On the application of Biot's theory to acoustic wave propagation in snow

A fluid-saturated, elastic, porous media model is used to describe acoustic wave propagation in snow. This model predicts the existence of two dilatational waves and a shear wave. In homogeneous, isotropic snow the two dilatational waves are uncoupled from one another but involve coupled motion between the interstitial air and ice skeleton. Dilatational waves of the first kind and shear waves are slightly dispersive and attenuated with distance. Dilatational waves of the second kind are strongly dispersive and highly attenuated. The model also predicts that the wave impedance for snow is close to that of air and that snow strongly absorbs acoustic wave energy.Available experimental phase velocity, impedance and attenuation data support the calculated results. Phase velocity measurements indicate three identifiable categories: fast dilatational waves (phase velocity ? 500 m/s), slow dilatational waves (phase velocity < 500 m/s) and shear waves. Wave impedance and attenuation measurements illustrate the low impedance, highly absorbing characteristics of snow. Additional impedance, attenuation and phase velocity data are required to further test and improve the model.     

Generation of SH-type waves in a poroelastic layer sandwiched between prestressed orthotropic and nonhomogeneous mantles

The present work is concerned with a detailed illustration on the study of horizontally polarized shear waves (SH-type) propagation in a prestressed fluid saturated anisotropic porous layer sandwiched by prestressed orthotropic medium and nonhomogeneous mantles. The frequency equation for the assumed model is derived and their medium characteristics, such as porosity, prestress, anisotropy, and nonhomogeneity, are discussed. Numerical treatment is given to analyze these effects on phase velocities of SH-type waves and is plotted in various graphs. The parametric study divulges that the magnitude of wave velocities increases with the increase of nonhomogeneity parameter and prestress parameter.     

Love type waves in a porous layer with irregular interface

The dispersion equation is derived relating to the frequency and the phase velocity of propagation of Love waves in a nondissipative liquid filled porous solid underlain by an isotropic and homogeneous half space. The rectangular irregularity in the interface between the upper porous layer and the lower semi-infinite medium with a source in it is studied herein. The modified dispersion equation of Mal and the standard dispersion equation of Love waves are deduced as particular cases. In the present study, the frequency equation is obtained by applying the method of perturbation and the phase velocity curves have been drawn for different irregularities by using the numerical parameteric values as suggested by Biot.     

Frequency Dependence of Second-Harmonic Generation in Lamb Waves

The frequency dependence of the second-harmonic generation in Lamb waves is studied theoretically and numerically in order to examine the role of phase matching for sensitive evaluation of material nonlinearity. Nonlinear Lamb wave propagation in an isotropic plate is analyzed using the perturbation technique and the modal decomposition in the neighborhood of a typical frequency satisfying the phase matching. The results show that the ratio of the amplitude of second-harmonic Lamb mode to the squared amplitude of fundamental Lamb mode grows cumulatively in a certain range of fundamental frequency for a finite propagation distance. It is also shown that the frequency for which this ratio reaches maximum is close but not equal to the phase-matching frequency when the propagation distance is finite. This feature is confirmed numerically using the finite-difference time-domain method incorporating material and geometrical nonlinearities. The fact that the amplitude of second-harmonic mode becomes high in a finite range of fundamental frequency proves robustness of the material evaluation method using second harmonics in Lamb waves.     

Shear wave propagation in viscoelastic heterogeneous layers lying over an initially stressed half-space

The role of the present article is to study the propagation of horizontally polarized shear waves in vertically heterogeneous viscoelastic double layers lying over a homogeneous half-space under initial stress. Both linear and exponential variations have been considered in the inhomogeneity associated to rigidity, internal friction, and density of the media. The dispersion equation of shear waves has been obtained in closed form. The dimensionless phase and damping velocities have been plotted against dimensionless wave number for different values of inhomogeneity parameters separately. Also, surface plots of phase velocity against dimensionless wave number and inhomogeneity parameters have been given.     

A new features on S-waves propagation in a nonhomogeneous anisotropic incompressible medium under influence of gravity field and initial stress with and without electromagnetic field and rotation

The present article is concerned with the investigation of the propagation of shear waves in a nonhomogeneous anisotropic incompressible medium under the effect of the electromagnetic field, gravity field, rotation, and initial stress taking into account a comparison between presence and absence of magnetic field, initial stress, and rotation. Analytical analysis reveals that the velocity of propagation of the shear waves depends upon the direction of propagation, the anisotropy, magnetic field, rotation, gravity field, nonhomogeneity of the medium, and the initial stress. The frequency equation that determines the velocity of the shear waves has been obtained. Some special cases are also deduced from the present investigation. In fact, these equations are an agreement with the corresponding classical results when the medium is isotropic. Numerical results have been given and illustrated graphically in each case considered. The results indicate that the effects of gravity field, initial stress, magnetic field, electric field, anisotropy, and rotation are very pronounced. Also, the absence of initial stress, magnetic field, and rotation tends to increasing of the S-waves velocity compared with presence of them.     

Lamb waves in a thin isotropic layer between two anisotropic layers

Attenuative Lamb wave propagation in adhesively bonded anisotropic composite plates is introduced. The isotropic adhesive exhibits viscous behavior to stimulate the poor curing of the middle layer. Viscosity is assumed to vary linearly with frequency, implying that attenuation per wavelength is constant. Attenuation can be implemented in the analysis through modification of elastic properties of isotropic adhesive. The new properties become complex, but cause no further complications in the analysis. The characteristic equation is the same as that used for the elastic plate case, except that both real and imaginary parts of the wave number (i.e., the attenuation) must be computed. Based on the Lowe's solution in finding the complex roots of characteristic equation, the effect of longitudinal and shear attenuation coefficients of the middle adhesive layer on phase velocity dispersion curves and attenuation dispersion curves of Lamb waves propagating in bonded anisotropic composites is visualized numerically.     

Shear horizontal wave propagation in periodically layeredcomposites

The transverse resonance approach to guided wave analysis is applied to shear horizontal (SH) wave propagation in periodically layered composites. It is found for SH waves that at high values of the guided wavevector β, the wave energy is trapped in the slower of the two media and propagates accordingly at the slower wavespeed. At low values of β, however, the modes demonstrate a clustering behavior, indicative of the underlying Floquet wave structure. The number of modes in a cluster is observed to correlate with the number of unit cells in the layered plate. New physical insights into the behavior of these systems are obtained by analyzing the partial waves of the guided SH modes in terms of Floquet waves. We show that the fast and slow shear waves in the periodically layered composite play an analogous role to the longitudinal and shear partial waves comprising Lamb waves in a homogeneous plate     

Propagation of magnetoelastic shear waves in an irregular self-reinforced layer

The propagation of horizontally polarised shear waves in an internal irregular magnetoelastic self-reinforced stratum which is sandwiched between two semi-infinite magnetoelastic self-reinforced media is studied. Two shapes of irregularities on the interface of layer and lower semi-infinite media are considered, namely rectangular and parabolic. The dispersion equation is obtained in closed form. The combined effects of reinforcement, magnetic field and irregularity are also studied. Some important features of the results are highlighted. It is also observed that the dispersion equation is in agreement with the classical Love-type wave equation for an isotropic layer sandwiched between two isotropic half-spaces in the absence of reinforcement, magnetic field and irregularity.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Rayleigh-Lamb waves in magneto-thermoelastic homogeneous isotropic plate

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. At short wavelength limits, the secular equations for symmetric and skew-symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite thickness plate in such a situation behaves like a semi-infinite medium. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.     

模拟岩芯中天然气水合物超声检测技术

天然气水合物广泛分布在大陆、岛屿的斜坡地带以及海洋和一些内陆湖的深水环境,基于双相多孔媒质理论,分析和研究在孔隙中天然气水合物发生相变过程引起的多孔介质物性的变化而导致的声波传播的改变,可以找出其中的变化规律,对于研究岩芯中的天然气水合物具有重要的理论意义和实际价值。在模拟岩芯中天然气水合物发生相变过程中,纵波和横波速度随着孔隙度的增大而减小;衰减随着孔隙度的增大而增大,这些结果表明了实验结果与理论结果基本吻合,并为进一步的实验工作打下了良好的基础。     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

Thermoelastic Lamb waves in a transversely isotropic plate bordered with layers of inviscid liquid

Analysis for the propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting plate bordered with layers of inviscid liquid or half space of inviscid liquid on both sides, is investigated in the context of coupled theory of thermoelasticity. Secular equations for homogeneous transversely isotropic plate in closed form and isolated mathematical conditions for symmetric and anti-symmetric wave modes in completely separate terms are derived. The results for isotropic materials and uncoupled theories of thermoelasticity have been obtained as particular cases. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion of wave propagation and occurs along an in-plane axis of symmetry. The special cases, such as short wavelength waves and thin plate waves of the secular equations are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for transversely isotropic plate of zinc material bordered with water. The dispersion curves for symmetric and anti-symmetric wave modes, attenuation coefficient and amplitudes of displacement and temperature change in case of fundamental symmetric (S₀) and skew symmetric (A₀) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.     

Wave propagation in micropolar mixture of porous media

This paper is concerned with the possible propagation of waves in an infinite porous continuum consisting of a micropolar elastic solid and a micropolar viscous fluid. Micropolar mixture theory of porous media developed by Eringen [A.C. Eringen, Micropolar mixture theory of porous media, J. Appl. Phys. 94 (2003) 4184–4190] is employed. It is found that there exist four coupled longitudinal waves (two coupled longitudinal displacement waves and two coupled longitudinal microrotational waves) and six coupled transverse waves in a continuum of this micropolar mixture. All the waves are found to attenuate and dispersive in nature. A problem of reflection of coupled longitudinal waves from a free boundary surface of a half-space consisting the mixture of a micropolar elastic solid and Newtonian liquid, is investigated. The expressions of various amplitude ratios and surface responses are derived. Numerical computations are performed to find out the phase velocity and attenuation of the waves. The variation of amplitude ratios, energy ratios and surface responses are also computed for a specific model. All the numerical results are depicted graphically. Some limiting cases have also been discussed.     

Reflection of plane waves at the free surface of a fibre-reinforced elastic half-space

The propagation of plane waves in fibre-reinforced, anisotropic, elastic media is discussed. The expressions for the phase velocity of quasi-P (qP) and quasi-SV (qSV) waves propagating in a plane containing the reinforcement direction are obtained as functions of the angle between the propagation and reinforcement directions. Closed form expressions for the amplitude ratios for qP and qSV waves reflected at the free surface of a fibre-reinforced, anisotropic, homogeneous, elastic half-space are obtained. These expressions are used to study the variation of amplitude ratios with angle of incidence. It is found that reinforcement has a significant effect on the amplitude ratios and critical angle     

Interaction of shear waves with a griffith crack situated in an infinitely long elastic strip

This paper deals with the propagation of shear waves in a wave guide which is in the form of an infinite elastic strip with free lateral surfaces. This strip contains a Griffith crack. An integral transform method is used to find the solution of the equation of motion from the linear theory for a homogeneous, isotropic elastic material. This method reduces the problem into an integral equation. It has been observed that only shear waves with frequencies less than a parameter-value, depending on the width of the wave guide, can propagate. The integral equation is solved numerically for a range of values of wave frequency and the width of the strip. These solutions are used to calculate the dynamic stress intensity factor, displacement on the surface of the crack and crack energy. The results are shown graphically.     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

Dispersion of elastic waves in periodically inhomogeneous media

Propagation of time-harmonic elastic waves through periodically inhomogeneous media is considered. The material inhomogeneity exists in a single direction along which the elastic waves propagate. Within the period of the linear elastic and isotropic medium, the density and elastic modulus vary either in a continuous or a discontinuous manner. The continuous variations are approximated by staircase functions so that the generic problem at hand is the propagation of elastic waves in a medium whose finite period consists of an arbitrary number of different homogeneous layers. A dynamic elasticity formulation is followed and the exact phase velocity is derived explicitly as a solution in closed form in terms of frequency and layer properties. Numerical examples are then presented for several inhomogeneous structures.     

Surface wave propagation in a fluid-saturated incompressible porous medium

A study of surface wave propagation in a fluid-saturated incompressible porous half-space lying under a uniform layer of liquid is presented. The dispersion relation connecting the phase velocity with wave number is derived. The variation of phase velocity and attenuation coefficients with wave number is presented graphically and discussed. As a particular case, the propagation of Rayleigh type surface waves at the free surface of an incompressible porous half-space is also deduced and discussed.