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An analytical study on the propagation characteristics of shear wave in a spherical layered structure comprising of an isotropic sandy material medium covered by a concentric spherical transversely isotropic sandy material layer of finite thickness has been carried out in the present work. The source of excitation for wave propagation is considered in the outer layer and the analytical treatment with contour integration and Fourier-Legendre Expansion theorem is utilized to accomplish closed form of dispersion relation. Further, Debye Asymptotic Expansion analysis is used to deal the complication caused by the inclusion of Bessel's function, Hankel's function and their derivatives in the solution procedure. With help of Debye Asymptotic Expansion analysis, the obtained dispersion relation converts in the form of elementary functions and found to be in well-agreement with pre-established and classical results through the particular cases. Numerical computations are done to illustrate the influence of the affecting parameters (anisotropy, sandiness and radii ratio) on dispersion curves graphically. Moreover, to expose the impact of anisotropy, numerical data of three distinct transversely isotropic materials (Magnesium, Zinc and Beryl) are taken into the account to establish the comparative study with isotropic material which serves the major highlights of the present study.

The reflection of three-dimensional (3D) plane waves in a highly anisotropic (triclinic) medium under the context of generalized thermoelasticity is studied. The thermoelastic nature of the 3D plane waves in an anisotropic medium is investigated in the perspective of the three-phase-lag (TPL), dual-phase-lag (DPL), Green-Naghdi-III (GN-III), Lord-Shulman (LS), and classical coupled (CL) theories. The reflection coefficients and energy ratios for all the reflected waves are obtained in a mathematical form. The rotational effects on the reflection characteristics of the 3D waves are discussed under the context of generalized thermoelasticity. Comparative analyses for the reflection coefficients of the waves among these generalized thermoelastic theories are performed. The energy ratios for each of the reflected waves establish the energy conservation law in the reflection phenomena of the plane waves. The highly anisotropic materials along with the rotation may have a significant role in the phenomenon of the reflection behavior of the 3D waves. Numerical computations are performed for the graphical representation of the study.

This article is intended to observe the reflection and transmission phenomena of three-dimensional plane waves at the interfaces of two distinct anisotropic triclinic media under the context of the...

Mathematical analysis is performed to examine the reflection and transmission phenomena of plane waves at the corrugated interface of crystalline structure separating two distinct monoclinic thermo...

The present study analysed the characteristics of a moving Griffith crack in a self-reinforced strip of finite thickness and infinite extent with the moving parallel punches of constant load acting on the boundaries of the strip at both sides due to the propagation of magnetoelastic plane waves under mechanical point loading. With the aid of integral transform technique, problem has been reduced to the pair of simultaneous singular integral equations with Cauchy-type singularities. The point load at the edge of the moving crack is considered in terms of Dirac delta function, and the expression of stress intensity factor (SIF) at the crack tip with constant point loading has been established in closed form by using the well-known properties of Hilbert transformation. Moreover, some of the special cases have been deduced from the obtained expression of SIF for the force of constant intensity, without punch pressure and anisotropy in the considered strip. Numerical computations and graphical demonstrations have been carried out to observe the profound effect of magnetoelastic coupling parameter, punch pressure, crack length, distinct positions of point load and the velocity of crack associated with magnetoelastic plane wave on SIF for self-reinforced materials and isotropic material strip. A comparative study of SIF at the tip of moving crack has been made for the self-reinforced and isotropic materials to highlight some of the important peculiarities of the problem.

This research article deals with the study of shear (SH) wave propagation in two dissimilar layered elastic medium with void pores over an inhomogeneous semi-infinite medium. The casewise study is ...

The present study is concerned with the dynamic response of an anisotropic composite structure due to a normal moving load on its irregular rough surface. The composite structure is comprised of an irregular incompressible heterogeneous transversely isotropic fluid-saturated poroelastic layer lying over a transversely isotropic substrate. The mathematical formulation of this structure gives rise to a boundary value problem with specified boundary conditions, and the perturbation method has been used to tackle the irregular surface problem. The expressions for the induced shear and normal stresses in layer and substrate of the composite structure are derived analytically in closed form due to the moving load. As a special case of the problem, the deduced expressions of the induced stresses are validated with the pre-established and standard results. The effect of several substantial parameters such as vertical depth, heterogeneity parameter, porosity parameter, frictional coefficient, irregularity depth, and irregularity factor on the induced shear as well as normal stresses of the layer and substrate has been delineated graphically by the numerical computation. Moreover, a comparative study of the various types of irregularity, namely rectangular irregularity, parabolic irregularity and no irregularity (regular boundary surface) on the induced shear and normal stresses in the layer and, substrate, is carried out by means of graphs, and some considerable peculiarities are outlined.

A theoretical approach is taken into consideration to investigate the propagation behaviour of shear acoustic waves in a piezoelectric cylindrical layered structure composed of a piezoelectric material cylinder imperfectly bonded to a concentric functionally graded piezoelectric material (FGPM) cylindrical layer of finite width. The functional gradient in the FGPM cylindrical layer is considered to vary continuously along the radial direction (function of radial coordinate), and the imperfection of the interface of the cylindrical structure is taken into account which may practically exist due to some mechanical and/or electrical damage. By means of mathematical transformation, the governing electromechanical coupled field differential equations are reduced to Bessel’s equations. An analytical treatment has been employed to determine the dispersion relations of propagating shear acoustic waves for both electrically short and electrically open conditions, which are further validated by reducing the obtained results to the pre-established standard results and classical Love wave equation as a special case of the problem. The effects of functional gradient parameter, radii ratio, wave number, order of Bessel’s function appearing in the dispersion relations and mechanical/electrical imperfection parameters associated with the imperfect bonding of a piezoelectric material cylinder and FGPM layer on the phase velocity of shear acoustic waves have been reported through numerical simulation and graphical demonstration. For the sake of numerical computation, the data of PZT-5H for the FGPM cylindrical layer and AlN for a piezoelectric material cylinder have been considered.

The present paper investigates Green’s function technique to study the impact of the non-linear heterogeneity on the propagation of the horizontally polarised shear (SH) wave in a composite layered structure due to the line source. The composite structure is comprised of two distinct isotropic homogeneous elastic layers of finite width lying over an isotropic heterogeneous semi-infinite elastic medium. A general quadratic heterogeneity (including the linear heterogeneity term) in the rigidity of the semi-infinite medium has been taken into account. An efficient analytical treatment involving Green’s function technique along with the application of Fourier transformation has been employed to establish the closed form of the dispersion equation for the propagating wave. As a special case of the problem, the closed form of the dispersion equation has been found in well agreement with the pre-established and classical results. The influence of linear and non-linear heterogeneities on the phase velocity of the horizontally polarised shear-wave has been analysed comparatively for numerous cases associated with the considered model and the corresponding single layer half-space model. It is reported that the phase velocity of the horizontally polarised shear-wave is more pronounced in the case of the corresponding single layer half-space structure as compared to the considered structure. Also, the impact of the general quadratic heterogeneity (supported by the linear heterogeneity) enhances the phase velocity most favourably as compared to the case of the simple quadratic heterogeneity, linear heterogeneity and homogeneity in the semi-infinite medium.

Propagation behavior of SH-wave in a layered structure comprises of a functionally (exponentially) graded fibre-reinforced substrate imperfectly bonded to a functionally (exponentially) graded Voigt-type viscoelastic stratum is studied. The complex form of frequency equation is achieved in closed-form whose real part represents dispersion relation and imaginary part represents damping equation. In isotropic case, dispersion relation coincides with classical Love- wave equation whereas damping equation vanishes identically for the classical case. The effects of imperfect bonding, wave number, functional gradient parameters of stratum and substrate, viscoelasticity in stratum and reinforcement in the substrate are analyzed on the phase as well as damped velocities of SH-wave. Furthermore, the impact of imperfect common interface on the propagation of SH-wave is examined meticulously by analyzing the effect of flexibility and viscoelastic component associated to the imperfect bonding of stratum and substrate. Numerical calculations and graphical demonstrations are carried out for the present study which unravels some important peculiarities.

The primary objective of this article is to investigate the behaviour of horizontally polarized shear (SH) wave propagation in piezoelectric composite structure consisting of functionally graded piezoelectric material layer imperfectly bonded to functionally graded porous piezoelectric material half-space. The linear form of functional gradedness varying continuously along with depth is considered in both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. The interface of the composite structure is considered to be damaged mechanically and/or electrically. Wentzel–Kramers–Brillouin asymptotic approach is adopted to solve the coupled electromechanical field differential equations of both functionally graded piezoelectric material layer and functionally graded porous piezoelectric material half-space. An analytical treatment has been employed to determine the dispersion relations of propagating SH-wave for both electrically short and electrically open conditions, which further reduced to the pre-established and classical results as special case of the problem. The effect of various affecting parameters, namely, functional gradedness, wave number, mechanical/electrical imperfection parameters in the presence and absence of porosity on the phase velocity of SH-wave, has been reported through numerical computation and graphical demonstration. In addition, the variation of the coupled electromechanical factor with dimensionless wave number and cut-off frequency with different modes of propagation of wave for electrically short and electrically open cases has also been discussed.

The present article delves the effect of curved boundary on the propagation characteristics of Rayleigh-type wave and SH wave in an initially stressed monoclinic media. The present communication fo...

A theoretical model is established to analyze the propagation behavior of Love-type wave in a composite structure which is comprised of two different functionally graded pre-stressed magnet...

The present paper articulates a mathematical model for the propagation of Shear wave in a layered structure comprised of slightly compressible finitely deformed layer over a foundation with pre-str...

The present article undertakes the study of propagation of SH-wave and Rayleigh-type wave in a layered structure with a layer overlying a semi-infinite medium composed of distinct initially stresse...

The rapid development of the modern age has increased the urge of using composite structures having applications in the realm of various engineering fields. Specifically, fibre-reinforced piezoelectric composites are in the forefront of the present era because of its light weight, great strength and hence improved performance over the piezoelectric materials alone. Therefore, the present paper delves with the problem of reflection and refraction of plane waves when it is incident at the interface of a Piezoelectric Fibre-reinforced Composite (PFRC) medium and Fibre-reinforced Composite (FRC) medium. It is assumed that the media are loosely bonded to each other and are under horizontal initial stresses. It is established that the boundary conditions are satisfied by the set of three coupled waves associated with the PFRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV), electrostatic wave (EA)) and two coupled waves associated with the FRC medium (namely quasi-longitudinal wave (qP), quasi-transverse wave (qSV)). The amplitude ratio of reflected and refracted waves are obtained with the aid of suitable boundary conditions at the common interface of the two media. The effect of anisotropy, initial stresses and loose bonding on the amplitude ratio are studied numerically and demonstrated by means of graphs. The effect of anisotropy is also studied on the slowness curves, plotted in slowness surface. Moreover, the relation for energy partition is also derived and it is established that the total normal energy flux balance at the interface is unity.

The analysis of wave propagation phenomenon piezoelectric-viscoelastic composites still remains an unexplored field of research. The usage of a passive polymer (Epoxy) with active piezoelectric ceramic causes viscoelasticity in the piezoelectric material which results into a piezoelectric-viscoelastic composite. The present study aims to analyze the propagation behavior of Love-type wave in an exponentially graded piezoelectric-viscoelastic material (EGPVM) stratum lying over a functionally graded piezoelectric-viscoelastic material (FGPVM) substrate due to an impulsive point source at its interfacial surface. The electro-visco-mechanical field equations are laid down for the piezoelectric-viscoelastic medium. The analytical solution procedure involves the use of suitable Green's function and admissible boundary conditions. The established frequency equation is in complex form; of which the real expression imparts the frequency curve and imaginary expression gives the attenuation curve of Love-type wave. To depict the results numerically, two distinct piezoelectric-viscoelastic materials (Epoxy-BNKLBT and Epoxy-KNLNTS ceramics) for EGPVM stratum and FGPVM substrate are taken into account. The phase velocity profile and attenuation coefficient profile of Love-type wave is portrayed graphically. Diagnostic results are simulated numerically which forefronts the effect of distinct parameters. The study manifests the impact of the material medium parameters, viz. piezoelectric constants, dielectric constants, piezoelectric loss moduli, dielectric loss moduli, exponential gradient parameter and magnifying gradient parameters on the phase velocity and attenuation coefficient of Love-type wave. For sake of validation, the obtained results are matched with the classical one, as a special case of the problem. The outcomes of the study may find its worth in better and optimum design of surface acoustic wave devices and Love wave sensors, keeping efficiency at its premium.

Purpose The purpose of this paper is to develop a numerical (finite-difference) model exploring phase and group velocities of SH-wave propagation in initially stressed transversely isotropic poroelastic multi-layered composite structures and initially stressed viscoelastic-dry-sandy multi-layered composite structures in two distinct cases. Design/methodology/approach With the aid of relevant constitutive relations, the non-vanishing equations of motions for the propagation SH-wave in the considered composite structures have been derived. Haskell matrix method and finite-difference scheme are adopted to deduce velocity equation for both the cases. Stability analysis for the adopted finite-difference scheme has been carried out and the expressions for phase as well as group velocity in terms of dispersion-parameter and stability-ratio have been deduced. Findings Velocity equations are derived for the propagation of SH-wave in both the composite structures. The obtained results are matched with the classical results for the case of double and triple-layered composite structure along with comparative analysis. Stability analysis have been carried out to develop expressions of phase as well as group velocity in terms of dispersion-parameter and stability-ratio. The effect of wavenumber, dispersion parameter along with initial-stress, porosity, sandiness, viscoelasticity, stability ratio, associated with the said composite structures on phase, damped and group velocities of SH-wave has been unveiled. Originality/value To the best of authors’ knowledge, numerical modelling and analysis of propagation characteristics of SH-wave in multi-layered initially stressed composite structures composed of transversely isotropic poroelastic materials and viscoelastic-dry-sandy materials remain unattempted inspite of its importance and relevance in many branches of science and engineering.

The effect of frictional boundary on the propagation of Rayleigh-type wave in an initially stressed inhomogeneous fiber-reinforced layer overlying an initially stressed homogeneous semi-infinite medium has been analyzed by an approximate analytical method. A realistic model has been considered for sliding boundary friction at the interface. The frequency equation has been obtained in closed form. The substantial effects of various affecting parameters, viz. reinforcement, inhomogeneity, bonding parameter, spectral decay parameter, and horizontal initial stress on phase and damped velocity have been discussed graphically in detail. The remarkable observation has been obtained through the comparative study in the presence and the absence of reinforcement in the layer.

The objective of this work is to investigate the propagation characteristics of edge wave in a composite structure comprised of two uniformly homogeneous viscoelastic incompressible sandy plates of finite width and infinite extent. An analytical approach is used to deduce the closed form of frequency equation concerning to phase as well as damped velocities and analyzed the various affecting parameters. The effects of influencing parameters such as viscoelastic parameter, sandy parameter of both plates and wave number on the phase as well as damped velocities of edge wave are depicted graphically with the help of numerical simulation. It has been found that all the affecting parameters have significant effects on the edge wave propagation in the composite structure.

The present article deals with the reflection and refraction phenomenon of a plane wave at the interface of two distinct functionally (exponentially) graded incompressible monoclinic media in the two separate cases. The first case (Case I) deliberates the influence of initial stress; however, the second case (Case II) analyses the influence of gravity associated with both upper and lower incompressible functionally graded monoclinic media on amplitude ratios of reflected and refracted waves. Two types of waves namely quasi-P and quasi-SV are generated due to the plane wave incident at the common interface of the considered structure. An analytical approach has been employed to compute velocity equations for each of the two cases. The dependency relations of dimensionless amplitude ratio of reflected and refracted waves on various affecting parameters along with angle of incidence have been established in closed form for both the cases. Moreover, the expressions for slowness section have also been derived for the corresponding cases and depicted by the means the graphs. Also as a special case of the problem, the deduced results are validated with the pre-established result. An analysis to unravel the effect of angle of incidence, gravity parameter, material gradient parameter and initial stress associated with lower and upper media on the reflected and refracted waves has also been made meticulously through numerical computations and graphical illustrations. Furthermore, through comparative analysis some important peculiarities in the phenomenon have also been highlighted.

The present article aims to unravel the propagation characteristics of a shear wave in the context of reinforcement and frictional bonding in a composite structure. The geometrical configuration of the composite structure is comprised with a fibre-reinforced layer and an isotropic homogeneous semi-infinite medium which are frictionally bonded to each other. An analytical technique is employed to find the complex form of the frequency equation which is separated into real and imaginary parts representing the dispersion and damping relation, respectively. As a particular case of the problem, the deduced results are matched with the classical Love equation. The numerical simulation is performed to graphically portray the analytical findings and to trace out the effect of reinforcement by a comparative study which is a major highlight of the study. The significant influence of reinforcement, frictional bonding, and spectral decay parameter on the phase, group, and damped velocities are revealed. The outcome of the present study may be helpful to gain deeper insight into the propagation characteristics of a shear wave in a frictionally bonded composite structure which may provide useful information in engineering applications.

The present study deals with the propagation characteristics of rectilinear semi-infinite non-centrally located interfacial crack associated with progressing Love-type wave in the structure comprised of two dissimilar transversely isotropic layers. The closed form expressions of stress intensity factor for different quasi-static conditions (viz. diverse loading and stress-free conditions on the edges of crack subjected to non-harmonic and harmonic loading) and also for static condition concerned with non-harmonic and harmonic loading have been derived by using Weiner-Hopf technique along with two-sided Fourier transform. The substantial influence of thickness ratio, inhomogeneity, stress amplitude ratio, displacement amplitude ratio, and different material combinations of layers on stress intensity factor at the crack tip has also been examined for the considered structure. Some notable characteristics are also highlighted and revealed by means of numerical results and graphs.

This theoretical work addressed an issue of the reflection and transmission of plane wave incident in a layered triclinic solids. Generalization of Snell’s law is applied and suitable boundary cond...

This article explores the effect of initial-stress, heterogeneity and anisotropy on the propagation of SH-wave (Case-1) and Rayleigh-type wave (Case-2) in a semi-infinite medium while propa...

With a motivation to gain physical insight of reflection as well as transmission phenomena in frozen (river/ocean) situation for example in Antarctica and other coldest place on Earth, the present article undertakes the analysis of reflection and transmission of a plane wave at the interfaces of layered structured comprised of a water layer of finite thickness sandwiched between an upper half-space constituted of ice and a lower isotropic elastic half-space, which may be useful in geophysical exploration in such conditions. A closed form expression of reflection/transmission coefficients of reflected and transmitted waves has been derived in terms of angles of incidence, propagation vector, displacement vector and elastic constants of the media. Expressions corresponding to the energy partition of various reflected and transmitted waves have also been established analytically. It has been remarkably shown that the law of conservation of energy holds good in the entire reflection and transmission phenomena for different angles of incidence. A numerical examples were performed so to graphically portray the analytical findings. Further the deduced results are validated with the pre-established classical results.

The aim of this paper is to establish the effect of curved boundaries with small but non-zero curvature on the displacement of a particle due to surface wave propagation in an important geo-media called reinforced composite media. The analysis has been carried out from an unusual stand point, which is to consider the effect of curved boundaries on displacement components during wave propagation. If the displacement components arising for stratified boundaries are termed as primary components, then secondary components should also exist for the curvature present in the boundaries. These secondary parts are composed of different harmonic components with their amplitudes depending on the extent of curvature of boundaries. Depending upon the shape of the boundaries, the wave numbers of the primary and secondary components relate one another. Graphs have been plotted to observe the effect of curved boundaries and initial stresses on displacement components. The clearly observable differences of the curves plotted for the cases of planar and non-planar boundaries forecast the important findings of this paper.

Green’s function plays an important role in solving the problems concerning point action or impulse responsible for wave motions in materials. Prime objective of the this article is to investigate the propagation behaviour of Love-type wave influenced by a point source in a composite structure comprising a functionally graded piezoelectric material layer lying over a functionally graded fibre-reinforced material half-space. Green’s function technique is adopted in order to obtain the dispersion equation, which is further reduced to the classical Love wave equation as a particular case of the problem. The effect of increasing thickness of functionally graded piezoelectric material layer on the circular frequency and wave number is unravelled and depicted graphically. Moreover, influence of heterogeneity, piezoelectricity and dielectric constant associated with functionally graded piezoelectric material layer and effect of heterogeneity parameter and corresponding magnification factor concerned with functional gradedness of functionally graded fibre-reinforced material half-space have been reported through numerical computation and graphical delineation. For sake of computation, numerical data of PZT-5H ceramics for the functionally graded piezoelectric material layer and carbon-fibre epoxy-resin for functionally graded fibre-reinforced material half-space have been considered. Comparative study is performed to elucidate the effect of presence and absence of reinforcement in functionally graded half-space on the phase velocity of Love-type wave propagating in composite structure.

Propagation of Rayleigh-type surface waves in an incompressible visco-elastic material over incompressible visco-elastic semi-infinite media under the effect of initial stresses is discussed. The dispersion equation is determined to study the effect of different types of parameters such as inhomogeneity, initial stress, wave number, phase velocity, damping factor, visco-elasticity, and incompressibility on the Rayleigh-type wave propagation. It is found that the affecting parameters have a significant effect on the wave propagation. Cardano’s and Ferrari’s methods are deployed to estimate the roots of differential equations associated with layer and semi-infinite media. The MATHEMATICA software is applied to explicate the effect of these parameters graphically.

The present study investigates the propagation characteristics of SH-type wave and a new type of dispersive surface wave in an irregular composite structure comprised of a layer overlying a half-space, both constituted by distinct homogeneous micropolar isotropic elastic materials. At the common interface of the composite structure, two types of irregularities viz. rectangular and parabolic shaped, are studied in two distinct cases. Closed-form of frequency equations of SH-type wave associated with these cases have been obtained and matched with the classical Love wave equation in the isotropic case of the composite structure without irregularity at the common interface. Existence of new type of dispersive surface wave along with its dispersion relation has been deduced in the closed-form by adopting a distinct mathematical treatment for various cases concerned with the presence and absence of microrotational components in the composite structure. It is also examined that the dispersion equation of new type of dispersive surface wave vanishes identically in isotropic case of the composite structure. To unravel the effect of irregularity at the common interface and micropolarity associated with micropolar composite structure on SH-type and new type of dispersive surface wave, numerical computation and graphical demonstrations have been carried out in a comparative manner which serves as a salient feature of the study.

The present analysis confers the propagation characteristics of horizontally polarized​ shear (SH) wave through a heterogeneous transversely isotropic fluid-saturated poroelastic sandwiched layer of finite width embedded between two heterogeneous isotropic elastic half-spaces due to the impact of an impulsive line source. The dissipation of energy caused by the relative fluid flow is neglected in transversely isotropic fluid-saturated poroelastic sandwiched layer. The heterogeneities in layer and half-spaces are considered with the respective spatial quadratic and exponential type variations in the elastic constants and densities. Green’s functions are obtained for this sandwiched layered structure by considering a charge-density/line-force (Dirac-delta function) at lower bonding surface of layer and half-space. Dispersion relation for the propagation of SH wave in aforesaid structure has been obtained with well-known properties of Green’s functions, Fourier’s transformation and appropriate boundary conditions. The obtained dispersion relation is reduced for a structure with a heterogeneous transversely isotropic fluid-saturated poroelastic layer of finite width overlying a heterogeneous isotropic elastic half-space in the particular case of problem. Moreover, the obtained dispersion relations are validated and matched with pre-established standard and classical results. The effect of various affecting parameters viz. anisotropy of layer, porosity of layer and heterogeneities of layer and half-spaces on phase velocity of propagating wave in said structure are shown graphically through numerical computations. Further, a comparative study of distinct cases of heterogeneous/homogeneous structures is also performed which serves as the major highlight of the present study.

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

The present paper is concerned with the propagation of shear wave in a cylindrical structure comprised of two concentric media by two distinct cases. In first case, media are homogeneous and in second case, media are heterogeneous. The heterogeneities are caused due to the radial variation in both the media distinctly. The dispersion relation for shear wave propagation in homogeneous and heterogeneous, fibre-reinforced media have been derived analytically in the closed form using Debye Asymptotic Expansion and verified with the existing literature and classical results. Numerical computation and graphical demonstration have been carried out to show the remarkable effect of various parameter viz. fibre-reinforcement, heterogeneities and radii ratio of the media on the intensity of frequency of shear wave propagation against the dimensionless wave number. A comparative study between the reinforcement and isotropic material with or without heterogeneity has been discussed extensively and unravel some important peculiarities.

The present study investigates the propagation of Rayleigh-type wave in a transversely isotropic viscoelastic layer in effect of yielding foundation and rigid foundation in two different cases for two considered models. Numerical computation and graphical demonstration have been carried out for the case when layer is comprised of transversely isotropic viscoelastic Mesaverde clay shale material (Model I) and simply isotropic viscoelastic material (Model II). Closed-form expression of phase velocity and damped velocity for both the cases are deduced analytically. Obtained result is found in well agreement to the established standard results existing in the literature. Significant effect of dilatational viscoelasticity, volume viscoelasticity and yielding parameter on phase and damped velocities for both the considered models has been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the context of the presen...

This paper deals with the propagation of Love-type wave in a composite isotropic structure embraced of tri layers elastic medium overlying a semi-infinite elastic medium. The heterogeneity ...

The investigated work analytically addresses the diffraction of horizontally polarised shear wave by a rigid strip in a pre-stressed transversely isotropic poroelastic infinite medium. The far field solution for the diffracted displacement of shear wave has been established in closed form. The diffraction patterns for displacement in the said medium have been computed numerically and its dependence on wave number has been depicted graphically. Further, the study also delineates the pronounced influence of various affecting parameters viz. anisotropy parameter, porosity parameter, speed of the shear wave, and incident angle on the diffracted displacement of the propagating wave. The effects of horizontal as well as vertical compressive and tensile pre-stresses on diffracted displacement of propagating wave have been examined meticulously in a comparative manner. It can be remarkably quoted that porosity prevailing in the medium disfavors the diffracted displacement of the propagating wave. In addition, some special cases have been deduced from the determined expression of the diffracted displacement of shear wave at a large distance from the strip.

In this paper, case wise studies have been made to investigate the possibility of propagation of Rayleigh-type wave in a composite structure comprised of two transversely-isotropic material layers with viscoelastic effect. The common interface between the layers is considered to be rigid whereas the base has been considered as rigid, stress-free and yielding in three different cases (Case-I, II and III). Closed-form of frequency equation and damped velocity equation has been established analytically for propagation of Rayleigh-type wave in a composite structure for all three cases. In special cases, frequency equations and damped velocity equations for the case of composite structure with rigid, stress-free and yielding base have been found in well-agreement to the established standard results pre-existing in the literature. Numerical and graphical computation of phase and damped velocity of Rayleigh-type wave propagating in the composite structure comprised of double transversely-isotropic viscoelastic Taylor sandstone material layers (Model-I) and double isotropic viscoelastic material layers (Model-II) have been carried out. Significant effect of anisotropy and width ratio of layers, dilatational and volume viscoelasticity associated with viscoelasticity of layer medium and yielding parameter associated with yielding base of composite structure on phase and damped velocities of Rayleigh-type wave for the considered models have been traced out. The comparative study has been performed to unravel the effect of viscoelasticity over elasticity and anisotropy over isotropy in the present problem.

An analytical treatment studying the propagation behavior of Love-type wave in a piezoelectric layer bonded perfectly to an isotropic heterogeneous layer overlying an unbounded isotropic homogeneou...

The present study aims to study the propagation of Rayleigh-type wave in a layer, composed of isotropic viscoelastic material of Voigt type, with the effect of yielding base and rigid base in two distinct cases. With the aid of an analytical treatment, closed-form expressions of phase velocity and damped velocity for both the cases are deduced. As a special case of the problem it is found that obtained results are in good agreement with the established standard results existing in the literature. It is established through the study that volume-viscoelastic and shear-viscoelastic material parameter and yielding parameter have significant effect on phase and damped velocities of Rayleigh-type wave in both the cases. Numerical calculations and graphical illustration have been carried out for both the considered cases in the presence and the absence of viscoelasticity. A comparative study has been performed to analyse the effect of layer with yielding base, traction-free base and rigid base on the phase and damped velocities of Rayleigh-type wave.

The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space due to a load moving with a constant velocity at a rough free surface. Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth (from the free surface), irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses, and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity, parabolic irregularity and no irregularity, which is manifested through graphs.

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