameters, effect of geometry, coupling between the Casimir force and size dependency effects and comparison with the van der Waals force regime are discussed.

On the stability analysis of approximate factorization methods for 3D Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Demuren, A. O.; Ibraheem, S. O.

1993-01-01

The convergence characteristics of various approximate factorizations for the 3D Euler and Navier-Stokes equations are examined using the von-Neumann stability analysis method. Three upwind-difference based factorizations and several central-difference based factorizations are considered for the Euler equations. In the upwind factorizations both the flux-vector splitting methods of Steger and Warming and van Leer are considered. Analysis of the Navier-Stokes equations is performed only on the Beam and Warming central-difference scheme. The range of CFL numbers over which each factorization is stable is presented for one-, two-, and three-dimensional flow. Also presented for each factorization is the CFL number at which the maximum eigenvalue is minimized, for all Fourier components, as well as for the high frequency range only. The latter is useful for predicting the effectiveness of multigrid procedures with these schemes as smoothers. Further, local mode analysis is performed to test the suitability of using a uniform flow field in the stability analysis. Some inconsistencies in the results from previous analyses are resolved.

Theory of electronic phase locking of an optical array without a reference beam

NASA Astrophysics Data System (ADS)

Shay, Thomas M.

2006-08-01

The first theory for two novel coherent beam combination architectures that are the first electronic beam combination architectures that completely eliminate the need for a separate reference beam are presented. Detailed theoretical models are developed and presented for the first time.

A linearized Euler analysis of unsteady flows in turbomachinery

NASA Technical Reports Server (NTRS)

Hall, Kenneth C.; Crawley, Edward F.

1987-01-01

A method for calculating unsteady flows in cascades is presented. The model, which is based on the linearized unsteady Euler equations, accounts for blade loading shock motion, wake motion, and blade geometry. The mean flow through the cascade is determined by solving the full nonlinear Euler equations. Assuming the unsteadiness in the flow is small, then the Euler equations are linearized about the mean flow to obtain a set of linear variable coefficient equations which describe the small amplitude, harmonic motion of the flow. These equations are discretized on a computational grid via a finite volume operator and solved directly subject to an appropriate set of linearized boundary conditions. The steady flow, which is calculated prior to the unsteady flow, is found via a Newton iteration procedure. An important feature of the analysis is the use of shock fitting to model steady and unsteady shocks. Use of the Euler equations with the unsteady Rankine-Hugoniot shock jump conditions correctly models the generation of steady and unsteady entropy and vorticity at shocks. In particular, the low frequency shock displacement is correctly predicted. Results of this method are presented for a variety of test cases. Predicted unsteady transonic flows in channels are compared to full nonlinear Euler solutions obtained using time-accurate, time-marching methods. The agreement between the two methods is excellent for small to moderate levels of flow unsteadiness. The method is also used to predict unsteady flows in cascades due to blade motion (flutter problem) and incoming disturbances (gust response problem).

On the statistical mechanics of the 2D stochastic Euler equation

NASA Astrophysics Data System (ADS)

Bouchet, Freddy; Laurie, Jason; Zaboronski, Oleg

2011-12-01

The dynamics of vortices and large scale structures is qualitatively very different in two dimensional flows compared to its three dimensional counterparts, due to the presence of multiple integrals of motion. These are believed to be responsible for a variety of phenomena observed in Euler flow such as the formation of large scale coherent structures, the existence of meta-stable states and random abrupt changes in the topology of the flow. In this paper we study stochastic dynamics of the finite dimensional approximation of the 2D Euler flow based on Lie algebra su(N) which preserves all integrals of motion. In particular, we exploit rich algebraic structure responsible for the existence of Euler's conservation laws to calculate the invariant measures and explore their properties and also study the approach to equilibrium. Unexpectedly, we find deep connections between equilibrium measures of finite dimensional su(N) truncations of the stochastic Euler equations and random matrix models. Our work can be regarded as a preparation for addressing the questions of large scale structures, meta-stability and the dynamics of random transitions between different flow topologies in stochastic 2D Euler flows.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures.

PubMed

Abazari, Amir Musa; Safavi, Seyed Mohsen; Rezazadeh, Ghader; Villanueva, Luis Guillermo

2015-11-11

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke's law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale.

Modelling the Size Effects on the Mechanical Properties of Micro/Nano Structures

PubMed Central

Abazari, Amir Musa; Safavi, Seyed Mohsen; Rezazadeh, Ghader; Villanueva, Luis Guillermo

2015-01-01

Experiments on micro- and nano-mechanical systems (M/NEMS) have shown that their behavior under bending loads departs in many cases from the classical predictions using Euler-Bernoulli theory and Hooke’s law. This anomalous response has usually been seen as a dependence of the material properties on the size of the structure, in particular thickness. A theoretical model that allows for quantitative understanding and prediction of this size effect is important for the design of M/NEMS. In this paper, we summarize and analyze the five theories that can be found in the literature: Grain Boundary Theory (GBT), Surface Stress Theory (SST), Residual Stress Theory (RST), Couple Stress Theory (CST) and Surface Elasticity Theory (SET). By comparing these theories with experimental data we propose a simplified model combination of CST and SET that properly fits all considered cases, therefore delivering a simple (two parameters) model that can be used to predict the mechanical properties at the nanoscale. PMID:26569256

Vanishing Viscosity Approach to the Compressible Euler Equations for Transonic Nozzle and Spherically Symmetric Flows

NASA Astrophysics Data System (ADS)

Chen, Gui-Qiang G.; Schrecker, Matthew R. I.

2018-04-01

We are concerned with globally defined entropy solutions to the Euler equations for compressible fluid flows in transonic nozzles with general cross-sectional areas. Such nozzles include the de Laval nozzles and other more general nozzles whose cross-sectional area functions are allowed at the nozzle ends to be either zero (closed ends) or infinity (unbounded ends). To achieve this, in this paper, we develop a vanishing viscosity method to construct globally defined approximate solutions and then establish essential uniform estimates in weighted L p norms for the whole range of physical adiabatic exponents γ\\in (1, ∞) , so that the viscosity approximate solutions satisfy the general L p compensated compactness framework. The viscosity method is designed to incorporate artificial viscosity terms with the natural Dirichlet boundary conditions to ensure the uniform estimates. Then such estimates lead to both the convergence of the approximate solutions and the existence theory of globally defined finite-energy entropy solutions to the Euler equations for transonic flows that may have different end-states in the class of nozzles with general cross-sectional areas for all γ\\in (1, ∞) . The approach and techniques developed here apply to other problems with similar difficulties. In particular, we successfully apply them to construct globally defined spherically symmetric entropy solutions to the Euler equations for all γ\\in (1, ∞).

Numerical solutions of acoustic wave propagation problems using Euler computations

NASA Technical Reports Server (NTRS)

Hariharan, S. I.

1984-01-01

This paper reports solution procedures for problems arising from the study of engine inlet wave propagation. The first problem is the study of sound waves radiated from cylindrical inlets. The second one is a quasi-one-dimensional problem to study the effect of nonlinearities and the third one is the study of nonlinearities in two dimensions. In all three problems Euler computations are done with a fourth-order explicit scheme. For the first problem results are shown in agreement with experimental data and for the second problem comparisons are made with an existing asymptotic theory. The third problem is part of an ongoing work and preliminary results are presented for this case.

Quasi-stationary mechanics of elastic continua with bending stiffness wrapping on a pulley system

NASA Astrophysics Data System (ADS)

Kaczmarczyk, S.; Mirhadizadeh, S.

2016-05-01

In many engineering applications elastic continua such as ropes and belts often are subject to bending when they pass over pulleys / sheaves. In this paper the quasi-stationary mechanics of a cable-pulley system is studied. The cable is modelled as a moving Euler- Bernoulli beam. The distribution of tension is non-uniform along its span and due to the bending stiffness the contact points at the pulley-beam boundaries are not unknown. The system is described by a set of nonlinear ordinary differential equations with undetermined boundary conditions. The resulting nonlinear Boundary Value Problem (BVP) with unknown boundaries is solved by converting the problem into the ‘standard’ form defined over a fixed interval. Numerical results obtained for a range of typical configurations with relevant boundary conditions applied demonstrate that due to the effects of bending stiffness the angels of wrap are reduced and the span tensions are increased.

A study of the vibrational energies of two coupled beams by finite element and green function (receptance) methods

NASA Astrophysics Data System (ADS)

Shankar, K.; Keane, A. J.

1995-04-01

The behaviour of two hinged-hinged beams, point coupled by springs (translational, rotary and a combination of both) with weak to strong coupling is studied from the point of view of vibrational energies, input power and power transferred through the coupling. Two configurations are studied: in the first case the beams are placed parallel to each other and only the transverse, Euler-Bernoulli modes are considered; the second configuration is more complicated with the beams placed perpendicular to each other, executing axial as well as transverse vibrations. These models are studied by using a finite element analysis (FEA) package and, alternatively, via the modally derived Green functions of the uncoupled subsystems. In both cases the beams are given proportional damping and one of the beams is driven by a point harmonic force. The effects of coupling stiffness and modal summation bandwidth are studied. It is shown that there is good agreement between the FEA and the Green function approach over a range of coupling strengths, but that at higher strengths the number of uncoupled modes used significantly affects the accuracy of the Green function method used here. The beams in the second configuration are then further studied from the point of view of SEA coupling loss factors. The frequency averaged coupling loss factors are calculated for weak and strong coupling, first by using a power injection method, where the power balance equations are formed on the assumption of only direct coupling loss factors. Then, the entire matrix of direct and indirect coupling loss factors is derived by using a deterministic modal approach. These are compared and the indirect coupling loss factors are found to be significant in magnitude in respect to the direct coupling loss factors. Several cases are studied in which the coupling powers and energy levels are predicted by using only the direct coupling loss factors and compared with the exact results obtained by using both direct

Refinement Of Hexahedral Cells In Euler Flow Computations

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1996-01-01

Topologically Independent Grid, Euler Refinement (TIGER) computer program solves Euler equations of three-dimensional, unsteady flow of inviscid, compressible fluid by numerical integration on unstructured hexahedral coordinate grid refined where necessary to resolve shocks and other details. Hexahedral cells subdivided, each into eight smaller cells, as needed to refine computational grid in regions of high flow gradients. Grid Interactive Refinement and Flow-Field Examination (GIRAFFE) computer program written in conjunction with TIGER program to display computed flow-field data and to assist researcher in verifying specified boundary conditions and refining grid.

On the Euler Function of the Catalan Numbers

DTIC Science & Technology

2012-02-26

ON THE EULER FUNCTION OF THE CATALAN NUMBERS FLORIAN LUCA AND PANTELIMON STĂNICĂ Abstract. We study the solutions of the equation φ(Cm)/φ(Cn) = r...where r is a fixed rational number , Ck is the kth Catalan number and φ is the Euler function. We note that the number r = 4 is special for this...observation concerning φ(Cn+1)/φ(Cn) For a positive integer n, let (1) Cn = 1 n+ 1 ( 2n n ) be the n-th Catalan number . For a positive integer m we put φ(m) for

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

ERIC Educational Resources Information Center

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

Multiple scattering theory for total skin electron beam design.

PubMed

Antolak, J A; Hogstrom, K R

1998-06-01

The purpose of this manuscript is to describe a method for designing a broad beam of electrons suitable for total skin electron irradiation (TSEI). A theoretical model of a TSEI beam from a linear accelerator with a dual scattering system has been developed. The model uses Fermi-Eyges theory to predict the planar fluence of the electron beam after it has passed through various materials between the source and the treatment plane, which includes scattering foils, monitor chamber, air, and a plastic diffusing plate. Unique to this model is its accounting for removal of the tails of the electron beam profile as it passes through the primary x-ray jaws. A method for calculating the planar fluence profile for an obliquely incident beam is also described. Off-axis beam profiles and percentage depth doses are measured with ion chambers, film, and thermoluminescent dosimeters (TLD). The measured data show that the theoretical model can accurately predict beam energy and planar fluence of the electron beam at normal and oblique incidence. The agreement at oblique angles is not quite as good but is sufficiently accurate to be of predictive value when deciding on the optimal angles for the clinical TSEI beams. The advantage of our calculational approach for designing a TSEI beam is that many different beam configurations can be tested without having to perform time-consuming measurements. Suboptimal configurations can be quickly dismissed, and the predicted optimal solution should be very close to satisfying the clinical specifications.

Evaluating the Risks: A Bernoulli Process Model of HIV Infection and Risk Reduction.

ERIC Educational Resources Information Center

Pinkerton, Steven D.; Abramson, Paul R.

1993-01-01

A Bernoulli process model of human immunodeficiency virus (HIV) is used to evaluate infection risks associated with various sexual behaviors (condom use, abstinence, or monogamy). Results suggest that infection is best mitigated through measures that decrease infectivity, such as condom use. (SLD)

Uniform Decay for Solutions of an Axially Moving Viscoelastic Beam

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

Kelleche, Abdelkarim, E-mail: kellecheabdelkarim@gmail.com; Tatar, Nasser-eddine, E-mail: tatarn@Kfupm.edu.sa

2017-06-15

The paper deals with an axially moving viscoelastic structure modeled as an Euler–Bernoulli beam. The aim is to suppress the transversal displacement (transversal vibrations) that occur during the axial motion of the beam. It is assumed that the beam is moving with a constant axial speed and it is subject to a nonlinear force at the right boundary. We prove that when the axial speed of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations. It is shown that the rate of decay of the energy dependsmore » on the kernel which arise in the viscoelastic term. We consider a general kernel and notice that solutions cannot decay faster than the kernel.« less

Numerical analysis of nonminimum phase zero for nonuniform link design

NASA Technical Reports Server (NTRS)

Girvin, Douglas L.; Book, Wayne J.

1991-01-01

As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links becomes more of an issue in control. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. This research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixed, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to the inverse dynamic algorithms that are currently under development.

Design and analytical modeling of magneto-electro-mechanical characteristics of a novel magneto-electro-elastic vibration-based energy harvesting system

NASA Astrophysics Data System (ADS)

Shishesaz, Mohammad; Shirbani, Meisam Moory; Sedighi, Hamid Mohammad; Hajnayeb, Ali

2018-07-01

In order to effectively design an energy harvesting system for any specific application, a model that accurately characterizes the energy harvesting parameters is needed. In the present paper a novel magneto-electro-elastic (MEE) cantilever beam has been proposed and modeled as an effective means to increase the harvested electrical power in a vibration-based energy harvesting system. The cantilever beam is composed of a linear homogeneous elastic substrate and two MEE layers with perfect bonds between their interfaces. Using the constitutive equations, Gauss's and Faraday's laws, based on the Euler-Bernoulli beam theory, the coupled magneto-electro-mechanical (MeM) differential equations are derived for a harmonic base excitation in the transversal direction with a superimposed small rotation. The resulting equations are then solved analytically to obtain the dynamic behavior as well as the harvested voltages and powers of the proposed energy harvesting system. Finally, parametric numerical studies are used to examine the effect of excitation frequency, external resistive loads, and material properties on the performance of the MEE energy harvester. The study reveals that the implementation of the coil circuit has resulted in an increase in the total useful harvested power. According to the numerical results, any increase in the Young's modulus and density of the substrate layer (across the ranges that have been studied and while the properties of the MEE layer are kept constant), increases the magnitude of the magnetoelectric harvested power in the unimorph MEE energy harvester system.

Numerical analysis of nonminimum phase zero for nonuniform link design

NASA Astrophysics Data System (ADS)

Girvin, Douglas L.; Book, Wayne J.

1991-11-01

As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links becomes more of an issue in control. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. This research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixed, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to the inverse dynamic algorithms that are currently under development.

A general multiblock Euler code for propulsion integration. Volume 3: User guide for the Euler code

NASA Technical Reports Server (NTRS)

Chen, H. C.; Su, T. Y.; Kao, T. J.

1991-01-01

This manual explains the procedures for using the general multiblock Euler (GMBE) code developed under NASA contract NAS1-18703. The code was developed for the aerodynamic analysis of geometrically complex configurations in either free air or wind tunnel environments (vol. 1). The complete flow field is divided into a number of topologically simple blocks within each of which surface fitted grids and efficient flow solution algorithms can easily be constructed. The multiblock field grid is generated with the BCON procedure described in volume 2. The GMBE utilizes a finite volume formulation with an explicit time stepping scheme to solve the Euler equations. A multiblock version of the multigrid method was developed to accelerate the convergence of the calculations. This user guide provides information on the GMBE code, including input data preparations with sample input files and a sample Unix script for program execution in the UNICOS environment.

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

NASA Astrophysics Data System (ADS)

Drivas, Theodore D.; Eyink, Gregory L.

2017-12-01

We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have non-negative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3-based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

Monitoring surgical and medical outcomes: the Bernoulli cumulative SUM chart. A novel application to assess clinical interventions

PubMed Central

Leandro, G; Rolando, N; Gallus, G; Rolles, K; Burroughs, A

2005-01-01

Background: Monitoring clinical interventions is an increasing requirement in current clinical practice. The standard CUSUM (cumulative sum) charts are used for this purpose. However, they are difficult to use in terms of identifying the point at which outcomes begin to be outside recommended limits. Objective: To assess the Bernoulli CUSUM chart that permits not only a 100% inspection rate, but also the setting of average expected outcomes, maximum deviations from these, and false positive rates for the alarm signal to trigger. Methods: As a working example this study used 674 consecutive first liver transplant recipients. The expected one year mortality set at 24% from the European Liver Transplant Registry average. A standard CUSUM was compared with Bernoulli CUSUM: the control value mortality was therefore 24%, maximum accepted mortality 30%, and average number of observations to signal was 500—that is, likelihood of false positive alarm was 1:500. Results: The standard CUSUM showed an initial descending curve (nadir at patient 215) then progressively ascended indicating better performance. The Bernoulli CUSUM gave three alarm signals initially, with easily recognised breaks in the curve. There were no alarms signals after patient 143 indicating satisfactory performance within the criteria set. Conclusions: The Bernoulli CUSUM is more easily interpretable graphically and is more suitable for monitoring outcomes than the standard CUSUM chart. It only requires three parameters to be set to monitor any clinical intervention: the average expected outcome, the maximum deviation from this, and the rate of false positive alarm triggers. PMID:16210461

Computational simulations of vocal fold vibration: Bernoulli versus Navier-Stokes.

PubMed

Decker, Gifford Z; Thomson, Scott L

2007-05-01

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.

Solving Nonlinear Euler Equations with Arbitrary Accuracy

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2005-01-01

A computer program that efficiently solves the time-dependent, nonlinear Euler equations in two dimensions to an arbitrarily high order of accuracy has been developed. The program implements a modified form of a prior arbitrary- accuracy simulation algorithm that is a member of the class of algorithms known in the art as modified expansion solution approximation (MESA) schemes. Whereas millions of lines of code were needed to implement the prior MESA algorithm, it is possible to implement the present MESA algorithm by use of one or a few pages of Fortran code, the exact amount depending on the specific application. The ability to solve the Euler equations to arbitrarily high accuracy is especially beneficial in simulations of aeroacoustic effects in settings in which fully nonlinear behavior is expected - for example, at stagnation points of fan blades, where linearizing assumptions break down. At these locations, it is necessary to solve the full nonlinear Euler equations, and inasmuch as the acoustical energy is of the order of 4 to 5 orders of magnitude below that of the mean flow, it is necessary to achieve an overall fractional error of less than 10-6 in order to faithfully simulate entropy, vortical, and acoustical waves.

Application of Artificial Intelligence For Euler Solutions Clustering

NASA Astrophysics Data System (ADS)

Mikhailov, V.; Galdeano, A.; Diament, M.; Gvishiani, A.; Agayan, S.; Bogoutdinov, Sh.; Graeva, E.; Sailhac, P.

Results of Euler deconvolution strongly depend on the selection of viable solutions. Synthetic calculations using multiple causative sources show that Euler solutions clus- ter in the vicinity of causative bodies even when they do not group densely about perimeter of the bodies. We have developed a clustering technique to serve as a tool for selecting appropriate solutions. The method RODIN, employed in this study, is based on artificial intelligence and was originally designed for problems of classification of large data sets. It is based on a geometrical approach to study object concentration in a finite metric space of any dimension. The method uses a formal definition of cluster and includes free parameters that facilitate the search for clusters of given proper- ties. Test on synthetic and real data showed that the clustering technique successfully outlines causative bodies more accurate than other methods of discriminating Euler solutions. In complicated field cases such as the magnetic field in the Gulf of Saint Malo region (Brittany, France), the method provides geologically insightful solutions. Other advantages of the clustering method application are: - Clusters provide solutions associated with particular bodies or parts of bodies permitting the analysis of different clusters of Euler solutions separately. This may allow computation of average param- eters for individual causative bodies. - Those measurements of the anomalous field that yield clusters also form dense clusters themselves. The application of cluster- ing technique thus outlines areas where the influence of different causative sources is more prominent. This allows one to focus on areas for reinterpretation, using different window sizes, structural indices and so on.

Summing up the Euler [phi] Function

ERIC Educational Resources Information Center

Loomis, Paul; Plytage, Michael; Polhill, John

2008-01-01

The Euler [phi] function counts the number of positive integers less than and relatively prime to a positive integer n. Here we look at perfect totient numbers, number for which [phi](n) + [phi]([phi](n)) + [phi]([phi]([phi](n))) + ... + 1 = n.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1993-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1992-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Unstructured Euler flow solutions using hexahedral cell refinement

NASA Technical Reports Server (NTRS)

Melton, John E.; Cappuccio, Gelsomina; Thomas, Scott D.

1991-01-01

An attempt is made to extend grid refinement into three dimensions by using unstructured hexahedral grids. The flow solver is developed using the TIGER (topologically Independent Grid, Euler Refinement) as the starting point. The program uses an unstructured hexahedral mesh and a modified version of the Jameson four-stage, finite-volume Runge-Kutta algorithm for integration of the Euler equations. The unstructured mesh allows for local refinement appropriate for each freestream condition, thereby concentrating mesh cells in the regions of greatest interest. This increases the computational efficiency because the refinement is not required to extend throughout the entire flow field.

A Higher-Order Bending Theory for Laminated Composite and Sandwich Beams

NASA Technical Reports Server (NTRS)

Cook, Geoffrey M.

1997-01-01

A higher-order bending theory is derived for laminated composite and sandwich beams. This is accomplished by assuming a special form for the axial and transverse displacement expansions. An independent expansion is also assumed for the transverse normal stress. Appropriate shear correction factors based on energy considerations are used to adjust the shear stiffness. A set of transverse normal correction factors is introduced, leading to significant improvements in the transverse normal strain and stress for laminated composite and sandwich beams. A closed-form solution to the cylindrical elasticity solutions for a wide range of beam aspect ratios and commonly used material systems. Accurate shear stresses for a wide range of laminates, including the challenging unsymmetric composite and sandwich laminates, are obtained using an original corrected integration scheme. For application of the theory to a wider range of problems, guidelines for finite element approximations are presented.

A size dependent dynamic model for piezoelectric nanogenerators: effects of geometry, structural and environmental parameters

NASA Astrophysics Data System (ADS)

Sadeghzadeh, Sadegh; Farshad Mir Saeed Ghazi, Seyyed

2018-03-01

Piezoelectric Nanogenerator (PENG) is one of the novel energy harvester systems that recently, has been a subject of interest for researchers. By the use of nanogenerators, it’s possible to harvest different forms of energy in the environment like mechanical vibrations and generate electricity. The structure of a PENG consists of vertical arrays of nanowires between two electrodes. In this paper, dynamic analysis of a PENG is studied numerically. The modified couple stress theory which includes one length scale material parameter is used to study the size-dependent behavior of PENGs. Then, by application of a complete form of linear hybrid piezoelectric—pyroelectric equations, and using the Euler-Bernoulli beam model, the equations of motion has been derived. Generalized Differential Quadrature (GDQ) method was employed to solve the equations of motion. The effect of damping ratio, temperature rise, excitation frequency and length scale parameter was studied. It was found that the PENG voltage maximizes at the resonant frequency of nanowire. The temperature rise has a significant effect on PENG’s efficiency. When temperature increases about 10 {{K}}, the maximum voltage increases about 26%. Increasing the damping ratio, the maximum voltage decreases gradually.

Wrinkling of flexoelectric nano-film/substrate systems

NASA Astrophysics Data System (ADS)

Su, Shengkai; Huang, Huaiwei; Liu, Yijie; Zhu, Zheng H.

2018-02-01

The study of wrinkling mechanisms essentially helps to establish stable and controllable performance in electronic products. To gain some basic understanding of the wrinkling process in flexoelectric dielectrics, this paper models the wrinkling of nano-film/substrate systems, typically seen in stretchable electronics, subjected to substrate prestrain and voltage loading on electrodes. Flexoelectricity is considered through the constitutive equations proposed by Shen and Hu, and Euler-Bernoulli beam theory is applied to formulate the expressions of wrinkling wavelength and amplitude through the Ritz method. The effects of flexoelectricity, surface parameters, prestrain, applied voltage, structural scale etc on wrinkling behaviors, including wrinkling deformation and the wrinkling critical condition, are discussed. Results reveal that the action of both flexoelectric and surface effects is significant over only a small scale range, with film thickness less than 10 nm. Alongside these issues, the fundamental difference between flexoelectric and piezoelectric effects on wrinkling behaviors is highlighted. Piezoelectricity may act as a promoter or suppressor of wrinkling initiation and amplitude, depending on the applied voltage, while flexoelectricity not only reduces the critical prestrain or voltage required for wrinkling, but also decreases the wrinkling wavelength and amplitude.

Tracking C. elegans and its neuromuscular activity using NemaFlex

NASA Astrophysics Data System (ADS)

van Bussel, Frank; Rahman, Mizanur; Hewitt, Jennifer; Blawzdziewicz, Jerzy; Driscoll, Monica; Szewczyk, Nathaniel; Vanapalli, Siva

Recently, a novel platform has been developed for studying the behavior and physical characteristics of the nematode C. elegans. This is NemaFlex, developed by the Vanapalli group at Texas Tech University to analyze movement and muscular strength of crawling C. elegans. NemaFlex is a microfluidic device consisting of an array of deformable PDMS pillars, with which the C. elegans interacts in the course of moving through the system. Deflection measurements then allow us to calculate the force exerted by the worm via Euler-Bernoulli beam theory. For the procedure to be fully automated a fairly sophisticated software analysis has to be developed in tandem with the physical device. In particular, the usefulness of the force calculations is highly dependent on the accuracy and volume of the deflection measurements, which would be prohibitively time-consuming if carried out by hand/eye. In order to correlate the force results with muscle activations the C. elegans itself has to be tracked simultaneously, and pillar deflections precisely associated with mechanical-contact on the worm's body. Here we will outline the data processing and analysis routines that have been implemented in order to automate the calculation of these forces and muscular activations.

Dynamic response of a poroelastic half-space to accelerating or decelerating trains

NASA Astrophysics Data System (ADS)

Cao, Zhigang; Boström, Anders

2013-05-01

The dynamic response of a fully saturated poroelastic half-space due to accelerating or decelerating trains is investigated by a semi-analytical method. The ground is modeled as a saturated poroelastic half-space and Biot's theory is applied to characterize the soil medium, taking the coupling effects between the soil skeleton and the pore fluid into account. A detailed track system is considered incorporating rails, sleepers and embankment, which are modeled as Euler-Bernoulli beams, an anisotropic Kirchhoff plate, and an elastic layer, respectively. The acceleration or deceleration of the train is simulated by properly choosing the time history of the train speed using Fourier transforms combined with Fresnel integrals in the transformed domain. The time domain results are obtained by the fast Fourier transform (FFT). It is found that the deceleration of moving trains can cause a significant increase to the ground vibrations as well as the excess pore water pressure responses at the train speed 200 km/h. Furthermore, the single-phase elastic soil model would underestimate the vertical displacement responses caused by both the accelerating and decelerating trains at the speed 200 km/h.

Effects of magnetic-fluid flow on structural instability of a carbon nanotube conveying nanoflow under a longitudinal magnetic field

NASA Astrophysics Data System (ADS)

Sadeghi-Goughari, Moslem; Jeon, Soo; Kwon, Hyock-Ju

2017-09-01

In drug delivery systems, carbon nanotubes (CNTs) can be used to deliver anticancer drugs into target site to kill metastatic cancer cells under the magnetic field guidance. Deep understanding of dynamic behavior of CNTs in drug delivery systems may enable more efficient use of the drugs while reducing systemic side effects. In this paper, we study the effect of magnetic-fluid flow on the structural instability of a CNT conveying nanoflow under a longitudinal magnetic field. The Navier-Stokes equation of magnetic-fluid flow is coupled with Euler-Bernoulli beam theory for modeling fluid structure interaction (FSI). Size effects of the magnetic fluid and the CNT are addressed through small-scale parameters including the Knudsen number (Kn) and the nonlocal parameter. Results show the positive role of magnetic properties of fluid flow on the structural stability of CNT. Specifically, magnetic force applied to the fluid flow has an effect of decreasing the structural stiffness of system while increasing the critical flow velocity. Furthermore, we discover that the nanoscale effects of CNT and fluid flow tend to amplify the influence of magnetic field on the vibrational behavior of the system.

Geometrical influence of a deposited particle on the performance of bridged carbon nanotube-based mass detectors

NASA Astrophysics Data System (ADS)

Ali-Akbari, H. R.; Ceballes, S.; Abdelkefi, A.

2017-10-01

A nonlocal continuum-based model is derived to simulate the dynamic behavior of bridged carbon nanotube-based nano-scale mass detectors. The carbon nanotube (CNT) is modeled as an elastic Euler-Bernoulli beam considering von-Kármán type geometric nonlinearity. In order to achieve better accuracy in characterization of the CNTs, the geometrical properties of an attached nano-scale particle are introduced into the model by its moment of inertia with respect to the central axis of the beam. The inter-atomic long-range interactions within the structure of the CNT are incorporated into the model using Eringen's nonlocal elastic field theory. In this model, the mass can be deposited along an arbitrary length of the CNT. After deriving the full nonlinear equations of motion, the natural frequencies and corresponding mode shapes are extracted based on a linear eigenvalue problem analysis. The results show that the geometry of the attached particle has a significant impact on the dynamic behavior of the CNT-based mechanical resonator, especially, for those with small aspect ratios. The developed model and analysis are beneficial for nano-scale mass identification when a CNT-based mechanical resonator is utilized as a small-scale bio-mass sensor and the deposited particles are those, such as proteins, enzymes, cancer cells, DNA and other nano-scale biological objects with different and complex shapes.

Nonlocal theory of beam-driven electron Bernstein waves

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

Jain, V.K.; Tripathi, V.K.

A nonlocal theory of electron Bernstein waves driven unstable by an axial beam (V = V/sub b/z-italic-circumflex) of finite width has been developed. Assuming a parabolic density profile for the background plasma, an equation describing the mode structure of the wave is obtained in the slab geometry. The eigenfunctions are found to be Hermite polynomials. Expressions for the growth rates of the instabilities caused by Cerenkov and slow cyclotron interactions are derived. The results of the theory are applied to explain some of the experimental observations of Jain and Christiansen (Phys. Lett. A 82, 127 (1981)).

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

NASA Technical Reports Server (NTRS)

Edwards, S.; Reuther, J.; Chattot, J. J.

1997-01-01

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

Distributed flexibility in inertial swimmers

NASA Astrophysics Data System (ADS)

Floryan, Daniel; Rowley, Clarence W.; Smits, Alexander J.

2017-11-01

To achieve fast and efficient swimming, the flexibility of the propulsive surfaces is an important feature. To better understand the effects of distributed flexibility (either through inhomogeneous material properties, varying geometry, or both) we consider the coupled solid and fluid mechanics of the problem. Here, we develop a simplified model of a flexible swimmer, using Euler-Bernoulli theory to describe the solid, Theodorsen's theory to describe the fluid, and a Blasius boundary layer to incorporate viscous effects. Our primary aims are to understand how distributed flexibility affects the thrust production and efficiency of a swimmer with imposed motion at its leading edge. In particular, we examine the modal shapes of the swimmer to gain physical insight into the observed trends. Supported under ONR MURI Grant N00014-14-1-0533, Program Manager Robert Brizzolara.

Solution of steady and unsteady transonic-vortex flows using Euler and full-potential equations

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Chuang, Andrew H.; Hu, Hong

1989-01-01

Two methods are presented for inviscid transonic flows: unsteady Euler equations in a rotating frame of reference for transonic-vortex flows and integral solution of full-potential equation with and without embedded Euler domains for transonic airfoil flows. The computational results covered: steady and unsteady conical vortex flows; 3-D steady transonic vortex flow; and transonic airfoil flows. The results are in good agreement with other computational results and experimental data. The rotating frame of reference solution is potentially efficient as compared with the space fixed reference formulation with dynamic gridding. The integral equation solution with embedded Euler domain is computationally efficient and as accurate as the Euler equations.

Management of colon stents based on Bernoulli's principle.

PubMed

Uno, Yoshiharu

2017-03-01

The colonic self-expanding metal stent (SEMS) has been widely used for "bridge to surgery" and palliative therapy. However, if the spread of SEMS is insufficient, not only can a decompression effect not be obtained but also perforation and obstructive colitis can occur. The mechanism of occurrence of obstructive colitis and perforation was investigated by flow dynamics. Bernoulli's principle was applied, assuming that the cause of inflammation and perforation represented the pressure difference in the proximal lumen and stent. The variables considered were proximal lumen diameter, stent lumen diameter, flow rate into the proximal lumen, and fluid density. To model the right colon, the proximal lumen diameter was set at 50 mm. To model the left-side colon, the proximal lumen diameter was set at 30 mm. For both the right colon model and the left-side colon model, the difference in pressure between the proximal lumen and the stent was less than 20 mmHg, when the diameter of the stent lumen was 14 mm or more. Both the right colon model and the left-side colon model were 30 mmHg or more at 200 mL s -1 when the stent lumen was 10 mm or less. Even with an inflow rate of 90-110 mL s -1 , the pressure was 140 mmHg when the stent lumen diameter was 5 mm. In theory, in order to maintain the effectiveness of SEMS, it is necessary to keep the diameter of the stent lumen at 14 mm or more.

Hilbert's sixth problem and the failure of the Boltzmann to Euler limit

NASA Astrophysics Data System (ADS)

Slemrod, Marshall

2018-04-01

This paper addresses the main issue of Hilbert's sixth problem, namely the rigorous passage of solutions to the mesoscopic Boltzmann equation to macroscopic solutions of the Euler equations of compressible gas dynamics. The results of the paper are that (i) in general Hilbert's program will fail because of the appearance of van der Waals-Korteweg capillarity terms in a macroscopic description of motion of a gas, and (ii) the van der Waals-Korteweg theory itself might satisfy Hilbert's quest for a map from the `atomistic view' to the laws of motion of continua. This article is part of the theme issue `Hilbert's sixth problem'.

Euler equation computations for the flow over a hovering helicopter rotor

NASA Technical Reports Server (NTRS)

Roberts, Thomas Wesley

1988-01-01

A numerical solution technique is developed for computing the flow field around an isolated helicopter rotor in hover. The flow is governed by the compressible Euler equations which are integrated using a finite volume approach. The Euler equations are coupled to a free wake model of the rotary wing vortical wake. This wake model is incorporated into the finite volume solver using a prescribed flow, or perturbation, technique which eliminates the numerical diffusion of vorticity due to the artificial viscosity of the scheme. The work is divided into three major parts: (1) comparisons of Euler solutions to experimental data for the flow around isolated wings show good agreement with the surface pressures, but poor agreement with the vortical wake structure; (2) the perturbation method is developed and used to compute the interaction of a streamwise vortex with a semispan wing. The rapid diffusion of the vortex when only the basic Euler solver is used is illustrated, and excellent agreement with experimental section lift coefficients is demonstrated when using the perturbation approach; and (3) the free wake solution technique is described and the coupling of the wake to the Euler solver for an isolated rotor is presented. Comparisons with experimental blade load data for several cases show good agreement, with discrepancies largely attributable to the neglect of viscous effects. The computed wake geometries agree less well with experiment, the primary difference being that too rapid a wake contraction is predicted for all the cases.

Topographical optimization of structures for use in musical instruments and other applications

NASA Astrophysics Data System (ADS)

Kirkland, William Brandon

Mallet percussion instruments such as the xylophone, marimba, and vibraphone have been produced and tuned since their inception by arduously grinding the keys to achieve harmonic ratios between their 1st, 2 nd, and 3rd transverse modes. In consideration of this, it would be preferable to have defined mathematical models such that the keys of these instruments can be produced quickly and reliably. Additionally, physical modeling of these keys or beams provides a useful application of non-uniform beam vibrations as studied by Euler-Bernoulli and Timoshenko beam theories. This thesis work presents a literature review of previous studies regarding mallet percussion instrument design and optimization of non-uniform keys. The progression of previous research from strictly mathematical approaches to finite element methods is shown, ultimately arriving at the most current optimization techniques used by other authors. However, previous research varies slightly in the relative degree of accuracy to which a non-uniform beam can be modeled. Typically, accuracies are shown in literature as 1% to 2% error. While this seems attractive, musical tolerances require 0.25% error and beams are otherwise unsuitable. This research seeks to build on and add to the previous field research by optimizing beam topology and machining keys within tolerances that no further tuning is required. The optimization methods relied on finite element analysis and used harmonic modal frequencies as constraints rather than arguments of an error function to be optimized. Instead, the beam mass was minimized while the modal frequency constraints were required to be satisfied within 0.25% tolerance. The final optimized and machined keys of an A4 vibraphone were shown to be accurate within the required musical tolerances, with strong resonance at the designed frequencies. The findings solidify a systematic method for designing musical structures for accuracy and repeatability upon manufacture.

Origins of astronautics in Switzerland

NASA Technical Reports Server (NTRS)

Wadlis, A.

1977-01-01

Swiss contributions to astronautics are recounted. Scientists mentioned include: Bernoulli and Euler for their early theoretical contributions; the balloonist, Auguste Piccard; J. Ackeret, for his contributions to the study of aerodynamics; the rocket propulsion pioneer, Josef Stemmer; and the Swiss space scientists, Eugster, Stettbacker, Zwicky, and Schurch.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-02-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Analytical and numerical analysis of imaging mechanism of dynamic scanning electron microscopy.

PubMed

Schröter, M-A; Holschneider, M; Sturm, H

2012-11-02

The direct observation of small oscillating structures with the help of a scanning electron beam is a new approach to study the vibrational dynamics of cantilevers and microelectromechanical systems. In the scanning electron microscope, the conventional signal of secondary electrons (SE, dc part) is separated from the signal response of the SE detector, which is correlated to the respective excitation frequency for vibration by means of a lock-in amplifier. The dynamic response is separated either into images of amplitude and phase shift or into real and imaginary parts. Spatial resolution is limited to the diameter of the electron beam. The sensitivity limit to vibrational motion is estimated to be sub-nanometer for high integration times. Due to complex imaging mechanisms, a theoretical model was developed for the interpretation of the obtained measurements, relating cantilever shapes to interaction processes consisting of incident electron beam, electron-lever interaction, emitted electrons and detector response. Conclusions drawn from this new model are compared with numerical results based on the Euler-Bernoulli equation.

Nonlinear dynamic analysis of cantilevered piezoelectric energy harvesters under simultaneous parametric and external excitations

NASA Astrophysics Data System (ADS)

Fang, Fei; Xia, Guanghui; Wang, Jianguo

2018-06-01

The nonlinear dynamics of cantilevered piezoelectric beams is investigated under simultaneous parametric and external excitations. The beam is composed of a substrate and two piezoelectric layers and assumed as an Euler-Bernoulli model with inextensible deformation. A nonlinear distributed parameter model of cantilevered piezoelectric energy harvesters is proposed using the generalized Hamilton's principle. The proposed model includes geometric and inertia nonlinearity, but neglects the material nonlinearity. Using the Galerkin decomposition method and harmonic balance method, analytical expressions of the frequency-response curves are presented when the first bending mode of the beam plays a dominant role. Using these expressions, we investigate the effects of the damping, load resistance, electromechanical coupling, and excitation amplitude on the frequency-response curves. We also study the difference between the nonlinear lumped-parameter and distributed-parameter model for predicting the performance of the energy harvesting system. Only in the case of parametric excitation, we demonstrate that the energy harvesting system has an initiation excitation threshold below which no energy can be harvested. We also illustrate that the damping and load resistance affect the initiation excitation threshold.

Stress analysis of rotating propellers subject to forced excitations

NASA Astrophysics Data System (ADS)

Akgun, Ulas

Turbine blades experience vibrations due to the flow disturbances. These vibrations are the leading cause for fatigue failure in turbine blades. This thesis presents the finite element analysis methods to estimate the maximum vibrational stresses of rotating structures under forced excitation. The presentation included starts with the derived equations of motion for vibration of rotating beams using energy methods under the Euler Bernoulli beam assumptions. The nonlinear large displacement formulation captures the centrifugal stiffening and gyroscopic effects. The weak form of the equations and their finite element discretization are shown. The methods implemented were used for normal modes analyses and forced vibration analyses of rotating beam structures. The prediction of peak stresses under simultaneous multi-mode excitation show that the maximum vibrational stresses estimated using the linear superposition of the stresses can greatly overestimate the stresses if the phase information due to damping (physical and gyroscopic effects) are neglected. The last section of this thesis also presents the results of a practical study that involves finite element analysis and redesign of a composite propeller.

Splitting methods for low Mach number Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Abarbanel, Saul; Dutt, Pravir; Gottlieb, David

1987-01-01

Examined are some splitting techniques for low Mach number Euler flows. Shortcomings of some of the proposed methods are pointed out and an explanation for their inadequacy suggested. A symmetric splitting for both the Euler and Navier-Stokes equations is then presented which removes the stiffness of these equations when the Mach number is small. The splitting is shown to be stable.

Track-before-detect labeled multi-bernoulli particle filter with label switching

NASA Astrophysics Data System (ADS)

Garcia-Fernandez, Angel F.

2016-10-01

This paper presents a multitarget tracking particle filter (PF) for general track-before-detect measurement models. The PF is presented in the random finite set framework and uses a labelled multi-Bernoulli approximation. We also present a label switching improvement algorithm based on Markov chain Monte Carlo that is expected to increase filter performance if targets get in close proximity for a sufficiently long time. The PF is tested in two challenging numerical examples.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips.

PubMed

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-03-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber.

Euler force actuation mechanism for siphon valving in compact disk-like microfluidic chips

PubMed Central

Deng, Yongbo; Fan, Jianhua; Zhou, Song; Zhou, Teng; Wu, Junfeng; Li, Yin; Liu, Zhenyu; Xuan, Ming; Wu, Yihui

2014-01-01

Based on the Euler force induced by the acceleration of compact disk (CD)-like microfluidic chip, this paper presents a novel actuation mechanism for siphon valving. At the preliminary stage of acceleration, the Euler force in the tangential direction of CD-like chip takes the primary place compared with the centrifugal force to function as the actuation of the flow, which fills the siphon and actuates the siphon valving. The Euler force actuation mechanism is demonstrated by the numerical solution of the phase-field based mathematical model for the flow in siphon valve. In addition, experimental validation is implemented in the polymethylmethacrylate-based CD-like microfluidic chip manufactured using CO2 laser engraving technique. To prove the application of the proposed Euler force actuation mechanism, whole blood separation and plasma extraction has been conducted using the Euler force actuated siphon valving. The newly introduced actuation mechanism overcomes the dependence on hydrophilic capillary filling of siphon by avoiding external manipulation or surface treatments of polymeric material. The sacrifice for highly integrated processing in pneumatic pumping technique is also prevented by excluding the volume-occupied compressed air chamber. PMID:24753736

Optimal design of a beam-based dynamic vibration absorber using fixed-points theory

NASA Astrophysics Data System (ADS)

Hua, Yingyu; Wong, Waion; Cheng, Li

2018-05-01

The addition of a dynamic vibration absorber (DVA) to a vibrating structure could provide an economic solution for vibration suppressions if the absorber is properly designed and located onto the structure. A common design of the DVA is a sprung mass because of its simple structure and low cost. However, the vibration suppression performance of this kind of DVA is limited by the ratio between the absorber mass and the mass of the primary structure. In this paper, a beam-based DVA (beam DVA) is proposed and optimized for minimizing the resonant vibration of a general structure. The vibration suppression performance of the proposed beam DVA depends on the mass ratio, the flexural rigidity and length of the beam. In comparison with the traditional sprung mass DVA, the proposed beam DVA shows more flexibility in vibration control design because it has more design parameters. With proper design, the beam DVA's vibration suppression capability can outperform that of the traditional DVA under the same mass constraint. The general approach is illustrated using a benchmark cantilever beam as an example. The receptance theory is introduced to model the compound system consisting of the host beam and the attached beam-based DVA. The model is validated through comparisons with the results from Abaqus as well as the Transfer Matrix method (TMM) method. Fixed-points theory is then employed to derive the analytical expressions for the optimum tuning ratio and damping ratio of the proposed beam absorber. A design guideline is then presented to choose the parameters of the beam absorber. Comparisons are finally presented between the beam absorber and the traditional DVA in terms of the vibration suppression effect. It is shown that the proposed beam absorber can outperform the traditional DVA by following this proposed guideline.

High resolution solutions of the Euler equations for vortex flows

NASA Technical Reports Server (NTRS)

Murman, E. M.; Powell, K. G.; Rizzi, A.

1985-01-01

Solutions of the Euler equations are presented for M = 1.5 flow past a 70-degree-swept delta wing. At an angle of attack of 10 degrees, strong leading-edge vortices are produced. Two computational approaches are taken, based upon fully three-dimensional and conical flow theory. Both methods utilize a finite-volume discretization solved by a pseudounsteady multistage scheme. Results from the two approaches are in good agreement. Computations have been done on a 16-million-word CYBER 205 using 196 x 56 x 96 and 128 x 128 cells for the two methods. A sizable data base is generated, and some of the practical aspects of manipulating it are mentioned. The results reveal many interesting physical features of the compressible vortical flow field and also suggest new areas needing research.

Unsteady transonic viscous-inviscid interaction using Euler and boundary-layer equations

NASA Technical Reports Server (NTRS)

Pirzadeh, Shahyar; Whitfield, Dave

1989-01-01

The Euler code is used extensively for computation of transonic unsteady aerodynamics. The boundary layer code solves the 3-D, compressible, unsteady, mean flow kinetic energy integral boundary layer equations in the direct mode. Inviscid-viscous coupling is handled using porosity boundary conditions. Some of the advantages and disadvantages of using the Euler and boundary layer equations for investigating unsteady viscous-inviscid interaction is examined.

Nanoscale piezoelectric vibration energy harvester design

NASA Astrophysics Data System (ADS)

Foruzande, Hamid Reza; Hajnayeb, Ali; Yaghootian, Amin

2017-09-01

Development of new nanoscale devices has increased the demand for new types of small-scale energy resources such as ambient vibrations energy harvesters. Among the vibration energy harvesters, piezoelectric energy harvesters (PEHs) can be easily miniaturized and fabricated in micro and nano scales. This change in the dimensions of a PEH leads to a change in its governing equations of motion, and consequently, the predicted harvested energy comparing to a macroscale PEH. In this research, effects of small scale dimensions on the nonlinear vibration and harvested voltage of a nanoscale PEH is studied. The PEH is modeled as a cantilever piezoelectric bimorph nanobeam with a tip mass, using the Euler-Bernoulli beam theory in conjunction with Hamilton's principle. A harmonic base excitation is applied as a model of the ambient vibrations. The nonlocal elasticity theory is used to consider the size effects in the developed model. The derived equations of motion are discretized using the assumed-modes method and solved using the method of multiple scales. Sensitivity analysis for the effect of different parameters of the system in addition to size effects is conducted. The results show the significance of nonlocal elasticity theory in the prediction of system dynamic nonlinear behavior. It is also observed that neglecting the size effects results in lower estimates of the PEH vibration amplitudes. The results pave the way for designing new nanoscale sensors in addition to PEHs.

Artificial ion beam instabilities. I - Linear theory. II - Simulations

NASA Astrophysics Data System (ADS)

Scales, W. A.; Kintner, P. M.

1990-07-01

Some of the important plasma instabilities that result when an artificial ion beam is injected into the ionospheric F region are studied using linear Vlasov theory. The variation in wave spectra at the receiver as the receiver and plasma gun separate perpendicularly to the magnetic field is consistent with a beam density decrease at or near the receiver. At separation distances that are large fractions of the beam gyrodiameter, usually narrow-band waves near the background lower hybrid and H+ gyroharmonic frequencies are measured. These observations are consistent with waves expected to be generated by beam densities on the order of or less than a few percent of the background density. At smaller separation distances, broadband waves are usually observed with frequencies from zero up to and above the lower hybrid frequency. Electrostatic particle simulation studies of the plasma instabilities indicate that the broadband fluidlike lower hybrid instability is the most important for background particle heating. Perpendicular H+ heating is more efficient than perpendicular O+ or parallel electron heating for the drift velocity regime most relevant to past experiments.

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Energy efficiency analysis of the manipulation process by the industrial objects with the use of Bernoulli gripping devices

NASA Astrophysics Data System (ADS)

Savkiv, Volodymyr; Mykhailyshyn, Roman; Duchon, Frantisek; Mikhalishin, Mykhailo

2017-11-01

The article deals with the topical issue of reducing energy consumption for transportation of industrial objects. The energy efficiency of the process of objects manipulation with the use of the orientation optimization method while gripping with the help of different methods has been studied. The analysis of the influence of the constituent parts of inertial forces, that affect the object of manipulation, on the necessary force characteristics and energy consumption of Bernoulli gripping device has been proposed. The economic efficiency of the use of the optimal orientation of Bernoulli gripping device while transporting the object of manipulation in comparison to the transportation without re-orientation has been proved.

The crack effect on instability in a machine tool spindle with gas bearings

NASA Astrophysics Data System (ADS)

Huang, Bo-Wun

2005-09-01

Gas-bearing spindles are required for increased spindle speed in precise machining. Due to manufacturing flaws or cyclic loading, cracks frequently appear in a rotating spindle systems. Cracks markedly affect the dynamic characteristics of rotating machinery. Hence, in this study, high-speed spindles with gas bearings and the crack effect on the instability dynamics are considered. Most investigations on dynamic characteristics of the spindle system were confined to ball-bearing-type spindles. This work examines the dynamic instability in a cracked rotating spindle system with gas bearings. A round Euler-Bernoulli beam is used to approximate the spindle. The Hamilton principle is applied to derive the equation of motion for the spindle system. The effects of crack depth, rotation speed and provided air pressure on the dynamic instability of a rotating spindle system are studied

Pseudorandom number generation using chaotic true orbits of the Bernoulli map

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

Saito, Asaki, E-mail: saito@fun.ac.jp; Yamaguchi, Akihiro

We devise a pseudorandom number generator that exactly computes chaotic true orbits of the Bernoulli map on quadratic algebraic integers. Moreover, we describe a way to select the initial points (seeds) for generating multiple pseudorandom binary sequences. This selection method distributes the initial points almost uniformly (equidistantly) in the unit interval, and latter parts of the generated sequences are guaranteed not to coincide. We also demonstrate through statistical testing that the generated sequences possess good randomness properties.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

PubMed Central

Brassey, Charlotte A.; Margetts, Lee; Kitchener, Andrew C.; Withers, Philip J.; Manning, Phillip L.; Sellers, William I.

2013-01-01

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σmin) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r2 = 0.56). Under bending, FEA values of maximum principal stress (σmax) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r2 = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τtorsion were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations. PMID:23173199

Fabrication of a self-sensing electroactive polymer bimorph actuator based on polyvinylidene fluoride and its electrostrictive terpolymer

NASA Astrophysics Data System (ADS)

Engel, Leeya; Van Volkinburg, Kyle R.; Ben-David, Moti; Washington, Gregory N.; Krylov, Slava; Shacham-Diamand, Yosi

2016-04-01

In this paper, we report on the fabrication of a self-sensing electroactive polymer cantilevered bimorph beam actuator and its frequency response. Tip deflections of the beam, induced by applying an AC signal across ferroelectric relaxor polyvinylidene fluoride-trifluoroethylene chlorotrifluoroethylene (P(VDF-TrFE-CTFE)), reached a magnitude of 350μm under a field of ~55MV/m and were recorded externally using a laser Doppler vibrometer (LDV). Deflections were determined simultaneously by applying a sensing model to the voltage measured across the bimorph's integrated layer of piezoelectric polymer polyvinylidene fluoride (PVDF). The sensing model treats the structure as a simple Euler- Bernoulli cantilevered beam with two distributed active elements represented through the use of generalized functions and offers a method through which real time tip deflection can be measured without the need for external visualization. When not being used as a sensing element, the PVDF layer can provide an additional means for actuation of the beam via the converse piezoelectric effect, resulting in bidirectional control of the beam's deflections. Integration of flexible sensing elements together with modeling of the electroactive polymer beam can benefit the developing field of polymer microactuators which have applications in soft robotics as "smart" prosthetics/implants, haptic displays, tools for less invasive surgery, and sensing.

Textbook Multigrid Efficiency for the Steady Euler Equations

NASA Technical Reports Server (NTRS)

Roberts, Thomas W.; Sidilkover, David; Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Symmetry limit theory for cantilever beam-columns subjected to cyclic reversed bending

NASA Astrophysics Data System (ADS)

Uetani, K.; Nakamura, Tsuneyoshi

THE BEHAVIOR of a linear strain-hardening cantilever beam-column subjected to completely reversed plastic bending of a new idealized program under constant axial compression consists of three stages: a sequence of symmetric steady states, a subsequent sequence of asymmetric steady states and a divergent behavior involving unbounded growth of an anti-symmetric deflection mode. A new concept "symmetry limit" is introduced here as the smallest critical value of the tip-deflection amplitude at which transition from a symmetric steady state to an asymmetric steady state can occur in the response of a beam-column. A new theory is presented for predicting the symmetry limits. Although this transition phenomenon is phenomenologically and conceptually different from the branching phenomenon on an equilibrium path, it is shown that a symmetry limit may theoretically be regarded as a branching point on a "steady-state path" defined anew. The symmetry limit theory and the fundamental hypotheses are verified through numerical analysis of hysteretic responses of discretized beam-column models.

Graph Theory

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

Sanfilippo, Antonio P.

2005-12-27

Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for themore » representation of grammar formalisms.« less

Symmetry investigations on the incompressible stationary axisymmetric Euler equations with swirl

NASA Astrophysics Data System (ADS)

Frewer, M.; Oberlack, M.; Guenther, S.

2007-08-01

We discuss the incompressible stationary axisymmetric Euler equations with swirl, for which we derive via a scalar stream function an equivalent representation, the Bragg-Hawthorne equation [Bragg, S.L., Hawthorne, W.R., 1950. Some exact solutions of the flow through annular cascade actuator discs. J. Aero. Sci. 17, 243]. Despite this obvious equivalence, we will show that under a local Lie point symmetry analysis the Bragg-Hawthorne equation exposes itself as not being fully equivalent to the original Euler equations. This is reflected in the way that it possesses additional symmetries not being admitted by its counterpart. In other words, a symmetry of the Bragg-Hawthorne equation is in general not a symmetry of the Euler equations. Not the differential Euler equations but rather a set of integro-differential equations attains full equivalence to the Bragg-Hawthorne equation. For these intermediate Euler equations, it is interesting to note that local symmetries of the Bragg-Hawthorne equation transform to local as well as to nonlocal symmetries. This behaviour, on the one hand, is in accordance with Zawistowski's result [Zawistowski, Z.J., 2001. Symmetries of integro-differential equations. Rep. Math. Phys. 48, 269; Zawistowski, Z.J., 2004. General criterion of invariance for integro-differential equations. Rep. Math. Phys. 54, 341] that it is possible for integro-differential equations to admit local Lie point symmetries. On the other hand, with this transformation process we collect symmetries which cannot be obtained when carrying out a usual local Lie point symmetry analysis. Finally, the symmetry classification of the Bragg-Hawthorne equation is used to find analytical solutions for the phenomenon of vortex breakdown.

Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

NASA Astrophysics Data System (ADS)

Escalante, Alberto; Medel-Portugal, C.

2018-04-01

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

The Bayesian Learning Automaton — Empirical Evaluation with Two-Armed Bernoulli Bandit Problems

NASA Astrophysics Data System (ADS)

Granmo, Ole-Christoffer

The two-armed Bernoulli bandit (TABB) problem is a classical optimization problem where an agent sequentially pulls one of two arms attached to a gambling machine, with each pull resulting either in a reward or a penalty. The reward probabilities of each arm are unknown, and thus one must balance between exploiting existing knowledge about the arms, and obtaining new information.

Higher-order paraxial theory of the propagation of ring rippled laser beam in plasma: Relativistic ponderomotive regime

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

Purohit, Gunjan, E-mail: gunjan75@gmail.com; Rawat, Priyanka; Chauhan, Prashant

This article presents higher-order paraxial theory (non-paraxial theory) for the ring ripple formation on an intense Gaussian laser beam and its propagation in plasma, taking into account the relativistic-ponderomotive nonlinearity. The intensity dependent dielectric constant of the plasma has been determined for the main laser beam and ring ripple superimposed on the main laser beam. The dielectric constant of the plasma is modified due to the contribution of the electric field vector of ring ripple. Nonlinear differential equations have been formulated to examine the growth of ring ripple in plasma, self focusing of main laser beam, and ring rippled lasermore » beam in plasma using higher-order paraxial theory. These equations have been solved numerically for different laser intensities and plasma frequencies. The well established experimental laser and plasma parameters are used in numerical calculation. It is observed that the focusing of the laser beams (main and ring rippled) becomes fast in the nonparaxial region by expanding the eikonal and other relevant quantities up to the fourth power of r. The splitted profile of laser beam in the plasma is observed due to uneven focusing/defocusing of the axial and off-axial rays. The growths of ring ripple increase when the laser beam intensity increases. Furthermore, the intensity profile of ring rippled laser beam gets modified due to the contribution of growth rate.« less

Development of upwind schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1987-01-01

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

Translational Bounds for Factorial n and the Factorial Polynomial

ERIC Educational Resources Information Center

Mahmood, Munir; Edwards, Phillip

2009-01-01

During the period 1729-1826 Bernoulli, Euler, Goldbach and Legendre developed expressions for defining and evaluating "n"! and the related gamma function. Expressions related to "n"! and the gamma function are a common feature in computer science and engineering applications. In the modern computer age people live in now, two common tests to…

Neuromorphic log-domain silicon synapse circuits obey bernoulli dynamics: a unifying tutorial analysis.

PubMed

Papadimitriou, Konstantinos I; Liu, Shih-Chii; Indiveri, Giacomo; Drakakis, Emmanuel M

2014-01-01

The field of neuromorphic silicon synapse circuits is revisited and a parsimonious mathematical framework able to describe the dynamics of this class of log-domain circuits in the aggregate and in a systematic manner is proposed. Starting from the Bernoulli Cell Formalism (BCF), originally formulated for the modular synthesis and analysis of externally linear, time-invariant logarithmic filters, and by means of the identification of new types of Bernoulli Cell (BC) operators presented here, a generalized formalism (GBCF) is established. The expanded formalism covers two new possible and practical combinations of a MOS transistor (MOST) and a linear capacitor. The corresponding mathematical relations codifying each case are presented and discussed through the tutorial treatment of three well-known transistor-level examples of log-domain neuromorphic silicon synapses. The proposed mathematical tool unifies past analysis approaches of the same circuits under a common theoretical framework. The speed advantage of the proposed mathematical framework as an analysis tool is also demonstrated by a compelling comparative circuit analysis example of high order, where the GBCF and another well-known log-domain circuit analysis method are used for the determination of the input-output transfer function of the high (4(th)) order topology.

Comparing two Bayes methods based on the free energy functions in Bernoulli mixtures.

PubMed

Yamazaki, Keisuke; Kaji, Daisuke

2013-08-01

Hierarchical learning models are ubiquitously employed in information science and data engineering. The structure makes the posterior distribution complicated in the Bayes method. Then, the prediction including construction of the posterior is not tractable though advantages of the method are empirically well known. The variational Bayes method is widely used as an approximation method for application; it has the tractable posterior on the basis of the variational free energy function. The asymptotic behavior has been studied in many hierarchical models and a phase transition is observed. The exact form of the asymptotic variational Bayes energy is derived in Bernoulli mixture models and the phase diagram shows that there are three types of parameter learning. However, the approximation accuracy or interpretation of the transition point has not been clarified yet. The present paper precisely analyzes the Bayes free energy function of the Bernoulli mixtures. Comparing free energy functions in these two Bayes methods, we can determine the approximation accuracy and elucidate behavior of the parameter learning. Our results claim that the Bayes free energy has the same learning types while the transition points are different. Copyright © 2013 Elsevier Ltd. All rights reserved.

Open quantum random walk in terms of quantum Bernoulli noise

NASA Astrophysics Data System (ADS)

Wang, Caishi; Wang, Ce; Ren, Suling; Tang, Yuling

2018-03-01

In this paper, we introduce an open quantum random walk, which we call the QBN-based open walk, by means of quantum Bernoulli noise, and study its properties from a random walk point of view. We prove that, with the localized ground state as its initial state, the QBN-based open walk has the same limit probability distribution as the classical random walk. We also show that the probability distributions of the QBN-based open walk include those of the unitary quantum walk recently introduced by Wang and Ye (Quantum Inf Process 15:1897-1908, 2016) as a special case.

eulerAPE: Drawing Area-Proportional 3-Venn Diagrams Using Ellipses

PubMed Central

Micallef, Luana; Rodgers, Peter

2014-01-01

Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data. PMID:25032825

eulerAPE: drawing area-proportional 3-Venn diagrams using ellipses.

PubMed

Micallef, Luana; Rodgers, Peter

2014-01-01

Venn diagrams with three curves are used extensively in various medical and scientific disciplines to visualize relationships between data sets and facilitate data analysis. The area of the regions formed by the overlapping curves is often directly proportional to the cardinality of the depicted set relation or any other related quantitative data. Drawing these diagrams manually is difficult and current automatic drawing methods do not always produce appropriate diagrams. Most methods depict the data sets as circles, as they perceptually pop out as complete distinct objects due to their smoothness and regularity. However, circles cannot draw accurate diagrams for most 3-set data and so the generated diagrams often have misleading region areas. Other methods use polygons to draw accurate diagrams. However, polygons are non-smooth and non-symmetric, so the curves are not easily distinguishable and the diagrams are difficult to comprehend. Ellipses are more flexible than circles and are similarly smooth, but none of the current automatic drawing methods use ellipses. We present eulerAPE as the first method and software that uses ellipses for automatically drawing accurate area-proportional Venn diagrams for 3-set data. We describe the drawing method adopted by eulerAPE and we discuss our evaluation of the effectiveness of eulerAPE and ellipses for drawing random 3-set data. We compare eulerAPE and various other methods that are currently available and we discuss differences between their generated diagrams in terms of accuracy and ease of understanding for real world data.

Discretization vs. Rounding Error in Euler's Method

ERIC Educational Resources Information Center

Borges, Carlos F.

2011-01-01

Euler's method for solving initial value problems is an excellent vehicle for observing the relationship between discretization error and rounding error in numerical computation. Reductions in stepsize, in order to decrease discretization error, necessarily increase the number of steps and so introduce additional rounding error. The problem is…

Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations

NASA Technical Reports Server (NTRS)

Darmofal, David L.

1998-01-01

An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Significance of size dependent and material structure coupling on the characteristics and performance of nanocrystalline micro/nano gyroscopes

NASA Astrophysics Data System (ADS)

Larkin, K.; Ghommem, M.; Abdelkefi, A.

2018-05-01

Capacitive-based sensing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) gyroscopes have significant advantages over conventional gyroscopes, such as low power consumption, batch fabrication, and possible integration with electronic circuits. However, inadequacies in the modeling of these inertial sensors have presented issues of reliability and functionality of micro-/nano-scale gyroscopes. In this work, a micromechanical model is developed to represent the unique microstructure of nanocrystalline materials and simulate the response of micro-/nano-gyroscope comprising an electrostatically-actuated cantilever beam with a tip mass at the free end. Couple stress and surface elasticity theories are integrated into the classical Euler-Bernoulli beam model in order to derive a size-dependent model. This model is then used to investigate the influence of size-dependent effects on the static pull-in instability, the natural frequencies and the performance output of gyroscopes as the scale decreases from micro-to nano-scale. The simulation results show significant changes in the static pull-in voltage and the natural frequency as the scale of the system is decreased. However, the differential frequency between the two vibration modes of the gyroscope is observed to drastically decrease as the size of the gyroscope is reduced. As such, the frequency-based operation mode may not be an efficient strategy for nano-gyroscopes. The results show that a strong coupling between the surface elasticity and material structure takes place when smaller grain sizes and higher void percentages are considered.

CFD analysis of multiphase blood flow within aorta and its thoracic branches of patient with coarctation of aorta using multiphase Euler - Euler approach

NASA Astrophysics Data System (ADS)

Ostrowski, Z.; Melka, B.; Adamczyk, W.; Rojczyk, M.; Golda, A.; Nowak, A. J.

2016-09-01

In the research a numerical Computational Fluid Dynamics (CFD) model of the pulsatile blood flow was created and analyzed. A real geometry of aorta and its thoracic branches of 8-year old patient diagnosed with a congenital heart defect - coarctation of aorta was used. The inlet boundary condition were implemented as the User Define Function according to measured values of volumetric blood flow. The blood flow was treated as multiphase: plasma, set as the primary fluid phase, was dominant with volume fraction of 0.585 and morphological elements of blood were treated in Euler-Euler approach as dispersed phases (with 90% Red Blood Cells and White Blood Cells as remaining solid volume fraction).

Cavitation Modeling in Euler and Navier-Stokes Codes

NASA Technical Reports Server (NTRS)

Deshpande, Manish; Feng, Jinzhang; Merkle, Charles L.

1993-01-01

Many previous researchers have modeled sheet cavitation by means of a constant pressure solution in the cavity region coupled with a velocity potential formulation for the outer flow. The present paper discusses the issues involved in extending these cavitation models to Euler or Navier-Stokes codes. The approach taken is to start from a velocity potential model to ensure our results are compatible with those of previous researchers and available experimental data, and then to implement this model in both Euler and Navier-Stokes codes. The model is then augmented in the Navier-Stokes code by the inclusion of the energy equation which allows the effect of subcooling in the vicinity of the cavity interface to be modeled to take into account the experimentally observed reduction in cavity pressures that occurs in cryogenic fluids such as liquid hydrogen. Although our goal is to assess the practicality of implementing these cavitation models in existing three-dimensional, turbomachinery codes, the emphasis in the present paper will center on two-dimensional computations, most specifically isolated airfoils and cascades. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce consistent predictions. Comparisons with experimental results also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects in both cryogenic and non-cryogenic fluids. The impact on CPU time and the code modifications required suggests that these models are appropriate for incorporation in current generation turbomachinery codes.

Mechanical properties of additively manufactured octagonal honeycombs.

PubMed

Hedayati, R; Sadighi, M; Mohammadi-Aghdam, M; Zadpoor, A A

2016-12-01

Honeycomb structures have found numerous applications as structural and biomedical materials due to their favourable properties such as low weight, high stiffness, and porosity. Application of additive manufacturing and 3D printing techniques allows for manufacturing of honeycombs with arbitrary shape and wall thickness, opening the way for optimizing the mechanical and physical properties for specific applications. In this study, the mechanical properties of honeycomb structures with a new geometry, called octagonal honeycomb, were investigated using analytical, numerical, and experimental approaches. An additive manufacturing technique, namely fused deposition modelling, was used to fabricate the honeycomb from polylactic acid (PLA). The honeycombs structures were then mechanically tested under compression and the mechanical properties of the structures were determined. In addition, the Euler-Bernoulli and Timoshenko beam theories were used for deriving analytical relationships for elastic modulus, yield stress, Poisson's ratio, and buckling stress of this new design of honeycomb structures. Finite element models were also created to analyse the mechanical behaviour of the honeycombs computationally. The analytical solutions obtained using Timoshenko beam theory were close to computational results in terms of elastic modulus, Poisson's ratio and yield stress, especially for relative densities smaller than 25%. The analytical solutions based on the Timoshenko analytical solution and the computational results were in good agreement with experimental observations. Finally, the elastic properties of the proposed honeycomb structure were compared to those of other honeycomb structures such as square, triangular, hexagonal, mixed, diamond, and Kagome. The octagonal honeycomb showed yield stress and elastic modulus values very close to those of regular hexagonal honeycombs and lower than the other considered honeycombs. Copyright © 2016 Elsevier B.V. All rights

Bifurcation Analysis of an Electrostatically Actuated Nano-Beam Based on Modified Couple Stress Theory

NASA Astrophysics Data System (ADS)

Rezaei Kivi, Araz; Azizi, Saber; Norouzi, Peyman

2017-12-01

In this paper, the nonlinear size-dependent static and dynamic behavior of an electrostatically actuated nano-beam is investigated. A fully clamped nano-beam is considered for the modeling of the deformable electrode of the NEMS. The governing differential equation of the motion is derived using Hamiltonian principle based on couple stress theory; a non-classical theory for considering length scale effects. The nonlinear partial differential equation of the motion is discretized to a nonlinear Duffing type ODE's using Galerkin method. Static and dynamic pull-in instabilities obtained by both classical theory and MCST are compared. At the second stage of analysis, shooting technique is utilized to obtain the frequency response curve, and to capture the periodic solutions of the motion; the stability of the periodic solutions are gained by Floquet theory. The nonlinear dynamic behavior of the deformable electrode due to the AC harmonic accompanied with size dependency is investigated.

Women and Mathematics in the Time of Euler

ERIC Educational Resources Information Center

Mayfield, Betty

2013-01-01

We explore mathematics written both by and for women in eighteenth-century Europe, and some of the interesting personalities involved: Maria Agnesi, Emilie du Chatelet, Laura Bassi, Princess Charlotte Ludovica Luisa, John Colson, Francesco Algarotti, and Leonhard Euler himself.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Nonlinear vibration of double-walled boron nitride and carbon nanopeapods under multi-physical fields with consideration of surface stress effects

NASA Astrophysics Data System (ADS)

Ghorbanpour Arani, A.; Sabzeali, M.; BabaAkbar Zarei, H.

2017-12-01

In this study, the nonlinear thermo-electro vibrations of double-walled boron nitride nanopeapods (DWBNNPPs) and double-walled carbon nanopeapods (DWCNPPs) under magnetic field embedded in an elastic medium is investigated. DWBNNPPs are made of piezoelectric and smart materials therefore, electric field is effective on them; meanwhile, DWCNPPs are made of carbon thus, magnetic field can be useful to control them. The Pasternak model is used to simulate the effects of elastic medium which surrounds the system. Nanotubes are modeled with assumption of the Euler-Bernoulli beam (EBB) theory and the surface effects are considered to achieve accurate response of the system. Moreover, interaction between two layers is modeled by van der Waals (vdW) forces. The equations of motion are derived using the energy method and the Hamilton principle. Then the governing equations are solved by using Galerkin's method and incremental harmonic balance method (IHBM). The influences of various parameters such as the magnetic field, different types of DWCNPPs and DWBNNPPs, elastic medium, existence of fullerene and surface effect on the vibration behavior of the system are investigated. The results demonstrate that DWBNNPPs have more influence on the frequency of the system than DWCNPPs. In addition, the presence of fullerene in nanotubes has a negative impact on the frequency behavior of revisionthe system.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Vibrational analysis of vertical axis wind turbine blades

NASA Astrophysics Data System (ADS)

Kapucu, Onur

The goal of this research is to derive a vibration model for a vertical axis wind turbine blade. This model accommodates the affects of varying relative flow angle caused by rotating the blade in the flow field, uses a simple aerodynamic model that assumes constant wind speed and constant rotation rate, and neglects the disturbance of wind due to upstream blade or post. The blade is modeled as elastic Euler-Bernoulli beam under transverse bending and twist deflections. Kinetic and potential energy equations for a rotating blade under deflections are obtained, expressed in terms of assumed modal coordinates and then plugged into Lagrangian equations where the non-conservative forces are the lift and drag forces and moments. An aeroelastic model for lift and drag forces, approximated with third degree polynomials, on the blade are obtained assuming an airfoil under variable angle of attack and airflow magnitudes. A simplified quasi-static airfoil theory is used, in which the lift and drag coefficients are not dependent on the history of the changing angle of attack. Linear terms on the resulting equations of motion will be used to conduct a numerical analysis and simulation, where numeric specifications are modified from the Sandia-17m Darrieus wind turbine by Sandia Laboratories.

Divergence instability of pipes conveying fluid with uncertain flow velocity

NASA Astrophysics Data System (ADS)

Rahmati, Mehdi; Mirdamadi, Hamid Reza; Goli, Sareh

2018-02-01

This article deals with investigation of probabilistic stability of pipes conveying fluid with stochastic flow velocity in time domain. As a matter of fact, this study has focused on the randomness effects of flow velocity on stability of pipes conveying fluid while most of research efforts have only focused on the influences of deterministic parameters on the system stability. The Euler-Bernoulli beam and plug flow theory are employed to model pipe structure and internal flow, respectively. In addition, flow velocity is considered as a stationary random process with Gaussian distribution. Afterwards, the stochastic averaging method and Routh's stability criterion are used so as to investigate the stability conditions of system. Consequently, the effects of boundary conditions, viscoelastic damping, mass ratio, and elastic foundation on the stability regions are discussed. Results delineate that the critical mean flow velocity decreases by increasing power spectral density (PSD) of the random velocity. Moreover, by increasing PSD from zero, the type effects of boundary condition and presence of elastic foundation are diminished, while the influences of viscoelastic damping and mass ratio could increase. Finally, to have a more applicable study, regression analysis is utilized to develop design equations and facilitate further analyses for design purposes.

Remote monitoring of bi-axial loads on a lifting surface moving unsteadily in water

NASA Astrophysics Data System (ADS)

Johnson, P. B.; Drake, K. R.; Eames, I.; Wojcik, A.

2014-12-01

A system of measuring the bi-axial load on a lifting surface (blade) which is freely moving and operates submerged in water at the laboratory scale is described. A blade with a span of 500 mm, a chord of 60 mm and a thickness of 9 mm (15% of the chord) was employed and the lift/drag forces were measured using a bespoke strain-gauge based load cell located at the mid-span of the blade, measuring bending moments in two independent directions. The requirement to move freely dictated that the load cell was encapsulated within the blade, along with signal conditioning circuitry, power supply and a data logger with wireless transmission. Submerged operation in water resulted in very short transmission distances, meaning that data were recorded and subsequently transferred using an aerial placed close to the blade while it was stationary. Assumptions based on Euler-Bernoulli beam bending theory were used to infer the total load from measurements of the bending moment at the mid-span and example data from a freely moving aerofoil on a Darrieus-type tidal energy extraction device are presented. The novelty of this system lies in its combination of free movement, submerged operation and small scale.

A square wave is the most efficient and reliable waveform for resonant actuation of micro switches

NASA Astrophysics Data System (ADS)

Ben Sassi, S.; Khater, M. E.; Najar, F.; Abdel-Rahman, E. M.

2018-05-01

This paper investigates efficient actuation methods of shunt MEMS switches and other parallel-plate actuators. We start by formulating a multi-physics model of the micro switch, coupling the nonlinear Euler-Bernoulli beam theory with the nonlinear Reynolds equation to describe the structural and fluidic domains, respectively. The model takes into account fringing field effects as well as mid-plane stretching and squeeze film damping nonlinearities. Static analysis is undertaken using the differential quadrature method (DQM) to obtain the pull-in voltage, which is verified by means of the finite element model and validated experimentally. We develop a reduced order model employing the Galerkin method for the structural domain and DQM for the fluidic domain. The proposed waveforms are intended to be more suitable for integrated circuit standards. The dynamic response of the micro switch to harmonic, square and triangular waveforms are evaluated and compared experimentally and analytically. Low voltage actuation is obtained using dynamic pull-in with the proposed waveforms. In addition, global stability analysis carried out for the three signals shows advantages of employing the square signal as the actuation method in enhancing the performance of the micro switch in terms of actuation voltage, switching time, and sensitivity to initial conditions.

Nonlinear bending models for beams and plates

PubMed Central

Antipov, Y. A.

2014-01-01

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

A new stream function formulation for the Euler equations

NASA Technical Reports Server (NTRS)

Atkins, H. L.; Hassan, H. A.

1983-01-01

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Measure-valued solutions to the complete Euler system revisited

NASA Astrophysics Data System (ADS)

Březina, Jan; Feireisl, Eduard

2018-06-01

We consider the complete Euler system describing the time evolution of a general inviscid compressible fluid. We introduce a new concept of measure-valued solution based on the total energy balance and entropy inequality for the physical entropy without any renormalization. This class of so-called dissipative measure-valued solutions is large enough to include the vanishing dissipation limits of the Navier-Stokes-Fourier system. Our main result states that any sequence of weak solutions to the Navier-Stokes-Fourier system with vanishing viscosity and heat conductivity coefficients generates a dissipative measure-valued solution of the Euler system under some physically grounded constitutive relations. Finally, we discuss the same asymptotic limit for the bi-velocity fluid model introduced by H.Brenner.

Analysis of piezoelectric energy harvester under modulated and filtered white Gaussian noise

NASA Astrophysics Data System (ADS)

Quaranta, Giuseppe; Trentadue, Francesco; Maruccio, Claudio; Marano, Giuseppe C.

2018-05-01

This paper proposes a comprehensive method for the electromechanical probabilistic analysis of piezoelectric energy harvesters subjected to modulated and filtered white Gaussian noise (WGN) at the base. Specifically, the dynamic excitation is simulated by means of an amplitude-modulated WGN, which is filtered through the Clough-Penzien filter. The considered piezoelectric harvester is a cantilever bimorph modeled as Euler-Bernoulli beam with a concentrated mass at the free-end, and its global behavior is approximated by the fundamental vibration mode (which is tuned with the dominant frequency of the dynamic input). A resistive electrical load is considered in the circuit. Once the Lyapunov equation of the coupled electromechanical problem has been formulated, an original and efficient semi-analytical procedure is proposed to estimate mean and standard deviation of the electrical energy extracted from the piezoelectric layers.

Theory of type 3b solar radio bursts. [plasma interaction and electron beams

NASA Technical Reports Server (NTRS)

Smith, R. A.; Delanoee, J.

1975-01-01

During the initial space-time evolution of an electron beam injected into the corona, the strong beam-plasma interaction occurs at the head of the beam, leading to the amplification of a quasi-monochromatic large-amplitude plasma wave that stabilizes by trapping the beam particles. Oscillation of the trapped particles in the wave troughs amplifies sideband electrostatic waves. The sidebands and the main wave subsequently decay to observable transverse electromagnetic waves through the parametric decay instability. This process gives rise to the elementary striation bursts. Owing to velocity dispersion in the beam and the density gradient of the corona, the entire process may repeat at a finite number of discrete plasma levels, producing chains of elementary bursts. All the properties of the type IIIb bursts are accounted for in the context of the theory.

A new Euler scheme based on harmonic-polygon approach for solving first order ordinary differential equation

NASA Astrophysics Data System (ADS)

Yusop, Nurhafizah Moziyana Mohd; Hasan, Mohammad Khatim; Wook, Muslihah; Amran, Mohd Fahmi Mohamad; Ahmad, Siti Rohaidah

2017-10-01

There are many benefits to improve Euler scheme for solving the Ordinary Differential Equation Problems. Among the benefits are simple implementation and low-cost computational. However, the problem of accuracy in Euler scheme persuade scholar to use complex method. Therefore, the main purpose of this research are show the construction a new modified Euler scheme that improve accuracy of Polygon scheme in various step size. The implementing of new scheme are used Polygon scheme and Harmonic mean concept that called as Harmonic-Polygon scheme. This Harmonic-Polygon can provide new advantages that Euler scheme could offer by solving Ordinary Differential Equation problem. Four set of problems are solved via Harmonic-Polygon. Findings show that new scheme or Harmonic-Polygon scheme can produce much better accuracy result.

Normal-Gamma-Bernoulli Peak Detection for Analysis of Comprehensive Two-Dimensional Gas Chromatography Mass Spectrometry Data.

PubMed

Kim, Seongho; Jang, Hyejeong; Koo, Imhoi; Lee, Joohyoung; Zhang, Xiang

2017-01-01

Compared to other analytical platforms, comprehensive two-dimensional gas chromatography coupled with mass spectrometry (GC×GC-MS) has much increased separation power for analysis of complex samples and thus is increasingly used in metabolomics for biomarker discovery. However, accurate peak detection remains a bottleneck for wide applications of GC×GC-MS. Therefore, the normal-exponential-Bernoulli (NEB) model is generalized by gamma distribution and a new peak detection algorithm using the normal-gamma-Bernoulli (NGB) model is developed. Unlike the NEB model, the NGB model has no closed-form analytical solution, hampering its practical use in peak detection. To circumvent this difficulty, three numerical approaches, which are fast Fourier transform (FFT), the first-order and the second-order delta methods (D1 and D2), are introduced. The applications to simulated data and two real GC×GC-MS data sets show that the NGB-D1 method performs the best in terms of both computational expense and peak detection performance.

Neuromorphic log-domain silicon synapse circuits obey bernoulli dynamics: a unifying tutorial analysis

PubMed Central

Papadimitriou, Konstantinos I.; Liu, Shih-Chii; Indiveri, Giacomo; Drakakis, Emmanuel M.

2014-01-01

The field of neuromorphic silicon synapse circuits is revisited and a parsimonious mathematical framework able to describe the dynamics of this class of log-domain circuits in the aggregate and in a systematic manner is proposed. Starting from the Bernoulli Cell Formalism (BCF), originally formulated for the modular synthesis and analysis of externally linear, time-invariant logarithmic filters, and by means of the identification of new types of Bernoulli Cell (BC) operators presented here, a generalized formalism (GBCF) is established. The expanded formalism covers two new possible and practical combinations of a MOS transistor (MOST) and a linear capacitor. The corresponding mathematical relations codifying each case are presented and discussed through the tutorial treatment of three well-known transistor-level examples of log-domain neuromorphic silicon synapses. The proposed mathematical tool unifies past analysis approaches of the same circuits under a common theoretical framework. The speed advantage of the proposed mathematical framework as an analysis tool is also demonstrated by a compelling comparative circuit analysis example of high order, where the GBCF and another well-known log-domain circuit analysis method are used for the determination of the input-output transfer function of the high (4th) order topology. PMID:25653579

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.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations.

PubMed

Madanu, Sushma B; Barbel, Stanley I; Ward, Thomas

2016-06-01

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude of vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.

Stability of the Euler resting N-body relative equilibria

NASA Astrophysics Data System (ADS)

Scheeres, D. J.

2018-03-01

The stability of a system of N equal-sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously analyzed in the finite density 3 and 4 body problems. Specific questions for the general case are how rapidly the system must spin for the configuration to stabilize, how rapidly it can spin before the components separate from each other, and how these results change as a function of N. This paper shows that the Euler Resting configuration can only be stable for up to 5 bodies and that for 6 or more bodies the configuration can never be stable. This places an ideal limit of 5:1 on the aspect ratio of a rubble pile body's shape.

Euler Strut: A Mechanical Analogy for Dynamics in the Vicinity of a Critical Point

ERIC Educational Resources Information Center

Bobnar, Jaka; Susman, Katarina; Parsegian, V. Adrian; Rand, Peter R.; Cepic, Mojca; Podgornik, Rudolf

2011-01-01

An anchored elastic filament (Euler strut) under an external point load applied to its free end is a simple model for a second-order phase transition. In the static case, a load greater than the critical load causes a Euler buckling instability, leading to a change in the filament's shape. The analysis of filament dynamics with an external point…

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Application of the generalized Euler series transformation for calculation of vibration-rotation energy levels of diatomic molecules

NASA Astrophysics Data System (ADS)

Kruglova, T. V.

2004-01-01

The detailed spectroscope information about highly excited molecules and radicals such us as H+3, H2, HI, H2O, CH2 is needed for a number of applications in the field of laser physics, astrophysics and chemistry. Studies of highly excited molecular vibration-rotation states face several problems connected with slowly convergence or even divergences of perturbation expansions. The physical reason for a perturbation expansion divergence is the large amplitude motion and strong vibration-rotation coupling. In this case one needs to use the special method of series summation. There were a number of papers devoted to this problem: papers 1-10 in the reference list are only example of studies on this topic. The present report is aimed at the application of GET method (Generalized Euler Transformation) to the diatomic molecule. Energy levels of a diatomic molecule is usually represented as Dunham series on rotational J(J+1) and vibrational (V+1/2) quantum numbers (within the perturbation approach). However, perturbation theory is not applicable for highly excited vibration-rotation states because the perturbation expansion in this case becomes divergent. As a consequence one need to use special method for the series summation. The Generalized Euler Transformation (GET) is known to be efficient method for summing of slowly convergent series, it was already used for solving of several quantum problems Refs.13 and 14. In this report the results of Euler transformation of diatomic molecule Dunham series are presented. It is shown that Dunham power series can be represented of functional series that is equivalent to its partial summation. It is also shown that transformed series has the butter convergent properties, than the initial series.

Consistency relations for spinning matter in gravitational theories

NASA Technical Reports Server (NTRS)

Ray, John R.; Smalley, Larry L.

1986-01-01

The consistency equations for a charged spinning fluid in the Einstein-Cartan theory are examined. The hydrodynamic laws associated with the theory of Ray and Smalley (1982, 1983) and the electromagnetic extension of Amorim (1984, 1985) are studied. The derivation of the consistency equation from the Euler equations for an improved perfect-fluid energy-momentum tensor is described.

Dynamic modelling and experimental study of cantilever beam with clearance

NASA Astrophysics Data System (ADS)

Li, B.; Jin, W.; Han, L.; He, Z.

2012-05-01

Clearances occur in almost all mechanical systems, typically such as the clearance between slide plate of gun barrel and guide. Therefore, to study the clearances of mechanisms can be very important to increase the working performance and lifetime of mechanisms. In this paper, rigid dynamic modelling of cantilever with clearance was done according to the subject investigated. In the rigid dynamic modelling, clearance is equivalent to the spring-dashpot model, the impact of beam and boundary face was also taken into consideration. In ADAMS software, the dynamic simulation was carried out according to the model above. The software simulated the movement of cantilever with clearance under external excitation. Research found: When the clearance is larger, the force of impact will become larger. In order to study how the stiffness of the cantilever's supporting part influences natural frequency of the system, A Euler beam which is restricted by a draught spring and a torsion spring at its end was raised. Through numerical calculation, the relationship between natural frequency and stiffness was found. When the value of the stiffness is close to the limit value, the corresponding boundary condition is illustrated. An ADAMS experiment was carried out to check the theory and the simulation.

Novel Euler-LaCoste linkage as a very low frequency vertical vibration isolator.

PubMed

Hosain, M A; Sirr, A; Ju, L; Blair, D G

2012-08-01

LaCoste linkage vibration isolators have shown excellent performance for ultra-low frequency vertical vibration isolation. However, such isolators depend on the use of conventional pre-stressed coil springs, which suffer from creep. Here, we show that compressional Euler springs can be configured to create a stable tension unit for use in a LaCoste structure. In a proof of concept experiment, we demonstrate a vertical resonance frequency of 0.15 Hz in an Euler-LaCoste configuration with 200 mm height. The system enables the use of very low creep maraging steel as spring elements to eliminate the creep while minimising spring mass and reducing the effect of parasitic resonances. Larger scale systems with optimized Euler spring boundary conditions should achieve performance suitable for applications on third generation gravitational wave detectors such as the proposed Einstein telescope.

Numerical analysis of right-half plane zeros for a single-link manipulator. M.S. Thesis

NASA Technical Reports Server (NTRS)

Girvin, Douglas Lynn

1992-01-01

The purpose of this research is to further develop an understanding of how nonminimum phase zero location is affected by structural link design. As the demand for light-weight robots that can operate in a large workspace increases, the structural flexibility of the links become more of an issue in controls problems. When the objective is to accurately position the tip while the robot is actuated at the base, the system is nonminimum phase. One important characteristic of nonminimum phase systems is system zeros in the right half of the Laplace plane. The ability to pick the location of these nonminimum phase zeros would give the designer a new freedom similar to pole placement. The research targets a single-link manipulator operating in the horizontal plane and modeled as a Euler-Bernoulli beam with pinned-free end conditions. Using transfer matrix theory, one can consider link designs that have variable cross-sections along the length of the beam. A FORTRAN program was developed to determine the location of poles and zeros given the system model. The program was used to confirm previous research on nonminimum phase systems, and develop a relationship for designing linearly tapered links. The method allows the designer to choose the location of the first pole and zero and then defines the appropriate taper to match the desired locations. With the pole and zero location fixes, the designer can independently change the link's moment of inertia about its axis of rotation by adjusting the height of the beam. These results can be applied to inverse dynamic algorithms currently under development at Georgia Tech.

New method for blowup of the Euler-Poisson system

NASA Astrophysics Data System (ADS)

Kwong, Man Kam; Yuen, Manwai

2016-08-01

In this paper, we provide a new method for establishing the blowup of C2 solutions for the pressureless Euler-Poisson system with attractive forces for RN (N ≥ 2) with ρ(0, x0) > 0 and Ω 0 i j ( x 0 ) = /1 2 [" separators=" ∂ i u j ( 0 , x 0 ) - ∂ j u i ( 0 , x 0 ) ] = 0 at some point x0 ∈ RN. By applying the generalized Hubble transformation div u ( t , x 0 ( t ) ) = /N a ˙ ( t ) a ( t ) to a reduced Riccati differential inequality derived from the system, we simplify the inequality into the Emden equation a ̈ ( t ) = - /λ a ( t ) N - 1 , a ( 0 ) = 1 , a ˙ ( 0 ) = /div u ( 0 , x 0 ) N . Known results on its blowup set allow us to easily obtain the blowup conditions of the Euler-Poisson system.

Towards a wave theory of charged beam transport: A collection of thoughts

NASA Technical Reports Server (NTRS)

Dattoli, G.; Mari, C.; Torre, A.

1992-01-01

We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport.

Theory and simulations of current drive via injection of an electron beam in the ACT-1 device

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

Okuda, H.; Horton, R.; Ono, M.

1985-02-01

One- and two-dimensional particle simulations of beam-plasma interaction have been carried out in order to understand current drive experiments that use an electron beam injected into the ACT-1 device. Typically, the beam velocity along the magnetic field is V = 10/sup 9/ cm/sec while the thermal velocity of the background electrons is v/sub t/ = 10/sup 8//cm. The ratio of the beam density to the background density is about 10% so that a strong beam-plasma instability develops causing rapid diffusion of beam particles. For both one- and two- dimensional simulations, it is found that a significant amount of beam andmore » background electrons is accelerated considerably beyond the initial beam velocity when the beam density is more than a few percent of the background plasma density. In addition, electron distribution along the magnetic field has a smooth negative slope, f' (v/sub parallel/) < 0, for v/ sub parallel/ > 0 extending v/sub parallel/ = 1.5 V approx. 2 V, which is in sharp contrast to the predictions from quasilinear theory. An estimate of the mean-free path for beam electrons due to Coulomb collisions reveals that the beam electrons can propagate a much longer distance than is predicted from a quasilinear theory, due to the presence of a high energy tail. These simulation results agree well with the experimental observations from the ACT-1 device.« less

Identities associated with Milne-Thomson type polynomials and special numbers.

PubMed

Simsek, Yilmaz; Cakic, Nenad

2018-01-01

The purpose of this paper is to give identities and relations including the Milne-Thomson polynomials, the Hermite polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the central factorial numbers, and the Cauchy numbers. By using fermionic and bosonic p -adic integrals, we derive some new relations and formulas related to these numbers and polynomials, and also the combinatorial sums.

A mixed volume grid approach for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Jorgenson, Philip C. E.

1996-01-01

An approach for solving the compressible Euler and Navier-Stokes equations upon meshes composed of nearly arbitrary polyhedra is described. Each polyhedron is constructed from an arbitrary number of triangular and quadrilateral face elements, allowing the unified treatment of tetrahedral, prismatic, pyramidal, and hexahedral cells, as well the general cut cells produced by Cartesian mesh approaches. The basics behind the numerical approach and the resulting data structures are described. The accuracy of the mixed volume grid approach is assessed by performing a grid refinement study upon a series of hexahedral, tetrahedral, prismatic, and Cartesian meshes for an analytic inviscid problem. A series of laminar validation cases are made, comparing the results upon differing grid topologies to each other, to theory, and experimental data. A computation upon a prismatic/tetrahedral mesh is made simulating the laminar flow over a wall/cylinder combination.

A nonlinear theory for spinning anisotropic beams using restrained warping functions

NASA Technical Reports Server (NTRS)

Ie, C. A.; Kosmatka, J. B.

1993-01-01

A geometrically nonlinear theory is developed for spinning anisotropic beams having arbitrary cross sections. An assumed displacement field is developed using the standard 3D kinematics relations to describe the global beam behavior supplemented with an additional field that represents the local deformation within the cross section and warping out of the cross section plane. It is assumed that the magnitude of this additional field is directly proportional to the local stress resultants. In order to take into account the effects of boundary conditions, a restraining function is introduced. This function plays the role of reducing the amount of free warping deformation throughout the field due to the restraint of the cross section(s) at the end(s) of the beam, e.g., in the case of a cantilever beam. Using a developed ordering scheme, the nonlinear strains are calculated to the third order. The FEM is developed using the weak form variational formulation. Preliminary interesting numerical results have been obtained that indicate the role of the restraining function in the case of a cantilever beam with circular cross section. These results are for the cases of a tip displacement (static) and free vibration studies for both isotropic and anisotropic materials with varied fiber orientations.

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

DOE PAGES

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.; ...

2017-04-29

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

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

Larios, Adam; Petersen, Mark R.; Titi, Edriss S.

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler-Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler-Voigt equations also require less resolution than simulations of the 3D Euler equations for xed values of the regularization parameter α > 0. Therefore, the new blow-up criteria allow one to gain information about possible singularity formationmore » in the 3D Euler equations indirectly; namely, by simulating the better-behaved 3D Euler-Voigt equations. The new criteria are only known to be suficient for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well-known to occur.« less

Transonic flow analysis for rotors. Part 3: Three-dimensional, quasi-steady, Euler calculation

NASA Technical Reports Server (NTRS)

Chang, I-Chung

1990-01-01

A new method is presented for calculating the quasi-steady transonic flow over a lifting or non-lifting rotor blade in both hover and forward flight by using Euler equations. The approach is to solve Euler equations in a rotor-fixed frame of reference using a finite volume method. A computer program was developed and was then verified by comparison with wind-tunnel data. In all cases considered, good agreement was found with published experimental data.

Extension of Ko Straight-Beam Displacement Theory to Deformed Shape Predictions of Slender Curved Structures

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran

2011-01-01

The Ko displacement theory originally developed for shape predictions of straight beams is extended to shape predictions of curved beams. The surface strains needed for shape predictions were analytically generated from finite-element nodal stress outputs. With the aid of finite-element displacement outputs, mathematical functional forms for curvature-effect correction terms are established and incorporated into straight-beam deflection equations for shape predictions of both cantilever and two-point supported curved beams. The newly established deflection equations for cantilever curved beams could provide quite accurate shape predictions for different cantilever curved beams, including the quarter-circle cantilever beam. Furthermore, the newly formulated deflection equations for two-point supported curved beams could provide accurate shape predictions for a range of two-point supported curved beams, including the full-circular ring. Accuracy of the newly developed curved-beam deflection equations is validated through shape prediction analysis of curved beams embedded in the windward shallow spherical shell of a generic crew exploration vehicle. A single-point collocation method for optimization of shape predictions is discussed in detail

Beam Development_V6MP

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

Gilpatrick, John D.

2014-03-24

This presentation includes slides on Conditions; Sternglass states; H+ beam interacts with a W sense wire – Sternglass theory for SE current; Observed H+ beam at 03WS001 location; Jan 23 data; H- beam at 03WS001 location, Jan 23 data, Sternglass theory for SE current; H- beam at 03WS001 location; Jan 23 data; H+ beam at 04WS001 location, Jan 23 data, Sternglass theory for SE current; H+ beam at 04WS001 location; Jan 23 data; H- beam at 10WS001 location, Nov 17, 2013 data, Sternglass theory for SE current; H- beam at 10WS001 location; Nov 17, 2013 data; H- beam at 11WS001more » location, Nov 17, 2013 data, Sternglass theory for SE current; and lastly H- beam at 11WS001 location; Nov 17, 2013 data.« less

Investigation of source location determination from Magsat magnetic anomalies: The Euler method approach

NASA Technical Reports Server (NTRS)

Ravat, Dhananjay

1996-01-01

The applicability of the Euler method of source location determination was investigated on several model situations pertinent to satellite-data scale situations as well as Magsat data of Europe. Our investigations enabled us to understand the end-member cases for which the Euler method will work with the present satellite magnetic data and also the cases for which the assumptions implicit in the Euler method will not be met by the present satellite magnetic data. These results have been presented in one invited lecture at the Indo-US workshop on Geomagnetism in Studies of the Earth's Interior in August 1994 in Pune, India, and at one presentation at the 21st General Assembly of the IUGG in July 1995 in Boulder, CO. A new method, called Anomaly Attenuation Rate (AAR) Method (based on the Euler method), was developed during this study. This method is scale-independent and is appropriate to locate centroids of semi-compact three dimensional sources of gravity and magnetic anomalies. The method was presented during 1996 Spring AGU meeting and a manuscript describing this method is being prepared for its submission to a high-ranking journal. The grant has resulted in 3 papers and presentations at national and international meetings and one manuscript of a paper (to be submitted shortly to a reputable journal).

Transonic flow solutions using a composite velocity procedure for potential, Euler and RNS equations

NASA Technical Reports Server (NTRS)

Gordnier, R. E.; Rubin, S. G.

1986-01-01

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible flow equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential-like function. This provides for an efficient solution procedure that is locally representative of both asymptotic inviscid and boundary layer theories. A modified conservative form of the axial momentum equation that is required to obtain rotational solutions in the inviscid region is presented and a combined conservation/nonconservation form is applied for evaluation of the reduced Navier-Stokes (RNS), Euler and potential equations. A variety of results is presented and the effects of the approximations on entropy production, shock capturing, and viscous interaction are discussed.

Euler's Identity, Leibniz Tables, and the Irrationality of Pi

ERIC Educational Resources Information Center

Jones, Timothy W.

2012-01-01

Using techniques that show that e and pi are transcendental, we give a short, elementary proof that pi is irrational based on Euler's identity. The proof involves evaluations of a polynomial using repeated applications of Leibniz formula as organized in a Leibniz table.

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory.

PubMed

Ma, Mingying; Wang, Xiangzhao; Wang, Fan

2006-11-10

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy.

Dynamic modelling and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances

NASA Astrophysics Data System (ADS)

Yang, Xinxin; Ge, Shuzhi Sam; He, Wei

2018-04-01

In this paper, both the closed-form dynamics and adaptive robust tracking control of a space robot with two-link flexible manipulators under unknown disturbances are developed. The dynamic model of the system is described with assumed modes approach and Lagrangian method. The flexible manipulators are represented as Euler-Bernoulli beams. Based on singular perturbation technique, the displacements/joint angles and flexible modes are modelled as slow and fast variables, respectively. A sliding mode control is designed for trajectories tracking of the slow subsystem under unknown but bounded disturbances, and an adaptive sliding mode control is derived for slow subsystem under unknown slowly time-varying disturbances. An optimal linear quadratic regulator method is proposed for the fast subsystem to damp out the vibrations of the flexible manipulators. Theoretical analysis validates the stability of the proposed composite controller. Numerical simulation results demonstrate the performance of the closed-loop flexible space robot system.

Convergence of finite difference transient response computations for thin shells.

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Geers, T. L.

1973-01-01

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Uniform high order spectral methods for one and two dimensional Euler equations

NASA Technical Reports Server (NTRS)

Cai, Wei; Shu, Chi-Wang

1991-01-01

Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two dimensional shock wave and a rotating vortex is simulated.

On the Local Type I Conditions for the 3D Euler Equations

NASA Astrophysics Data System (ADS)

Chae, Dongho; Wolf, Jörg

2018-05-01

We prove local non blow-up theorems for the 3D incompressible Euler equations under local Type I conditions. More specifically, for a classical solution {v\\in L^∞ (-1,0; L^2 ( B(x_0,r)))\\cap L^∞_{loc} (-1,0; W^{1, ∞} (B(x_0, r)))} of the 3D Euler equations, where {B(x_0,r)} is the ball with radius r and the center at x 0, if the limiting values of certain scale invariant quantities for a solution v(·, t) as {t\\to 0} are small enough, then { \

A computational procedure for the dynamics of flexible beams within multibody systems. Ph.D. Thesis Final Technical Report

NASA Technical Reports Server (NTRS)

Downer, Janice Diane

1990-01-01

The dynamic analysis of three dimensional elastic beams which experience large rotational and large deformational motions are examined. The beam motion is modeled using an inertial reference for the translational displacements and a body-fixed reference for the rotational quantities. Finite strain rod theories are then defined in conjunction with the beam kinematic description which accounts for the effects of stretching, bending, torsion, and transverse shear deformations. A convected coordinate representation of the Cauchy stress tensor and a conjugate strain definition is introduced to model the beam deformation. To treat the beam dynamics, a two-stage modification of the central difference algorithm is presented to integrate the translational coordinates and the angular velocity vector. The angular orientation is then obtained from the application of an implicit integration algorithm to the Euler parameter/angular velocity kinematical relation. The combined developments of the objective internal force computation with the dynamic solution procedures result in the computational preservation of total energy for undamped systems. The present methodology is also extended to model the dynamics of deployment/retrieval of the flexible members. A moving spatial grid corresponding to the configuration of a deployed rigid beam is employed as a reference for the dynamic variables. A transient integration scheme which accurately accounts for the deforming spatial grid is derived from a space-time finite element discretization of a Hamiltonian variational statement. The computational results of this general deforming finite element beam formulation are compared to reported results for a planar inverse-spaghetti problem.

Hydrodynamic Coherence and Vortex Solutions of the Euler-Helmholtz Equation

NASA Astrophysics Data System (ADS)

Fimin, N. N.; Chechetkin, V. M.

2018-03-01

The form of the general solution of the steady-state Euler-Helmholtz equation (reducible to the Joyce-Montgomery one) in arbitrary domains on the plane is considered. This equation describes the dynamics of vortex hydrodynamic structures.

Energy broadening in electron beams: A comparison of existing theories and Monte Carlo simulation

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

Jansen, G.H.; Groves, T.R.; Stickel, W.

1985-01-01

Different theories on the Boersch effect are applied to a simple beam geometry with one crossover in drift space.The results are compared with each other, with Monte Carlo simulations, and with the experiment. The most complete and accurate theory is given by van Leeuwen and Jansen. This theory predicts energy spreads within 10% of the Monte Carlo results for operating conditions usually given in systems with thermionic emission sources. No comprehensive theory, however, of energy broadening in electron guns has yet been presented. Nevertheless, the theory of van Leeuwen and Jansen was found to predict the experimental values by trendmore » and within a factor of 2.« less

Remembrances of Ulf Svante von Euler.

PubMed

Igić, Rajko

2018-05-21

I first met Ulf Svante von Euler when he came to Belgrade, in 1968, to attend an international symposium on the occasion of the 50 th anniversary of the Medical Faculty. I was at that time a graduate student at the Medical Faculty in Sarajevo, and a new researcher. I had finished medical school in Belgrade and had worked for two years as a physician in the northern part of Serbia. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

The 3D Euler solutions using automated Cartesian grid generation

NASA Technical Reports Server (NTRS)

Melton, John E.; Enomoto, Francis Y.; Berger, Marsha J.

1993-01-01

Viewgraphs on 3-dimensional Euler solutions using automated Cartesian grid generation are presented. Topics covered include: computational fluid dynamics (CFD) and the design cycle; Cartesian grid strategy; structured body fit; grid generation; prolate spheroid; and ONERA M6 wing.

Vibration control of beams using constrained layer damping with functionally graded viscoelastic cores: theory and experiments

NASA Astrophysics Data System (ADS)

El-Sabbagh, A.; Baz, A.

2006-03-01

Conventionally, the viscoelastic cores of Constrained Layer Damping (CLD) treatments are made of materials that have uniform shear modulus. Under such conditions, it is well-recognized that these treatments are only effective near their edges where the shear strains attain their highest values. In order to enhance the damping characteristics of the CLD treatments, we propose to manufacture the cores from Functionally Graded ViscoElastic Materials (FGVEM) that have optimally selected gradient of the shear modulus over the length of the treatments. With such optimized distribution of the shear modulus, the shear strain can be enhanced, and the energy dissipation can be maximized. The theory governing the vibration of beams treated with CLD, that has functionally graded viscoelastic cores, is presented using the finite element method (FEM). The predictions of the FEM are validated experimentally for plain beams, beams treated conventional CLD, and beams with CLD/FGVEM of different configurations. The obtained results indicate a close agreement between theory and experiments. Furthermore, the obtained results demonstrate the effectiveness of the new class of CLD with functionally graded cores in enhancing the energy dissipation over the conventional CLD over a broad frequency band. Extension of the proposed one-dimensional beam/CLD/FGVEM system to more complex structures is a natural extension to the present study.

Euler flow predictions for an oscillating cascade using a high resolution wave-split scheme

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Swafford, Timothy W.; Reddy, T. S. R.

1991-01-01

A compressible flow code that can predict the nonlinear unsteady aerodynamics associated with transonic flows over oscillating cascades is developed and validated. The code solves the two dimensional, unsteady Euler equations using a time-marching, flux-difference splitting scheme. The unsteady pressures and forces can be determined for arbitrary input motions, although only harmonic pitching and plunging motions are addressed. The code solves the flow equations on a H-grid which is allowed to deform with the airfoil motion. Predictions are presented for both flat plate cascades and loaded airfoil cascades. Results are compared to flat plate theory and experimental data. Predictions are also presented for several oscillating cascades with strong normal shocks where the pitching amplitudes, cascade geometry and interblade phase angles are varied to investigate nonlinear behavior.

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

NASA Astrophysics Data System (ADS)

Tajaddodianfar, Farid; Hairi Yazdi, Mohammad Reza; Pishkenari, Hossein Nejat

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.

Micro-mechanical modelling of cellulose aerogels from molten salt hydrates.

PubMed

Rege, Ameya; Schestakow, Maria; Karadagli, Ilknur; Ratke, Lorenz; Itskov, Mikhail

2016-09-14

In this paper, a generalised micro-mechanical model capable of capturing the mechanical behaviour of polysaccharidic aerogels, in particular cellulose aerogels, is proposed. To this end, first the mechanical structure and properties of these highly nanoporous cellulose aerogels prepared from aqueous salt hydrate melts (calcium thiocyanate, Ca(SCN)2·6H2O and zinc chloride, ZnCl2·4H2O) are studied. The cellulose content within these aerogels is found to have a direct relation to the microstructural quantities such as the fibril length and diameter. This, along with porosity, appears to influence the resulting mechanical properties. Furthermore, experimental characterisation of cellulose aerogels was done using scanning electron microscopy (SEM), pore-size data analysis, and compression tests. Cellulose aerogels are of a characteristic cellular microstructures and accordingly a network formed by square shaped cells is considered in the micro-mechanical model proposed in this paper. This model is based on the non-linear bending and collapse of such cells of varying pore sizes. The extended Euler-Bernoulli beam theory for large deflections is used to describe the bending in the cell walls. The proposed model is physically motivated and demonstrates a good agreement with our experimental data of both ZnCl2 and Ca(SCN)2 based cellulose aerogels with different cellulose contents.

Flutter instability of cantilevered carbon nanotubes caused by magnetic fluid flow subjected to a longitudinal magnetic field

NASA Astrophysics Data System (ADS)

Sadeghi-Goughari, Moslem; Jeon, Soo; Kwon, Hyock-Ju

2018-04-01

CNT (Carbon nanotube)-based fluidic systems hold a great potential for emerging medical applications such as drug delivery for cancer therapy. CNTs can be used to deliver anticancer drugs into a target site under a magnetic field guidance. One of the critical issues in designing such systems is how to avoid the vibration induced by the fluid flow, which is undesirable and may even promote the structural instability. The main objective of the present research is to develop a fluid structure interaction (FSI) model to investigate the flutter instability of a cantilevered CNT induced by a magnetic fluid flow under a longitudinal magnetic field. The CNT is assumed to be embedded in a viscoelastic matrix to consider the effect of biological medium around it. To obtain a dynamical model for the system, the Navier-Stokes theory of magnetic-fluid flow is coupled to the Euler-Bernoulli beam model for CNT. The small size effects of the magnetic fluid and CNT are considered through the small scale parameters including Knudsen number (Kn) and the nonlocal parameter. Then, the extended Galerkin's method is applied to solve the FSI governing equations, and to derive the stability diagrams of the system. Results show how the magnetic properties of the fluid flow have an effect on improving the stability of the cantilevered CNT by increasing the flutter velocity.

Symplectic analysis of vertical random vibration for coupled vehicle track systems

NASA Astrophysics Data System (ADS)

Lu, F.; Kennedy, D.; Williams, F. W.; Lin, J. H.

2008-10-01

A computational model for random vibration analysis of vehicle-track systems is proposed and solutions use the pseudo excitation method (PEM) and the symplectic method. The vehicle is modelled as a mass, spring and damping system with 10 degrees of freedom (dofs) which consist of vertical and pitching motion for the vehicle body and its two bogies and vertical motion for the four wheelsets. The track is treated as an infinite Bernoulli-Euler beam connected to sleepers and hence to ballast and is regarded as a periodic structure. Linear springs couple the vehicle and the track. Hence, the coupled vehicle-track system has only 26 dofs. A fixed excitation model is used, i.e. the vehicle does not move along the track but instead the track irregularity profile moves backwards at the vehicle velocity. This irregularity is assumed to be a stationary random process. Random vibration theory is used to obtain the response power spectral densities (PSDs), by using PEM to transform this random multiexcitation problem into a deterministic harmonic excitation one and then applying symplectic solution methodology. Numerical results for an example include verification of the proposed method by comparing with finite element method (FEM) results; comparison between the present model and the traditional rigid track model and; discussion of the influences of track damping and vehicle velocity.

Energy harvesting from mastication forces via a smart tooth

NASA Astrophysics Data System (ADS)

Bani-Hani, Muath; Karami, M. Amin

2016-04-01

The batteries of the current pacing devices are relatively large and occupy over 60 percent of the size of pulse generators. Therefore, they cannot be placed in the subtle areas of human body. In this paper, the mastication force and the resulting tooth pressure are converted to electricity. The pressure energy can be converted to electricity by using the piezoelectric effect. The tooth crown is used as a power autonomous pulse generator. We refer to this envisioned pulse generator as the smart tooth. The smart tooth is in the form of a dental implant. A piezoelectric vibration energy harvester is designed and modeled for this purpose. The Piezoelectric based energy harvesters investigated and analyzed in this paper initially includes a single degree of freedom piezoelectric based stack energy harvester which utilizes a harvesting circuit employing the case of a purely resistive circuit. The next step is utilizing and investigating a bimorph piezoelectric beam which is integrated/embedded in the smart tooth implant. Mastication process causes the bimorph beam to buckle or return to unbuckled condition. The transitions results in vibration of the piezoelectric beam and thus generate energy. The power estimated by the two mechanisms is in the order of hundreds of microwatts. Both scenarios of the energy harvesters are analytically modeled. The exact analytical solution of the piezoelectric beam energy harvester with Euler-Bernoulli beam assumptions is presented. The electro-mechanical coupling and the geometric nonlinearities have been included in the model for the piezoelectric beam.

Newton's Laws, Euler's Laws and the Speed of Light

ERIC Educational Resources Information Center

Whitaker, Stephen

2009-01-01

Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…

A Direct and Non-Singular UKF Approach Using Euler Angle Kinematics for Integrated Navigation Systems

PubMed Central

Ran, Changyan; Cheng, Xianghong

2016-01-01

This paper presents a direct and non-singular approach based on an unscented Kalman filter (UKF) for the integration of strapdown inertial navigation systems (SINSs) with the aid of velocity. The state vector includes velocity and Euler angles, and the system model contains Euler angle kinematics equations. The measured velocity in the body frame is used as the filter measurement. The quaternion nonlinear equality constraint is eliminated, and the cross-noise problem is overcome. The filter model is simple and easy to apply without linearization. Data fusion is performed by an UKF, which directly estimates and outputs the navigation information. There is no need to process navigation computation and error correction separately because the navigation computation is completed synchronously during the filter time updating. In addition, the singularities are avoided with the help of the dual-Euler method. The performance of the proposed approach is verified by road test data from a land vehicle equipped with an odometer aided SINS, and a singularity turntable test is conducted using three-axis turntable test data. The results show that the proposed approach can achieve higher navigation accuracy than the commonly-used indirect approach, and the singularities can be efficiently removed as the result of dual-Euler method. PMID:27598169

Variational Approach in the Theory of Liquid-Crystal State

NASA Astrophysics Data System (ADS)

Gevorkyan, E. V.

2018-03-01

The variational calculus by Leonhard Euler is the basis for modern mathematics and theoretical physics. The efficiency of variational approach in statistical theory of liquid-crystal state and in general case in condensed state theory is shown. The developed approach in particular allows us to introduce correctly effective pair interactions and optimize the simple models of liquid crystals with help of realistic intermolecular potentials.

An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Coirier, William John

1994-01-01

A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a

Euler-Vector Clustering of GPS Velocities Defines Microplate Geometry in Southwest Japan

NASA Astrophysics Data System (ADS)

Savage, J. C.

2018-02-01

I have used Euler-vector clustering to assign 469 GEONET stations in southwest Japan to k clusters (k = 2, 3,..., 9) so that, for any k, the velocities of stations within each cluster are most consistent with rigid-block motion on a sphere. That is, I attempt to explain the raw (i.e., uncorrected for strain accumulation), 1996-2006 velocities of those 469 Global Positioning System stations by rigid motion of k clusters on the surface of a spherical Earth. Because block geometry is maintained as strain accumulates, Euler-vector clustering may better approximate the block geometry than the values of the associated Euler vectors. The microplate solution for each k is constructed by merging contiguous clusters that have closely similar Euler vectors. The best solution consists of three microplates arranged along the Nankaido Trough-Ryukyu Trench between the Amurian and Philippine Sea Plates. One of these microplates, the South Kyushu Microplate (an extension of the Ryukyu forearc into the southeast corner of Kyushu), had previously been identified from paleomagnetic rotations. Relative to ITRF2000 the three microplates rotate at different rates about neighboring poles located close to the northwest corner of Shikoku. The microplate model is identical to that proposed in the block model of Wallace et al. (2009, https://doi.org/10.1130/G2522A.1) except in southernmost Kyushu. On Shikoku and Honshu, but not Kyushu, the microplate model is consistent with that proposed in the block models of Nishimura and Hashimoto (2006, https://doi.org/10.1016/j.tecto.2006.04.017) and Loveless and Meade (2010, https://doi.org/10.1029/2008JB006248) without the low-slip-rate boundaries proposed in the latter.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Multi stage unreliable retrial Queueing system with Bernoulli vacation

NASA Astrophysics Data System (ADS)

Radha, J.; Indhira, K.; Chandrasekaran, V. M.

2017-11-01

In this work we considered the Bernoulli vacation in group arrival retrial queues with unreliable server. Here, a server providing service in k stages. Any arriving group of units finds the server free, one from the group entering the first stage of service and the rest are joining into the orbit. After completion of the i th, (i=1,2,…k) stage of service, the customer may go to (i+1)th stage with probability θi , or leave the system with probability qi = 1 - θi , (i = 1,2,…k - 1) and qi = 1, (i = k). The server may enjoy vacation (orbit is empty or not) with probability v after finishing the service or continuing the service with probability 1-v. After finishing the vacation, the server search for the customer in the orbit with probability θ or remains idle for new arrival with probability 1-θ. We analyzed the system using the method of supplementary variable.

Electrostatic and aerodynamic forced vibrations of a thin flexible electrode: Quasi-periodic vs. chaotic oscillations

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

Madanu, Sushma B.; Barbel, Stanley I.; Ward, Thomas

In this paper, transverse vibrations of an electrostatically actuated thin flexible cantilever perturbed by low-speed air flow are studied using both experiments and numerical modeling. In the experiments, the dynamic characteristics of the cantilever are studied by supplying a DC voltage with an AC component for electrostatic forcing and a constant uniform air flow around the cantilever system for aerodynamic forcing. A range of control parameters leading to stable vibrations are established using a dimensionless operating parameter that is the ratio of the induced and the free stream velocities. Numerical results are validated with experimental data. Assuming the amplitude ofmore » vibrations are small, then a non-linear dynamic Euler-Bernoulli beam equation with viscous damping and gravitational effects is used to model the equation of motion. Aerodynamic forcing is modelled as a temporally sinusoidal and uniform force acting perpendicular to the beam length. The forcing amplitude is found to be proportional to the square of the air flow velocity. Numerical results strongly agree with the experiments predicting accurate vibration amplitude, displacement frequency, and quasi-periodic displacement of the cantilever tip.« less

Dynamic characteristics of a novel damped outrigger system

NASA Astrophysics Data System (ADS)

Tan, Ping; Fang, Chuangjie; Zhou, Fulin

2014-06-01

This paper presents exact analytical solutions for a novel damped outrigger system, in which viscous dampers are vertically installed between perimeter columns and the core of a high-rise building. An improved analytical model is developed by modeling the effect of the damped outrigger as a general rotational spring acting on a Bernoulli-Euler beam. The equivalent rotational spring stiffness incorporating the combined effects of dampers and axial stiffness of perimeter columns is derived. The dynamic stiffness method (DSM) is applied to formulate the governing equation of the damped outrigger system. The accuracy and efficiency are verified in comparison with those obtained from compatibility equations and boundary equations. Parametric analysis of three non-dimensional factors is conducted to evaluate the influences of various factors, such as the stiffness ratio of the core to the beam, position of the damped outrigger, and the installed damping coefficient. Results show that the modal damping ratio is significantly influenced by the stiffness ratio of the core to the column, and is more sensitive to damping than the position of the damped outrigger. The proposed analytical model in combination with DSM can be extended to the study of structures with more outriggers.

Anisotropic fractal media by vector calculus in non-integer dimensional space

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensionalmore » space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.« less

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

Wang, Y. B.; Zhu, X. W., E-mail: xiaowuzhu1026@znufe.edu.cn; Dai, H. H.

Though widely used in modelling nano- and micro- structures, Eringen’s differential model shows some inconsistencies and recent study has demonstrated its differences between the integral model, which then implies the necessity of using the latter model. In this paper, an analytical study is taken to analyze static bending of nonlocal Euler-Bernoulli beams using Eringen’s two-phase local/nonlocal model. Firstly, a reduction method is proved rigorously, with which the integral equation in consideration can be reduced to a differential equation with mixed boundary value conditions. Then, the static bending problem is formulated and four types of boundary conditions with various loadings aremore » considered. By solving the corresponding differential equations, exact solutions are obtained explicitly in all of the cases, especially for the paradoxical cantilever beam problem. Finally, asymptotic analysis of the exact solutions reveals clearly that, unlike the differential model, the integral model adopted herein has a consistent softening effect. Comparisons are also made with existing analytical and numerical results, which further shows the advantages of the analytical results obtained. Additionally, it seems that the once controversial nonlocal bar problem in the literature is well resolved by the reduction method.« less

Anisotropic fractal media by vector calculus in non-integer dimensional space

NASA Astrophysics Data System (ADS)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Thickness ratio effects on quasistatic actuation and sensing behavior of laminate magnetoelectric cantilevers

NASA Astrophysics Data System (ADS)

Wang, Yezuo; Atulasimha, Jayasimha; Clarke, Joshua; Sundaresan, Vishnu B.

2010-04-01

In this work, the magnetoelectric cantilever composed of a layer of Galfenol and a layer of PZT-5H is studied for novel applications such as surgical ablation tools and cutting tools for machining applications. For developing a suitable model for the magnetoelectric cantilever, an energy based approach for the non-linear constitutive behavior of the magnetostrictive material and linear piezoelectric constitutive equations will be coupled with Euler Bernoulli model for composite beams. The cantilever is held in a uniform magnetic field and the magnetic field is measured by a Gaussmeter. The tip-deflection of the cantilever is detected by a laser triangulation sensor. The piezoelectric response can be studied with low noise preamplifier. Four PZT-5H layers with different thickness are separately bonded on the top of the same Galfenol layer and characterized to study the thickness ratio effects on the quasistatic actuation and sensing behavior of the composite cantilever.

High-speed trains subject to abrupt braking

NASA Astrophysics Data System (ADS)

Tran, Minh Thi; Ang, Kok Keng; Luong, Van Hai; Dai, Jian

2016-12-01

The dynamic response of high-speed train subject to braking is investigated using the moving element method. Possible sliding of wheels over the rails is accounted for. The train is modelled as a 15-DOF system comprising of a car body, two bogies and four wheels interconnected by spring-damping units. The rail is modelled as a Euler-Bernoulli beam resting on a two-parameter elastic damped foundation. The interaction between the moving train and track-foundation is accounted for through the normal and tangential wheel-rail contact forces. The effects of braking torque, wheel-rail contact condition, initial train speed and severity of railhead roughness on the dynamic response of the high-speed train are investigated. For a given initial train speed and track irregularity, the study revealed that there is an optimal braking torque that would result in the smallest braking distance with no occurrence of wheel sliding, representing a good compromise between train instability and safety.

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.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Extraction of space-charge-dominated ion beams from an ECR ion source: Theory and simulation

NASA Astrophysics Data System (ADS)

Alton, G. D.; Bilheux, H.

2004-05-01

Extraction of high quality space-charge-dominated ion beams from plasma ion sources constitutes an optimization problem centered about finding an optimal concave plasma emission boundary that minimizes half-angular divergence for a given charge state, independent of the presence or lack thereof of a magnetic field in the extraction region. The curvature of the emission boundary acts to converge/diverge the low velocity beam during extraction. Beams of highest quality are extracted whenever the half-angular divergence, ω, is minimized. Under minimum half-angular divergence conditions, the plasma emission boundary has an optimum curvature and the perveance, P, current density, j+ext, and extraction gap, d, have optimum values for a given charge state, q. Optimum values for each of the independent variables (P, j+ext and d) are found to be in close agreement with those derived from elementary analytical theory for extraction with a simple two-electrode extraction system, independent of the presence of a magnetic field. The magnetic field only increases the emittances of beams through additional aberrational effects caused by increased angular divergences through coupling of the longitudinal to the transverse velocity components of particles as they pass though the mirror region of the electron cyclotron resonance (ECR) ion source. This article reviews the underlying theory of elementary extraction optics and presents results derived from simulation studies of extraction of space-charge dominated heavy-ion beams of varying mass, charge state, and intensity from an ECR ion source with emphasis on magnetic field induced effects.

Concepts for radically increasing the numerical convergence rate of the Euler equations

NASA Technical Reports Server (NTRS)

Nixon, David; Tzuoo, Keh-Lih; Caruso, Steven C.; Farshchi, Mohammad; Klopfer, Goetz H.; Ayoub, Alfred

1987-01-01

Integral equation and finite difference methods have been developed for solving transonic flow problems using linearized forms of the transonic small disturbance and Euler equations. A key element is the use of a strained coordinate system in which the shock remains fixed. Additional criteria are developed to determine the free parameters in the coordinate straining; these free parameters are functions of the shock location. An integral equation analysis showed that the shock is located by ensuring that no expansion shocks exist in the solution. The expansion shock appears as oscillations in the solution near the sonic line, and the correct shock location is determined by removing these oscillations. A second objective was to study the ability of the Euler equation to model separated flow.

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

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

Kong, Bo; Fox, Rodney O.; Feng, Heng

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE PAGES

Kong, Bo; Fox, Rodney O.; Feng, Heng; ...

2017-02-16

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Forecasting of foreign exchange rates of Taiwan’s major trading partners by novel nonlinear Grey Bernoulli model NGBM(1, 1)

NASA Astrophysics Data System (ADS)

Chen, Chun-I.; Chen, Hong Long; Chen, Shuo-Pei

2008-08-01

The traditional Grey Model is easy to understand and simple to calculate, with satisfactory accuracy, but it is also lack of flexibility to adjust the model to acquire higher forecasting precision. This research studies feasibility and effectiveness of a novel Grey model together with the concept of the Bernoulli differential equation in ordinary differential equation. In this research, the author names this newly proposed model as Nonlinear Grey Bernoulli Model (NGBM). The NGBM is nonlinear differential equation with power index n. By controlling n, the curvature of the solution curve could be adjusted to fit the result of one time accumulated generating operation (1-AGO) of raw data. One extreme case from Grey system textbook is studied by NGBM, and two published articles are chosen for practical tests of NGBM. The results prove the novel NGBM is feasible and efficient. Finally, NGBM is used to forecast 2005 foreign exchange rates of twelve Taiwan major trading partners, including Taiwan.

The stochastic model for ternary and quaternary alloys: Application of the Bernoulli relation to the phonon spectra of mixed crystals

NASA Astrophysics Data System (ADS)

Marchewka, M.; Woźny, M.; Polit, J.; Kisiel, A.; Robouch, B. V.; Marcelli, A.; Sheregii, E. M.

2014-03-01

To understand and interpret the experimental data on the phonon spectra of the solid solutions, it is necessary to describe mathematically the non-regular distribution of atoms in their lattices. It appears that such description is possible in case of the strongly stochastically homogenous distribution which requires a great number of atoms and very carefully mixed alloys. These conditions are generally fulfilled in case of high quality homogenous semiconductor solid solutions of the III-V and II-VI semiconductor compounds. In this case, we can use the Bernoulli relation describing probability of the occurrence of one n equivalent event which can be applied, to the probability of finding one from n configurations in the solid solution lattice. The results described in this paper for ternary HgCdTe and GaAsP as well as quaternary ZnCdHgTe can provide an affirmative answer to the question: whether stochastic geometry, e.g., the Bernoulli relation, is enough to describe the observed phonon spectra.

Unique Properties and Prospects: Quantum Theory of the Orbital Angular Momentum of Ince-Gauss Beams

NASA Astrophysics Data System (ADS)

Plick, William; Krenn, Mario; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton

2012-02-01

The Ince-Gauss modes represent a new addition to the standard solutions to the paraxial wave equation. Parametrized by the ellipticity of the beam, they span the solution space between the Hermite-Gauss and the Laguerre-Gauss modes. These beams may be decomposed in either basis, and single photons in the Ince-Gauss modes exist naturally as superpositions of either Laguerre-Gauss or Hermite-Gauss modes. We present the fully quantum theory of the orbital angular momentum of these beams. Interesting features that arise are: stable beams with fractional orbital angular momentum, non-monotonic behavior of the OAM with respect to ellipticity, and the possibility of orthogonal modes possessing the same OAM. We believe that these modes may open up a fully new parameter space for quantum informatics and communication, and thus are worthy of thorough study.

Elasticity Theory Solution of the Problem on Plane Bending of a Narrow Layered Cantilever Beam by Loads at Its Free End

NASA Astrophysics Data System (ADS)

Goryk, A. V.; Koval'chuk, S. B.

2018-05-01

An exact elasticity theory solution for the problem on plane bending of a narrow layered composite cantilever beam by tangential and normal loads distributed on its free end is presented. Components of the stress-strain state are found for the whole layers package by directly integrating differential equations of the plane elasticity theory problem by using an analytic representation of piecewise constant functions of the mechanical characteristics of layer materials. The continuous solution obtained is realized for a four-layer beam with account of kinematic boundary conditions simulating the rigid fixation of its one end. The solution obtained allows one to predict the strength and stiffness of composite cantilever beams and to construct applied analytical solutions for various problems on the elastic bending of layered beams.

Prediction of Undsteady Flows in Turbomachinery Using the Linearized Euler Equations on Deforming Grids

NASA Technical Reports Server (NTRS)

Clark, William S.; Hall, Kenneth C.

1994-01-01

A linearized Euler solver for calculating unsteady flows in turbomachinery blade rows due to both incident gusts and blade motion is presented. The model accounts for blade loading, blade geometry, shock motion, and wake motion. Assuming that the unsteadiness in the flow is small relative to the nonlinear mean solution, the unsteady Euler equations can be linearized about the mean flow. This yields a set of linear variable coefficient equations that describe the small amplitude harmonic motion of the fluid. These linear equations are then discretized on a computational grid and solved using standard numerical techniques. For transonic flows, however, one must use a linear discretization which is a conservative linearization of the non-linear discretized Euler equations to ensure that shock impulse loads are accurately captured. Other important features of this analysis include a continuously deforming grid which eliminates extrapolation errors and hence, increases accuracy, and a new numerically exact, nonreflecting far-field boundary condition treatment based on an eigenanalysis of the discretized equations. Computational results are presented which demonstrate the computational accuracy and efficiency of the method and demonstrate the effectiveness of the deforming grid, far-field nonreflecting boundary conditions, and shock capturing techniques. A comparison of the present unsteady flow predictions to other numerical, semi-analytical, and experimental methods shows excellent agreement. In addition, the linearized Euler method presented requires one or two orders-of-magnitude less computational time than traditional time marching techniques making the present method a viable design tool for aeroelastic analyses.

Discovering Euler Circuits and Paths through a Culturally Relevant Lesson

ERIC Educational Resources Information Center

Robichaux, Rebecca R.; Rodrigue, Paulette R.

2006-01-01

This article describes a middle school discrete mathematics lesson that uses the context of catching crawfish to provide students with a hands-on experience related to Euler circuits and paths. The lesson promotes mathematical communication through the use of cooperative learning as well as connections between mathematics and the real world…

Generation of unstructured grids and Euler solutions for complex geometries

NASA Technical Reports Server (NTRS)

Loehner, Rainald; Parikh, Paresh; Salas, Manuel D.

1989-01-01

Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields.

On the estimation variance for the specific Euler-Poincaré characteristic of random networks.

PubMed

Tscheschel, A; Stoyan, D

2003-07-01

The specific Euler number is an important topological characteristic in many applications. It is considered here for the case of random networks, which may appear in microscopy either as primary objects of investigation or as secondary objects describing in an approximate way other structures such as, for example, porous media. For random networks there is a simple and natural estimator of the specific Euler number. For its estimation variance, a simple Poisson approximation is given. It is based on the general exact formula for the estimation variance. In two examples of quite different nature and topology application of the formulas is demonstrated.

Modeling and optimization of shape memory-superelastic antagonistic beam assembly

NASA Astrophysics Data System (ADS)

Tabesh, Majid; Elahinia, Mohammad H.

2010-04-01

Superelasticity (SE), shape memory effect (SM), high damping capacity, corrosion resistance, and biocompatibility are the properties of NiTi that makes the alloy ideal for biomedical devices. In this work, the 1D model developed by Brinson was modified to capture the shape memory effect, superelasticity and hysteresis behavior, as well as partial transformation in both positive and negative directions. This model was combined with the Euler beam equation which, by approximation, considers 1D compression and tension stress-strain relationships in different layers of a 3D beam assembly cross-section. A shape memory-superelastic NiTi antagonistic beam assembly was simulated with this model. This wire-tube assembly is designed to enhance the performance of the pedicle screws in osteoporotic bones. For the purpose of this study, an objective design is pursued aiming at optimizing the dimensions and initial configurations of the SMA wire-tube assembly.

Photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian beams

NASA Astrophysics Data System (ADS)

Karbstein, Felix; Mosman, Elena A.

2017-12-01

In this article, we provide analytical expressions for the photon polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our results are based on a locally constant field approximation of the one-loop Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by construction they are limited to slowly varying electromagnetic fields, varying on spatial and temporal scales significantly larger than the Compton wavelength/time of the electron. The latter criterion is fulfilled by all laser beams currently available in the laboratory. Our findings will, e.g., be relevant for the study of vacuum birefringence experienced by probe photons brought into collision with a high-intensity laser pulse which can be represented as a superposition of either Hermite- or Laguerre-Gaussian modes.

Generalization of the Euler-type solution to the wave equation

NASA Astrophysics Data System (ADS)

Borisov, Victor V.

2001-08-01

Generalization of the Euler-type solution to the wave equation is given. Peculiarities of the space-time structure of obtained waves are considered. For some particular cases interpretation of these waves as `subliminal' and `superluminal' is discussed. The possibility of description of electromagnetic waves by means of the scalar solutions is shown.

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

NASA Technical Reports Server (NTRS)

Cockburn, Bernardo; Shu, Chi-Wang

1991-01-01

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Euler equation existence, non-uniqueness and mesh converged statistics

PubMed Central

Glimm, James; Sharp, David H.; Lim, Hyunkyung; Kaufman, Ryan; Hu, Wenlin

2015-01-01

We review existence and non-uniqueness results for the Euler equation of fluid flow. These results are placed in the context of physical models and their solutions. Non-uniqueness is in direct conflict with the purpose of practical simulations, so that a mitigating strategy, outlined here, is important. We illustrate these issues in an examination of mesh converged turbulent statistics, with comparison to laboratory experiments. PMID:26261361

Local Stretching Theories

DTIC Science & Technology

2010-06-24

diffusivity of the scalar. (If the scalar is heat, then the Schmidt number becomes the Prandtl number.) Momentum diffuses significantly faster than the...derive the Cramér function explicitly in the simple case where the xi have a Bernoulli distribution, though the general formula for S may be derived by...an analogous procedure. 5 Large deviation CLT for the Bernoulli distribution Let xi have the PDF of a fair coin, p(xi) = 1 2δ(xi + 1) + 1 2δ(xi − 1

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

NASA Technical Reports Server (NTRS)

Batina, John T.

1991-01-01

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Numerical solutions of incompressible Navier-Stokes equations using modified Bernoulli's law

NASA Astrophysics Data System (ADS)

Shatalov, A.; Hafez, M.

2003-11-01

Simulations of incompressible flows are important for many practical applications in aeronautics and beyond, particularly in the high Reynolds number regime. The present formulation is based on Helmholtz velocity decomposition where the velocity is presented as the gradient of a potential plus a rotational component. Substituting in the continuity equation yields a Poisson equation for the potential which is solved with a zero normal derivative at solid surfaces. The momentum equation is used to update the rotational component with no slip/no penetration surface boundary conditions. The pressure is related to the potential function through a special relation which is a generalization of Bernoulli's law, with a viscous term included. Results of calculations for two- and three-dimensional problems prove that the present formulation is a valid approach, with some possible benefits compared to existing methods.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

Linear Equations with the Euler Totient Function

DTIC Science & Technology

2007-02-13

unclassified c . THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 2 FLORIAN LUCA, PANTELIMON STĂNICĂ...of positive integers n such that φ(n) = φ(n+ 1), and that the set of Phibonacci numbers is A(1,1,−1) + 2. Theorem 2.1. Let C (t, a) = t3 logH(a). Then...the estimate #Aa(x) C (t, a) x log log log x√ log log x LINEAR EQUATIONS WITH THE EULER TOTIENT FUNCTION 3 holds uniformly in a and 1 ≤ t < y. Note

Sign reversals of the output autocorrelation function for the stochastic Bernoulli-Verhulst equation

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

Lumi, N., E-mail: Neeme.Lumi@tlu.ee; Mankin, R., E-mail: Romi.Mankin@tlu.ee

2015-10-28

We consider a stochastic Bernoulli-Verhulst equation as a model for population growth processes. The effect of fluctuating environment on the carrying capacity of a population is modeled as colored dichotomous noise. Relying on the composite master equation an explicit expression for the stationary autocorrelation function (ACF) of population sizes is found. On the basis of this expression a nonmonotonic decay of the ACF by increasing lag-time is shown. Moreover, in a certain regime of the noise parameters the ACF demonstrates anticorrelation as well as related sign reversals at some values of the lag-time. The conditions for the appearance of thismore » highly unexpected effect are also discussed.« less

The stochastic model for ternary and quaternary alloys: Application of the Bernoulli relation to the phonon spectra of mixed crystals

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

Marchewka, M., E-mail: marmi@ur.edu.pl; Woźny, M.; Polit, J.

2014-03-21

To understand and interpret the experimental data on the phonon spectra of the solid solutions, it is necessary to describe mathematically the non-regular distribution of atoms in their lattices. It appears that such description is possible in case of the strongly stochastically homogenous distribution which requires a great number of atoms and very carefully mixed alloys. These conditions are generally fulfilled in case of high quality homogenous semiconductor solid solutions of the III–V and II–VI semiconductor compounds. In this case, we can use the Bernoulli relation describing probability of the occurrence of one n equivalent event which can be applied,more » to the probability of finding one from n configurations in the solid solution lattice. The results described in this paper for ternary HgCdTe and GaAsP as well as quaternary ZnCdHgTe can provide an affirmative answer to the question: whether stochastic geometry, e.g., the Bernoulli relation, is enough to describe the observed phonon spectra.« less

A second-order accurate kinetic-theory-based method for inviscid compressible flows

NASA Technical Reports Server (NTRS)

Deshpande, Suresh M.

1986-01-01

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Euler potentials of current-free fields expressed in spherical harmonics

NASA Technical Reports Server (NTRS)

Stern, David P.

1994-01-01

Given a magnetic field B = -del(vector differential operator)(sub gamma) with gamma expanded in spherical harmonics, it is shown that analytic Euler potentials may be derived for B if gamma is asymmetrical but contains only the contribution of a single index n. This work generalizes a result for sectorial harmonics with n = m, derived by Willis and Gardiner (1988).

Lagrangians and Euler morphisms from connections on the frame bundle

NASA Astrophysics Data System (ADS)

Kurek, J.; Mikulski, W. M.

2011-07-01

We classify all natural operators transforming torsion free classical linear connections ∇ on m-dimensional manifolds M into r-th order Lagrangians λ(∇) and Euler morphisms E(∇) on the linear frame bundle P1M. We also briefly write how this classification result can be generalized on higher order frame bundles PkM instead of P1M.

An installed nacelle design code using a multiblock Euler solver. Volume 2: User guide

NASA Technical Reports Server (NTRS)

Chen, H. C.

1992-01-01

This is a user manual for the general multiblock Euler design (GMBEDS) code. The code is for the design of a nacelle installed on a geometrically complex configuration such as a complete airplane with wing/body/nacelle/pylon. It consists of two major building blocks: a design module developed by LaRC using directive iterative surface curvature (DISC); and a general multiblock Euler (GMBE) flow solver. The flow field surrounding a complex configuration is divided into a number of topologically simple blocks to facilitate surface-fitted grid generation and improve flow solution efficiency. This user guide provides input data formats along with examples of input files and a Unix script for program execution in the UNICOS environment.

Chebyshev collocation approach for vibration analysis of functionally graded porous beams based on third-order shear deformation theory

NASA Astrophysics Data System (ADS)

Wattanasakulpong, Nuttawit; Chaikittiratana, Arisara; Pornpeerakeat, Sacharuck

2018-06-01

In this paper, vibration analysis of functionally graded porous beams is carried out using the third-order shear deformation theory. The beams have uniform and non-uniform porosity distributions across their thickness and both ends are supported by rotational and translational springs. The material properties of the beams such as elastic moduli and mass density can be related to the porosity and mass coefficient utilizing the typical mechanical features of open-cell metal foams. The Chebyshev collocation method is applied to solve the governing equations derived from Hamilton's principle, which is used in order to obtain the accurate natural frequencies for the vibration problem of beams with various general and elastic boundary conditions. Based on the numerical experiments, it is revealed that the natural frequencies of the beams with asymmetric and non-uniform porosity distributions are higher than those of other beams with uniform and symmetric porosity distributions.

Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

NASA Astrophysics Data System (ADS)

Krasovskii, A. A.; Lebedev, P. D.; Tarasyev, A. M.

2017-05-01

We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.

Sampling schemes and parameter estimation for nonlinear Bernoulli-Gaussian sparse models

NASA Astrophysics Data System (ADS)

Boudineau, Mégane; Carfantan, Hervé; Bourguignon, Sébastien; Bazot, Michael

2016-06-01

We address the sparse approximation problem in the case where the data are approximated by the linear combination of a small number of elementary signals, each of these signals depending non-linearly on additional parameters. Sparsity is explicitly expressed through a Bernoulli-Gaussian hierarchical model in a Bayesian framework. Posterior mean estimates are computed using Markov Chain Monte-Carlo algorithms. We generalize the partially marginalized Gibbs sampler proposed in the linear case in [1], and build an hybrid Hastings-within-Gibbs algorithm in order to account for the nonlinear parameters. All model parameters are then estimated in an unsupervised procedure. The resulting method is evaluated on a sparse spectral analysis problem. It is shown to converge more efficiently than the classical joint estimation procedure, with only a slight increase of the computational cost per iteration, consequently reducing the global cost of the estimation procedure.

Development of an Aeroelastic Code Based on an Euler/Navier-Stokes Aerodynamic Solver

NASA Technical Reports Server (NTRS)

Bakhle, Milind A.; Srivastava, Rakesh; Keith, Theo G., Jr.; Stefko, George L.; Janus, Mark J.

1996-01-01

This paper describes the development of an aeroelastic code (TURBO-AE) based on an Euler/Navier-Stokes unsteady aerodynamic analysis. A brief review of the relevant research in the area of propulsion aeroelasticity is presented. The paper briefly describes the original Euler/Navier-Stokes code (TURBO) and then details the development of the aeroelastic extensions. The aeroelastic formulation is described. The modeling of the dynamics of the blade using a modal approach is detailed, along with the grid deformation approach used to model the elastic deformation of the blade. The work-per-cycle approach used to evaluate aeroelastic stability is described. Representative results used to verify the code are presented. The paper concludes with an evaluation of the development thus far, and some plans for further development and validation of the TURBO-AE code.

The most precise computations using Euler's method in standard floating-point arithmetic applied to modelling of biological systems.

PubMed

Kalinina, Elizabeth A

2013-08-01

The explicit Euler's method is known to be very easy and effective in implementation for many applications. This article extends results previously obtained for the systems of linear differential equations with constant coefficients to arbitrary systems of ordinary differential equations. Optimal (providing minimum total error) step size is calculated at each step of Euler's method. Several examples of solving stiff systems are included. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Conical Euler simulation and active suppression of delta wing rocking motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

A conical Euler code was developed to study unsteady vortex-dominated flows about rolling highly-swept delta wings, undergoing either forced or free-to-roll motions including active roll suppression. The flow solver of the code involves a multistage Runge-Kutta time-stepping scheme which uses a finite volume spatial discretization of the Euler equations on an unstructured grid of triangles. The code allows for the additional analysis of the free-to-roll case, by including the rigid-body equation of motion for its simultaneous time integration with the governing flow equations. Results are presented for a 75 deg swept sharp leading edge delta wing at a freestream Mach number of 1.2 and at alpha equal to 10 and 30 deg angle of attack. A forced harmonic analysis indicates that the rolling moment coefficient provides: (1) a positive damping at the lower angle of attack equal to 10 deg, which is verified in a free-to-roll calculation; (2) a negative damping at the higher angle of attack equal to 30 deg at the small roll amplitudes. A free-to-roll calculation for the latter case produces an initially divergent response, but as the amplitude of motion grows with time, the response transitions to a wing-rock type of limit cycle oscillation. The wing rocking motion may be actively suppressed, however, through the use of a rate-feedback control law and antisymmetrically deflected leading edge flaps. The descriptions of the conical Euler flow solver and the free-to-roll analysis are presented. Results are also presented which give insight into the flow physics associated with unsteady vortical flows about forced and free-to-roll delta wings, including the active roll suppression of this wing-rock phenomenon.

One-dimensional high-order compact method for solving Euler's equations

NASA Astrophysics Data System (ADS)

Mohamad, M. A. H.; Basri, S.; Basuno, B.

2012-06-01

In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector splitting. From this observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The AUSM scheme is based on the third-order compact scheme to the approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with computational results

Restricted Euler dynamics along trajectories of small inertial particles in turbulence

NASA Astrophysics Data System (ADS)

Johnson, Perry; Meneveau, Charles

2016-11-01

The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple, low-dimensional dynamical system representation of Lagrangian evolution of velocity gradients in fluid turbulence, at least for short times. Here we derive a new restricted Euler dynamical system for the velocity gradient evolution of inertial particles such as solid particles in a gas or droplets and bubbles in turbulent liquid flows. The model is derived in the limit of small (sub Kolmogorov scale) particles and low Stokes number. The system exhibits interesting fixed points, stability and invariant properties. Comparisons with data from Direct Numerical Simulations show that the model predicts realistic trends such as the tendency of increased straining over rotation along heavy particle trajectories and, for light particles such as bubbles, the tendency of severely reduced self-stretching of strain-rate. Supported by a National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1232825 and by a Grant from The Gulf of Mexico Research Initiative.

Prediction of drag at subsonic and transonic speeds using Euler methods

NASA Technical Reports Server (NTRS)

Nikfetrat, K.; Van Dam, C. P.; Vijgen, P. M. H. W.; Chang, I. C.

1992-01-01

A technique for the evaluation of aerodynamic drag from flowfield solutions based on the Euler equations is discussed. The technique is limited to steady attached flows around three-dimensional configurations in the absence of active systems such as surface blowing/suction and propulsion. It allows the decomposition of the total drag into induced drag and wave drag and, consequently, it provides more information on the drag sources than the conventional surface-pressure integration technique. The induced drag is obtained from the integration of the kinetic energy (per unit distance) of the trailing vortex system on a wake plane and the wave drag is obtained from the integration of the entropy production on a plane just downstream of the shocks. The drag-evaluation technique is applied to three-dimensional flowfield solutions for the ONERA M6 wing as well as an aspect-ratio-7 wing with an elliptic spanwise chord distribution and an NACA-0012 section shape. Comparisons between the drag obtained with the present technique and the drag based on the integration of surface pressures are presented for two Euler codes.

Simulations of dynamics of plunge and pitch of a three-dimensional flexible wing in a low Reynolds number flow

NASA Astrophysics Data System (ADS)

Qi, Dewei; Liu, Yingming; Shyy, Wei; Aono, Hikaru

2010-09-01

The lattice Boltzmann flexible particle method (LBFPM) is used to simulate fluid-structure interaction and motion of a flexible wing in a three-dimensional space. In the method, a beam with rectangular cross section has been discretized into a chain of rigid segments. The segments are connected through ball and socket joints at their ends and may be bent and twisted. Deformation of flexible structure is treated with a linear elasticity model through bending and twisting. It is demonstrated that the flexible particle method (FPM) can approximate the nonlinear Euler-Bernoulli beam equation without resorting to a nonlinear elasticity model. Simulations of plunge and pitch of flexible wing at Reynolds number Re=136 are conducted in hovering condition by using the LBFPM. It is found that both lift and drag forces increase first, then decrease dramatically as the bending rigidity in spanwise direction decreases and that the lift and drag forces are sensitive to rigidity in a certain range. It is shown that the downwash flows induced by wing tip and trailing vortices in wake area are larger for a flexible wing than for a rigid wing, lead to a smaller effective angle of attack, and result in a larger lift force.

A linear complementarity method for the solution of vertical vehicle-track interaction

NASA Astrophysics Data System (ADS)

Zhang, Jian; Gao, Qiang; Wu, Feng; Zhong, Wan-Xie

2018-02-01

A new method is proposed for the solution of the vertical vehicle-track interaction including a separation between wheel and rail. The vehicle is modelled as a multi-body system using rigid bodies, and the track is treated as a three-layer beam model in which the rail is considered as an Euler-Bernoulli beam and both the sleepers and the ballast are represented by lumped masses. A linear complementarity formulation is directly established using a combination of the wheel-rail normal contact condition and the generalised-α method. This linear complementarity problem is solved using the Lemke algorithm, and the wheel-rail contact force can be obtained. Then the dynamic responses of the vehicle and the track are solved without iteration based on the generalised-α method. The same equations of motion for the vehicle and track are adopted at the different wheel-rail contact situations. This method can remove some restrictions, that is, time-dependent mass, damping and stiffness matrices of the coupled system, multiple equations of motion for the different contact situations and the effect of the contact stiffness. Numerical results demonstrate that the proposed method is effective for simulating the vehicle-track interaction including a separation between wheel and rail.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Batina, John T.; Yang, Henry T. Y.

1992-01-01

Quality assessment procedures are described for two-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate accuracy of an implicit upwind Euler solution algorithm.

Effect of Coannular Flow on Linearized Euler Equation Predictions of Jet Noise

NASA Technical Reports Server (NTRS)

Hixon, R.; Shih, S.-H.; Mankbadi, Reda R.

1997-01-01

An improved version of a previously validated linearized Euler equation solver is used to compute the noise generated by coannular supersonic jets. Results for a single supersonic jet are compared to the results from both a normal velocity profile and an inverted velocity profile supersonic jet.

Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper [1], focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.

A Thermodynamically General Theory for Convective Circulations and Vortices

NASA Astrophysics Data System (ADS)

Renno, N. O.

2007-12-01

Convective circulations and vortices are common features of atmospheres that absorb low-entropy-energy at higher temperatures than they reject high-entropy-energy to space. These circulations range from small to planetary-scale and play an important role in the vertical transport of heat, momentum, and tracer species. Thus, the development of theoretical models for convective phenomena is important to our understanding of many basic features of planetary atmospheres. A thermodynamically general theory for convective circulations and vortices is proposed. The theory includes irreversible processes and quantifies the pressure drop between the environment and any point in a convective updraft. The article's main result is that the proposed theory provides an expression for the pressure drop along streamlines or streamtubes that is a generalization of Bernoulli's equation to convective circulations. We speculate that the proposed theory not only explains the intensity, but also shed light on other basic features of convective circulations and vortices.

Renormalization group theory for percolation in time-varying networks.

PubMed

Karschau, Jens; Zimmerling, Marco; Friedrich, Benjamin M

2018-05-22

Motivated by multi-hop communication in unreliable wireless networks, we present a percolation theory for time-varying networks. We develop a renormalization group theory for a prototypical network on a regular grid, where individual links switch stochastically between active and inactive states. The question whether a given source node can communicate with a destination node along paths of active links is equivalent to a percolation problem. Our theory maps the temporal existence of multi-hop paths on an effective two-state Markov process. We show analytically how this Markov process converges towards a memoryless Bernoulli process as the hop distance between source and destination node increases. Our work extends classical percolation theory to the dynamic case and elucidates temporal correlations of message losses. Quantification of temporal correlations has implications for the design of wireless communication and control protocols, e.g. in cyber-physical systems such as self-organized swarms of drones or smart traffic networks.

Accurate upwind methods for the Euler equations

NASA Technical Reports Server (NTRS)

Huynh, Hung T.

1993-01-01

A new class of piecewise linear methods for the numerical solution of the one-dimensional Euler equations of gas dynamics is presented. These methods are uniformly second-order accurate, and can be considered as extensions of Godunov's scheme. With an appropriate definition of monotonicity preservation for the case of linear convection, it can be shown that they preserve monotonicity. Similar to Van Leer's MUSCL scheme, they consist of two key steps: a reconstruction step followed by an upwind step. For the reconstruction step, a monotonicity constraint that preserves uniform second-order accuracy is introduced. Computational efficiency is enhanced by devising a criterion that detects the 'smooth' part of the data where the constraint is redundant. The concept and coding of the constraint are simplified by the use of the median function. A slope steepening technique, which has no effect at smooth regions and can resolve a contact discontinuity in four cells, is described. As for the upwind step, existing and new methods are applied in a manner slightly different from those in the literature. These methods are derived by approximating the Euler equations via linearization and diagonalization. At a 'smooth' interface, Harten, Lax, and Van Leer's one intermediate state model is employed. A modification for this model that can resolve contact discontinuities is presented. Near a discontinuity, either this modified model or a more accurate one, namely, Roe's flux-difference splitting. is used. The current presentation of Roe's method, via the conceptually simple flux-vector splitting, not only establishes a connection between the two splittings, but also leads to an admissibility correction with no conditional statement, and an efficient approximation to Osher's approximate Riemann solver. These reconstruction and upwind steps result in schemes that are uniformly second-order accurate and economical at smooth regions, and yield high resolution at discontinuities.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

1992-01-01

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

Distributed parameter modeling to prevent charge cancellation for discrete thickness piezoelectric energy harvester

NASA Astrophysics Data System (ADS)

Krishnasamy, M.; Qian, Feng; Zuo, Lei; Lenka, T. R.

2018-03-01

The charge cancellation due to the change of strain along single continuous piezoelectric layer can remarkably affect the performance of a cantilever based harvester. In this paper, analytical models using distributed parameters are developed with some extent of averting the charge cancellation in cantilever piezoelectric transducer where the piezoelectric layers are segmented at strain nodes of concerned vibration mode. The electrode of piezoelectric segments are parallelly connected with a single external resistive load in the 1st model (Model 1). While each bimorph piezoelectric layers are connected in parallel to a resistor to form an independent circuit in the 2nd model (Model 2). The analytical expressions of the closed-form electromechanical coupling responses in frequency domain under harmonic base excitation are derived based on the Euler-Bernoulli beam assumption for both models. The developed analytical models are validated by COMSOL and experimental results. The results demonstrate that the energy harvesting performance of the developed segmented piezoelectric layer models is better than the traditional model of continuous piezoelectric layer.

Computational investigation of large-scale vortex interaction with flexible bodies

NASA Astrophysics Data System (ADS)

Connell, Benjamin; Yue, Dick K. P.

2003-11-01

The interaction of large-scale vortices with flexible bodies is examined with particular interest paid to the energy and momentum budgets of the system. Finite difference direct numerical simulation of the Navier-Stokes equations on a moving curvilinear grid is coupled with a finite difference structural solver of both a linear membrane under tension and linear Euler-Bernoulli beam. The hydrodynamics and structural dynamics are solved simultaneously using an iterative procedure with the external structural forcing calculated from the hydrodynamics at the surface and the flow-field velocity boundary condition given by the structural motion. We focus on an investigation into the canonical problem of a vortex-dipole impinging on a flexible membrane. It is discovered that the structural properties of the membrane direct the interaction in terms of the flow evolution and the energy budget. Pressure gradients associated with resonant membrane response are shown to sustain the oscillatory motion of the vortex pair. Understanding how the key mechanisms in vortex-body interactions are guided by the structural properties of the body is a prerequisite to exploiting these mechanisms.

Attitude tracking control of flexible spacecraft with large amplitude slosh

NASA Astrophysics Data System (ADS)

Deng, Mingle; Yue, Baozeng

2017-12-01

This paper is focused on attitude tracking control of a spacecraft that is equipped with flexible appendage and partially filled liquid propellant tank. The large amplitude liquid slosh is included by using a moving pulsating ball model that is further improved to estimate the settling location of liquid in microgravity or a zero-g environment. The flexible appendage is modelled as a three-dimensional Bernoulli-Euler beam, and the assumed modal method is employed. A hybrid controller that combines sliding mode control with an adaptive algorithm is designed for spacecraft to perform attitude tracking. The proposed controller has proved to be asymptotically stable. A nonlinear model for the overall coupled system including spacecraft attitude dynamics, liquid slosh, structural vibration and control action is established. Numerical simulation results are presented to show the dynamic behaviors of the coupled system and to verify the effectiveness of the control approach when the spacecraft undergoes the disturbance produced by large amplitude slosh and appendage vibration. Lastly, the designed adaptive algorithm is found to be effective to improve the precision of attitude tracking.

Perturbational blowup solutions to the compressible Euler equations with damping.

PubMed

Cheung, Ka Luen

2016-01-01

The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions. In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant. With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points. The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.

Stochastic cooling of bunched beams from fluctuation and kinetic theory

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

Chattopadhyay, S.

1982-09-01

A theoretical formalism for stochastic phase-space cooling of bunched beams in storage rings is developed on the dual basis of classical fluctuation theory and kinetic theory of many-body systems in phase-space. The physics is that of a collection of three-dimensional oscillators coupled via retarded nonconservative interactions determined by an electronic feedback loop. At the heart of the formulation is the existence of several disparate time-scales characterizing the cooling process. Both theoretical approaches describe the cooling process in the form of a Fokker-Planck transport equation in phase-space valid up to second order in the strength and first order in the auto-correlationmore » of the cooling signal. With neglect of the collective correlations induced by the feedback loop, identical expressions are obtained in both cases for the coherent damping and Schottky noise diffusion coefficients. These are expressed in terms of Fourier coefficients in a harmonic decomposition in angle of the generalized nonconservative cooling force written in canonical action-angle variables of the particles in six-dimensional phase-space. Comparison of analytic results to a numerical simulation study with 90 pseudo-particles in a model cooling system is presented.« less

On the commutator of C^{\\infty}} -symmetries and the reduction of Euler-Lagrange equations

NASA Astrophysics Data System (ADS)

Ruiz, A.; Muriel, C.; Olver, P. J.

2018-04-01

A novel procedure to reduce by four the order of Euler-Lagrange equations associated to nth order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two \

Algorithms for the Euler and Navier-Stokes equations for supercomputers

NASA Technical Reports Server (NTRS)

Turkel, E.

1985-01-01

The steady state Euler and Navier-Stokes equations are considered for both compressible and incompressible flow. Methods are found for accelerating the convergence to a steady state. This acceleration is based on preconditioning the system so that it is no longer time consistent. In order that the acceleration technique be scheme-independent, this preconditioning is done at the differential equation level. Applications are presented for very slow flows and also for the incompressible equations.

Experimental and Theoretical Progress on the GEM Theory

NASA Astrophysics Data System (ADS)

Brandenburg, J. E.

This paper reports experimental and theoretical progress on the GEM unification theory. In theoretical progress, the derivation of the GEM theory using it in a fully covariant form is achieved based on the principle of self-cancellation of the ZPF EM stress-momentum tensor. This derivation reveals that the final Gravity-EM system obeys a Helmholtz-like equation resembling that governing sound propagation. Finally an improved derivation of the formula for the Newton Gravitation constant is shown, qresulting in the formula G = e2/(4πɛ0 me mp) α exp (-2 (α-.86/σ2…) = 6.673443 x10-11 N-m2 kg-2 that agrees with experimental values to 3 parts per 100,000. Experiments have found parity violating weight reductions in gyroscopes driven by rotating EM fields. These experiments appear to confirm gravity modification using electromagnetism predicted by the GEM theory through the Vacuum Bernoulli Equation.

Comparison of a Convected Helmholtz and Euler Model for Impedance Eduction in Flow

NASA Technical Reports Server (NTRS)

Watson, Willie R.; Jones, Michael G.

2006-01-01

Impedances educed from a well-tested convected Helmholtz model are compared to that of a recently developed linearized Euler model using two ceramic test liners under the assumed conditions or uniform flow and a plane wave source. The convected Helmholtz model is restricted to uniform mean flow whereas the linearized Euler model can account for the effect or the shear layer. Test data to educe the impedance is acquired from measurements obtained in the NASA Langley Research Center Grazing Incidence Tube for mean flow Mach numbers ranging from 0.0 to 0.5 and source frequencies ranging from 0.5 kHz to 3.0 kHz. The unknown impedance of the liner b educed by judiciously chooingth e impedance via an optimization method to match the measured acoustic pressure on the wall opposite the test liner. Results are presented on four spatial grids using three different optimization methods (contour deformation, Davidon-Fletcher Powell, and the Genetic Algorithm). All three optimization methods converge to the same impedance when used with the same model and to nearly identical impedances when used on different models. h anomaly was observed only at 0.5 kHz for high mean flow speeds. The anomaly is likely due to the use of measured data in a flow regime where shear layer effects are important but are neglected in the math models. Consistency between the impedances educed using the two models provides confidence that the linearized Euler model is ready For application to more realistic flows, such as those containing shear layers.

Paleomagnetic Euler Poles and the Apparent Polar Wander and Absolute Motion of North America Since the Carboniferous

NASA Astrophysics Data System (ADS)

Gordon, Richard G.; Cox, Allan; O'Hare, Scott

1984-10-01

The apparent polar wander path for a plate is determined from paleomagnetic data by plotting a time sequence of paleomagnetic poles, each representing the location of the earth's spin axis as seen from the plate. Apparent polar wander paths consist of long, gently curved segments termed tracks linked by short segments with sharp curvature termed cusps. The tracks correspond to time intervals when the direction of plate motion was constant, and the cusps correspond to time intervals when the direction of plate motion was changing. Apparent polar wander tracks, like hot spot tracks, tend to lie along small circles. The center of a circle is called a hot spot Euler pole in the case of hot spot tracks and a paleomagnetic Euler pole in the case of paleomagnetic apparent polar wander paths. Both types of tracks mark the motion of a plate with respect to a point, a rising mantle plume in the case of hot spot tracks and the earth's paleomagnetic axis in the case of apparent polar wander paths. Unlike approaches uced in previous studies, paleomagnetic Euler pole analysis yields all three components of motion—including the east-west motion—of a plate with respect to the paleomagnetic axis. A new method for analyzing paleomagnetic poles along a track by using a maximum likelihood criterion gives the best fit paleomagnetic Euler pole and an ellipsoid of 95% confidence about the paleomagnetic Euler pole. In analyzing synthetic and real data, we found that the ellipsoids are elongate, the long axes being aligned with a great circle drawn from the paleomagnetic Euler pole to the center of the apparent polar wander track. This elongation is caused by the azimuths of circular tracks being better defined than their radii of curvature. A Jurassic-Cretaceous paleomagnetic Euler pole for North America was determined from 13 paleomagnetic poles. This track begins with the Wingate and Kayenta formations (about 200 Ma) and ends with the Niobrara Formation (about 87 Ma). Morgan's hot

Solution of the nonlinear mixed Volterra-Fredholm integral equations by hybrid of block-pulse functions and Bernoulli polynomials.

PubMed

Mashayekhi, S; Razzaghi, M; Tripak, O

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Solution of the Nonlinear Mixed Volterra-Fredholm Integral Equations by Hybrid of Block-Pulse Functions and Bernoulli Polynomials

PubMed Central

Mashayekhi, S.; Razzaghi, M.; Tripak, O.

2014-01-01

A new numerical method for solving the nonlinear mixed Volterra-Fredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The operational matrices of integration and product are given. These matrices are then utilized to reduce the nonlinear mixed Volterra-Fredholm integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. PMID:24523638

Theory and simulation of electron beam dynamics in the AWE superswarf magnetically immersed diode

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

Oliver, B.V.; Welch, D.R.; Olson, C.L.

1999-07-01

Results from numerical simulation and analytic theory of magnetically immersed diode behavior on the United Kingdom's Atomic Weapons Establishment (AWE) Superswarf accelerator are presented. The immersed diode consists of a cylindrical needle point cathode immersed in a strong {approximately}10--20 T solenoidal magnetic field. The anode-cathode (A-K) accelerating gap is held at vacuum and is {approximately}5--10 cm in length, with the anode/target located at the mid-plane of the solenoid. Typical accelerator parameters are 5--6 MeV and 40 kA. Ions emitted from the anode target stream toward the cathode and interact strongly with the electron beam. Collective oscillations between the beam electronsmore » and counter-streaming ions are driven unstable and results in a corkscrew rotation of the beam, yielding a time-integrated spot size substantially larger than that expected from single particle motion. This magnetized ion-hose instability is three dimensional. On the other hand, beam transverse temperature variations, although slightly enhanced in 3D, are primarily due to changes in the effective potential at the cathode (a combination of both the electrostatic and vector potential) and are manifest in 2D. Simulation studies examining spot and dose variation with varying cathode diameter and A-K gap distance are presented and confirm the above mentioned trends. Conclusions are that the diode current is determined by standard di-polar space-charge limited emissions, the minimum beam spot-size is limited by the ion-hose instability saturation amplitude, and the beam transverse temperature at the target is a function of the initial conditions on the cathode. Comparison to existing data will also be presented.« less

Comprehensive nonlocal analysis of piezoelectric nanobeams with surface effects in bending, buckling and vibrations under magneto-electro-thermo-mechanical loading

NASA Astrophysics Data System (ADS)

Ebrahimi-Nejad, Salman; Boreiry, Mahya

2018-03-01

The bending, buckling and vibrational behavior of size-dependent piezoelectric nanobeams under thermo-magneto-mechano-electrical environment are investigated by performing a parametric study, in the presence of surface effects. The Gurtin-Murdoch surface elasticity and Eringen’s nonlocal elasticity theories are applied in the framework of Euler–Bernoulli beam theory to obtain a new non-classical size-dependent beam model for dynamic and static analyses of piezoelectric nanobeams. In order to satisfy the surface equilibrium equations, cubic variation of stress with beam thickness is assumed for the bulk stress component which is neglected in classical beam models. Results are obtained for clamped - simply-supported (C-S) and simply-supported - simply-supported (S-S) boundary conditions using a proposed analytical solution method. Numerical examples are presented to demonstrate the effects of length, surface effects, nonlocal parameter and environmental changes (temperature, magnetic field and external voltage) on deflection, critical buckling load and natural frequency for each boundary condition. Results of this study can serve as benchmarks for the design and analysis of nanostructures of magneto-electro-thermo-elastic materials.

Theory of bright-field scanning transmission electron microscopy for tomography

NASA Astrophysics Data System (ADS)

Levine, Zachary H.

2005-02-01

Radiation transport theory is applied to electron microscopy of samples composed of one or more materials. The theory, originally due to Goudsmit and Saunderson, assumes only elastic scattering and an amorphous medium dominated by atomic interactions. For samples composed of a single material, the theory yields reasonable parameter-free agreement with experimental data taken from the literature for the multiple scattering of 300-keV electrons through aluminum foils up to 25μm thick. For thin films, the theory gives a validity condition for Beer's law. For thick films, a variant of Molière's theory [V. G. Molière, Z. Naturforschg. 3a, 78 (1948)] of multiple scattering leads to a form for the bright-field signal for foils in the multiple-scattering regime. The signal varies as [tln(e1-2γt/τ)]-1 where t is the path length of the beam, τ is the mean free path for elastic scattering, and γ is Euler's constant. The Goudsmit-Saunderson solution interpolates numerically between these two limits. For samples with multiple materials, elemental sensitivity is developed through the angular dependence of the scattering. From the elastic scattering cross sections of the first 92 elements, a singular-value decomposition of a vector space spanned by the elastic scattering cross sections minus a delta function shows that there is a dominant common mode, with composition-dependent corrections of about 2%. A mathematically correct reconstruction procedure beyond 2% accuracy requires the acquisition of the bright-field signal as a function of the scattering angle. Tomographic reconstructions are carried out for three singular vectors of a sample problem with four elements Cr, Cu, Zr, and Te. The three reconstructions are presented jointly as a color image; all four elements are clearly identifiable throughout the image.

Quantum power functional theory for many-body dynamics

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

Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de

2015-11-07

We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.

An optimized Nash nonlinear grey Bernoulli model based on particle swarm optimization and its application in prediction for the incidence of Hepatitis B in Xinjiang, China.

PubMed

Zhang, Liping; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2014-06-01

In this paper, by using a particle swarm optimization algorithm to solve the optimal parameter estimation problem, an improved Nash nonlinear grey Bernoulli model termed PSO-NNGBM(1,1) is proposed. To test the forecasting performance, the optimized model is applied for forecasting the incidence of hepatitis B in Xinjiang, China. Four models, traditional GM(1,1), grey Verhulst model (GVM), original nonlinear grey Bernoulli model (NGBM(1,1)) and Holt-Winters exponential smoothing method, are also established for comparison with the proposed model under the criteria of mean absolute percentage error and root mean square percent error. The prediction results show that the optimized NNGBM(1,1) model is more accurate and performs better than the traditional GM(1,1), GVM, NGBM(1,1) and Holt-Winters exponential smoothing method. Copyright © 2014. Published by Elsevier Ltd.

The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory

PubMed Central

Bosbach, Wolfram A.

2015-01-01

Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603

Recursive Newton-Euler formulation of manipulator dynamics

NASA Technical Reports Server (NTRS)

Nasser, M. G.

1989-01-01

A recursive Newton-Euler procedure is presented for the formulation and solution of manipulator dynamical equations. The procedure includes rotational and translational joints and a topological tree. This model was verified analytically using a planar two-link manipulator. Also, the model was tested numerically against the Walker-Orin model using the Shuttle Remote Manipulator System data. The hinge accelerations obtained from both models were identical. The computational requirements of the model vary linearly with the number of joints. The computational efficiency of this method exceeds that of Walker-Orin methods. This procedure may be viewed as a considerable generalization of Armstrong's method. A six-by-six formulation is adopted which enhances both the computational efficiency and simplicity of the model.

Stochastic Optimal Prediction with Application to Averaged Euler Equations

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

Bell, John; Chorin, Alexandre J.; Crutchfield, William

Optimal prediction (OP) methods compensate for a lack of resolution in the numerical solution of complex problems through the use of an invariant measure as a prior measure in the Bayesian sense. In first-order OP, unresolved information is approximated by its conditional expectation with respect to the invariant measure. In higher-order OP, unresolved information is approximated by a stochastic estimator, leading to a system of random or stochastic differential equations. We explain the ideas through a simple example, and then apply them to the solution of Averaged Euler equations in two space dimensions.

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

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

Hong QIn, Ronald Davidson

2011-07-18

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.« less

Generalized Courant-Snyder theory and Kapchinskij-Vladimirskij distribution for high-intensity beams in a coupled transverse focusing lattice

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

Qin Hong; Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026; Davidson, Ronald C.

2011-05-15

The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in an uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant.more » This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation and reduces beam pulsation.« less

Conical Euler solution for a highly-swept delta wing undergoing wing-rock motion

NASA Technical Reports Server (NTRS)

Lee, Elizabeth M.; Batina, John T.

1990-01-01

Modifications to an unsteady conical Euler code for the free-to-roll analysis of highly-swept delta wings are described. The modifications involve the addition of the rolling rigid-body equation of motion for its simultaneous time-integration with the governing flow equations. The flow solver utilized in the Euler code includes a multistage Runge-Kutta time-stepping scheme which uses a finite-volume spatial discretization on an unstructured mesh made up of triangles. Steady and unsteady results are presented for a 75 deg swept delta wing at a freestream Mach number of 1.2 and an angle of attack of 30 deg. The unsteady results consist of forced harmonic and free-to-roll calculations. The free-to-roll case exhibits a wing rock response produced by unsteady aerodynamics consistent with the aerodynamics of the forced harmonic results. Similarities are shown with a wing-rock time history from a low-speed wind tunnel test.

Towards Perfectly Absorbing Boundary Conditions for Euler Equations

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Hu, Fang Q.; Hussaini, M. Yousuff

1997-01-01

In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

Improved Gaussian Beam-Scattering Algorithm

NASA Technical Reports Server (NTRS)

Lock, James A.

1995-01-01

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Solution of the surface Euler equations for accurate three-dimensional boundary-layer analysis of aerodynamic configurations

NASA Technical Reports Server (NTRS)

Iyer, V.; Harris, J. E.

1987-01-01

The three-dimensional boundary-layer equations in the limit as the normal coordinate tends to infinity are called the surface Euler equations. The present paper describes an accurate method for generating edge conditions for three-dimensional boundary-layer codes using these equations. The inviscid pressure distribution is first interpolated to the boundary-layer grid. The surface Euler equations are then solved with this pressure field and a prescribed set of initial and boundary conditions to yield the velocities along the two surface coordinate directions. Results for typical wing and fuselage geometries are presented. The smoothness and accuracy of the edge conditions obtained are found to be superior to the conventional interpolation procedures.

Bernoulli, Darwin, and Sagan: the probability of life on other planets

NASA Astrophysics Data System (ADS)

Rossmo, D. Kim

2017-04-01

The recent discovery that billions of planets in the Milky Way Galaxy may be in circumstellar habitable zones has renewed speculation over the possibility of extraterrestrial life. The Drake equation is a probabilistic framework for estimating the number of technological advanced civilizations in our Galaxy; however, many of the equation's component probabilities are either unknown or have large error intervals. In this paper, a different method of examining this question is explored, one that replaces the various Drake factors with the single estimate for the probability of life existing on Earth. This relationship can be described by the binomial distribution if the presence of life on a given number of planets is equated to successes in a Bernoulli trial. The question of exoplanet life may then be reformulated as follows - given the probability of one or more independent successes for a given number of trials, what is the probability of two or more successes? Some of the implications of this approach for finding life on exoplanets are discussed.

A roadmap for optimal control: the right way to commute.

PubMed

Ross, I Michael

2005-12-01

Optimal control theory is the foundation for many problems in astrodynamics. Typical examples are trajectory design and optimization, relative motion control of distributed space systems and attitude steering. Many such problems in astrodynamics are solved by an alternative route of mathematical analysis and deep physical insight, in part because of the perception that an optimal control framework generates hard problems. Although this is indeed true of the Bellman and Pontryagin frameworks, the covector mapping principle provides a neoclassical approach that renders hard problems easy. That is, although the origins of this philosophy can be traced back to Bernoulli and Euler, it is essentially modern as a result of the strong linkage between approximation theory, set-valued analysis and computing technology. Motivated by the broad success of this approach, mission planners are now conceiving and demanding higher performance from space systems. This has resulted in new set of theoretical and computational problems. Recently, under the leadership of NASA-GRC, several workshops were held to address some of these problems. This paper outlines the theoretical issues stemming from practical problems in astrodynamics. Emphasis is placed on how it pertains to advanced mission design problems.

Centrifuge Rotor Models: A Comparison of the Euler-Lagrange and the Bond Graph Modeling Approach

NASA Technical Reports Server (NTRS)

Granda, Jose J.; Ramakrishnan, Jayant; Nguyen, Louis H.

2006-01-01

A viewgraph presentation on centrifuge rotor models with a comparison using Euler-Lagrange and bond graph methods is shown. The topics include: 1) Objectives; 2) MOdeling Approach Comparisons; 3) Model Structures; and 4) Application.

Implementation of a parallel unstructured Euler solver on the CM-5

NASA Technical Reports Server (NTRS)

Morano, Eric; Mavriplis, D. J.

1995-01-01

An efficient unstructured 3D Euler solver is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow solver is discussed.

Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.

PubMed

Ahmadi, S M; Campoli, G; Amin Yavari, S; Sajadi, B; Wauthle, R; Schrooten, J; Weinans, H; Zadpoor, A A

2014-06-01

Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations. Copyright © 2014 Elsevier Ltd

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

NASA Astrophysics Data System (ADS)

Nazockdast, Ehssan; Rahimian, Abtin; Zorin, Denis; Shelley, Michael

2017-01-01

We present a novel platform for the large-scale simulation of three-dimensional fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space in three dimensions. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling. This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular assemblies of flexible fibers. We use non-local slender body theory to compute the fluid-structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multipole method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by nonlinear Euler-Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit time-stepping to resolve large fiber deformations, and to allow time-steps not excessively constrained by temporal stiffness or fiber-fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of

Ripple pattern formation on silicon surfaces by low-energy ion-beam erosion: Experiment and theory

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

Ziberi, B.; Frost, F.; Rauschenbach, B.

The topography evolution of Si surfaces during low-energy noble-gas ion-beam erosion (ion energy {<=}2000 eV) at room temperature has been studied. Depending on the ion-beam parameters, self-organized ripple patterns evolve on the surface with a wavelength {lambda}<100 nm. Ripple patterns were found to occur at near-normal ion incidence angles (5 deg. -30 deg.) with the wave vector oriented parallel to the ion-beam direction. The ordering and homogeneity of these patterns increase with ion fluence, leading to very-well-ordered ripples. The ripple wavelength remains constant with ion fluence. Also, the influence of ion energy on the ripple wavelength is investigated. Additionally itmore » is shown that the mass of the bombarding ion plays a decisive role in the ripple formation process. Ripple patterns evolve for Ar{sup +},Kr{sup +}, and Xe{sup +} ions, while no ripples are observed using Ne{sup +} ions. These results are discussed in the context of continuum theories and by using Monte Carlo simulations.« less

Mechanical Properties of Additively Manufactured Thick Honeycombs.

PubMed

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-07-23

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson's ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

Mechanical Properties of Additively Manufactured Thick Honeycombs

PubMed Central

Hedayati, Reza; Sadighi, Mojtaba; Mohammadi Aghdam, Mohammad; Zadpoor, Amir Abbas

2016-01-01

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions. PMID:28773735