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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...

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.

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.

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 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 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 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...

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 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.

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 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.

This study reports a theoretical investigation of the propagation of SH-wave in a piezoelectric layer superimposed on a self-reinforced layer overlying an isotropic gravitational half-space. The expressions of the dispersion relation of SH-wave have been established for electrically open and electrically short conditions in closed form. For the purpose of numerical computation, lithium niobate piezoelectric material has been considered. The dispersion curves have been depicted graphically and the prominent impacts of piezoelectric constant, dielectric constant, reinforced parameter, width ratio, and Biot’s gravity parameter on the phase velocity of SH-wave have been unraveled for both the electrical conditions. As a special case of the problem, it is found that the obtained dispersion relation concurs with classical Love wave equation for both the electrical conditions. Moreover, some important peculiarities have also been traced out through numerical computations for both the electrical cases.

The present paper is concerned with the stresses produced due to a load moving on the irregular surface of an ice sheet floating on water. The irregularity of the ice medium is of parabolic type, and a rectangular irregularity has also been considered as a special case. The mathematical formulation of this physical problem gives rise to a boundary value problem with the specified boundary conditions. The perturbation method is applied to find the displacement field. Closed-form expressions of the normal and shear stresses developed in the ice medium and semi-infinite water medium due to moving load and irregularity have been derived using the boundary conditions. The variations of dimensionless normal and shear stresses with different depth below the surface are computed for a realistic numerical model and discussed. The same numerical data are used for surface plots to analyze the combined variation of non-dimensional stresses and velocity ratio against depth. From the outcome of the numerical study, the normal and shear stresses developed in both the ice and water media are found to be very sensitive to the changes in frictional coefficient, dimensionless wave number and irregularity factor present in the medium.

In this paper the study of propagation of Rayleigh type wave in a homogeneous initially stressed isotropic viscoelastic layer of Voigt-type resting on a rigid base has been dealt. The closed form expression of phase velocity is deduced analytically and obtained result is found to be in well agreement with the pre-established result in a special case. Numerical computation has been carried out for the derived dispersion equation to analyse the effect of viscoelastic parameters and initial stress on phase velocity of Rayleigh type wave. It is observed that viscoelastic parameters and initial stress parameter have significant effect on the phase velocity of Rayleigh-type wave which has been illustrated graphically.

In this paper we study the propagation of Rayleigh-type wave in a heterogeneous transversely isotropic elastic layer with initial stress resting on a rigid foundation. Frequency equation is obtained in closed form. The frequency equation being a function of phase velocity, wave number, initial stress and heterogeneous parameter associated with the rigidity and density of inhomogeneous layer reveals the fact that Rayleigh-type wave propagation is greatly influenced by above stated parameters. In Numerical and graphical computation the significant effects of distortional velocity have been carried out. Moreover, the obtained dispersion relation is found in well–agreement to the classical case in isotropic and transversely isotropic layer resting on a rigid foundation.

In the present paper the study of shear wave propagation in a cylindrical fibre-reinforced earth model has been discussed in the presence of radial inhomogeneity. The dispersion equation of shear wave propagation has been derived by using Debye asymptotic expansion for upper layer and lower layer to be heterogeneous and homogeneous respectively. The oncoming results are verified with the classical result of Love wave in the absence of reinforcement and inhomogeneity parameter. The variation of dimensionless phase velocity has been plotted against dimensionless wave number to show the effect of inhomogeneity parameter, reinforcement and the ratio of radii.

The present paper is concerned with the propagation of shear waves in a heterogeneous isotropic layer lying over a semi-infinite homogeneous isotropic half-space due to a point source. The dispersion equation of shear waves has been established with the help of Green's function technique and Fourier transform. The deduced dispersion equation for this study agrees well with the classical Love wave equation in the absence of heterogeneity. Significant effect of heterogeneity on the phase velocity of shear wave has been observed. The dimensionless phase velocity against dimensionless wave number has been plotted and the influence of heterogeneity parameter is also revealed graphically through numerical computation.

An investigation concerned with the dynamic response of a composite structure to a moving load on its uppermost rough surface has been carried out analytically. The composite structure is c...

The present work delves into the propagation of a horizontally polarised shear (SH) wave in an infinitely long cylindrical structure comprised of three concentric isotropic layered media. The model has been formulated in cylindrical co-ordinates and an analytical approach is employed to achieve the closed form of the dispersion relation. The application of the Debye Asymptotic Analysis to tackle the complexity arisen due to the involvement of Hankel’s function in the solution treatment is one of the key features of the present article. With the aid of the Debye Asymptotic Analysis, the dispersion equation is shown to be in well agreement with the classical Love wave equation in the absence of the outermost layer medium. The present analysis highlights the influence of the wave number and various radii ratios of the concentric cylindrical layered elastic medium on the phase velocity of the shear wave propagating in the embraced structure. Numerical computations have been carried out to accomplish the graphical demonstration unravelling some important peculiarities associated with the propagation characteristics of the shear wave in the considered cylindrical structure.

The present paper articulates a mathematical model for the propagation of horizontally polarised shear (SH) wave in an initially stressed composite layered structure under the influence of an impulsive line source. The initially stressed composite structure is comprised of a transversely isotropic fluid saturated porous layer over a foundation with dry sandy elastic stratum and functionally graded substrate (semi-infinite medium) in which the bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. Green's functions are derived for the composite layered structure by taking a line force/charge density (Dirac delta function) at the lower interface of intermediate stratum into the account. An efficient analytical treatment involving Green's function technique along with Fourier's transform has been employed to establish the closed form of dispersion equation for the propagating wave. As a special case of the problem, the closed form of dispersion equation has been deduced for a structure with a single layer overlying a semi-infinite medium. These deduced results are validated with pre-established results and classical Love wave equation. Numerical computation has been carried out to demonstrate graphically the effect of various affecting parameters, viz. wave number, initial stress, porosity, sandiness parameter, width ratio, imperfect bonding parameters and functional gradient parameters on the phase velocity of shear wave. Some remarkable results regarding the propagation behaviour of shear wave in the considered composite layered structure due to various affecting parameters serve as the major highlights of the present work which has significant relevance to field of geophysics, earthquake engineering and civil engineering.

Assumption that the common interfaces of the media are perfectly bonded may not be always true. Situation may arise that composition of the two medium may be responsible for weakening the contact between them. So, it becomes obligatory to consider a loosely bonded interface in such cases which may affect the propagation of elastic waves through them. This paper thrashes out the propagation of torsional surface wave in an initially stressed visco-elastic layer sandwiched between upper and lower initially stressed dry-sandy Gibson half-spaces, theoretically. Both the upper and lower dry-sandy Gibson half-spaces are considered to be loosely-bonded with the sandwiched layer. Mathematical model is proposed and solution in terms of Whittaker's and Bessel's function is obtained. Velocity equation is obtained in closed form, its real part deals with the dispersion phenomenon whereas its imaginary part provides the damping characteristics. Influence of heterogeneities, sandiness, gravity parameters, initial-stresses, loose-bonding and internal-friction on the phase and damped velocities of torsional wave are computed numerically and depicted graphically. Deduced dispersion equation and damped velocity equation matches with classical Love-wave equation and vanishes identically for the isotropic case respectively.

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.

The present article investigates the characteristic of moving load and effect of irregularity, hydrostatic stress, and magneto-elastic coupling parameter on the stresses developed due to moving load on the surface of an irregular magneto-elastic monoclinic half-space subjected to the friction associated with a rough surface. Boundary conditions are listed for which corresponding analyses can be performed analogously. The expressions for stresses are obtained analytically. Numerical computation of the obtained results are carried out for three different materials with monoclinic symmetry (lithium niobate, lithium tantalate, and quartz); the significant effects of affecting parameters on these relations are distinctly marked by means of graphs.

This article delves to study the effect of corrugated boundary surfaces on the propagation of horizontally-polarized shear waves (SH-waves) in a magnetoelastic transversely isotropic layer under a hydrostatic state of stress lying over an elastic half-space under gravity. A dispersion equation has been derived in closed-form and is found to be in good agreement to the classical Love-wave equation. The effect of magnetoelasticity, hydrostatic state of stress, gravity, corrugation, position parameter, and undulation on the phase velocity of the SH-wave has been identified. Numerical computation along with graphical demonstration has been carried out for cadmium, magnesium, and zinc materials of hexagonal symmetry to highlight some significant facts.

These days fibre-reinforced materials are frequently used in construction sector for example in dams, bridges etc. Also the earth structure and artificial structure made by human may contain irregularity or corrugation, therefore, propagation of waves and vibrations through these structures gets affected by them. Motivated by these facts the present problem aims to study the propagation of torsional surface wave in a fibre-reinforced layer with corrugated boundary surface overlying an initially stressed transversely isotropic half-space. The closed form of the dispersion equation has been deduced and the notable effect of reinforcement, undulatory parameter of corrugated boundary surfaces of the layer, corrugation parameter of upper and lower boundary surfaces of the layer, initial stress acting in half-space and wave number on the phase velocity of torsional surface wave has been exhibited. The numerical computation along with graphical illustration has been carried out for fibre-reinforced layer of carbon fibre-epoxy resin and T300/5208 graphite/epoxy material for the transversely isotropic half-space. As a special case of the problem, deduced dispersion equation is found in well-agreement with the classical Love wave equation. Comparative study for reinforced and reinforced free layer has been performed and also depicted graphically. Moreover some analysis is made to highlight the important peculiarities of the problem.

The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.

This paper studies the reflection and transmission of a plane wave through a fluid layer of finite width sandwiched between two dissimilar monoclinic elastic half-spaces. Closed-form expressions for the phase velocity of quasi-waves (qP and qSV) have been obtained. The reflection/transmission coefficients and energy divisions have been procured for all the reflected and transmitted waves in terms of phase velocity, propagation vector, elastic constants and width of the layer. It has been noticed that these epitomes depend not only upon the incident angle and width of the layer, but also on the character of incident wave. Energy proportions have been calculated numerically to validate the rule of energy conservation at different angles of incidence. Graphical representation has been performed to demonstrate the analytical findings.

Purpose– The response of moving load over a surface is a subject of investigation because of its possible applications in determining the strength of a structure. Recently, with the enlargement of high-speed train networks, concern has been expressed about the effects of moving loads on the track, embankment and nearby structures. Earth surface and artificial structure are not always regular in nature. Irregularities are also responsible for structural collapse of long bridge and highway of plateau area under the action of moving loads. The purpose of this paper is to investigate the influence of irregularity on dynamic response due to a moving shear load.Design/methodology/approach– At first the authors developed the mathematical model for the problem which is comprised of equation of motion together with boundary conditions. Perturbation technique has been used to derive the stresses produced in an irregular orthotropic half-space (which is influenced by gravity) due to a moving shear load. MATLAB and MATHEMATICA softwares have been employed for numerical computation as well as graphical illustration.Findings– In this paper the authors have discussed the stresses produced in an irregular gravitating orthotropic half-space due to a moving shear load. The expression for shear stress has been established in closed form. Substantial effects of depth, irregularity factor, maximum depth of irregularity and gravitational parameter on shear stress have been reported. These effects are also exhibited by means of graphical illustration and numerical computation for an orthotropic material T300/5208 graphite/epoxy which is broadly used in aircraft designing. Moreover, comparison made through meticulous examination for different types of irregularity, presence and absence of anisotropy and gravity are highlighted.Practical implications– A number of classical fatigue failures occur in aircraft structures. The moving load responsible for such fatigue failure may occur during manufacturing process, servicing, etc. Apart from these the aircraft structures may also experience load because of environmental damages (such as lightning strike, overheat) and mechanical damages (like impact damage, overload/bearing failure). Therefore the present study is likely to find application in the field of construction of highways, airport runways and earthquake engineering.Originality/value– To the best of the authors’ knowledge no problem related to moving load on irregular orthotropic half-space under influence of gravity has been attempted by any author till date. Furthermore comparative study for different types of irregularity, presence and absence of anisotropy and influence of gravity on the dynamic response of moving load are novel and major highlights of the present study.

A mathematical model has been developed for the analytical study of propagation of crack due to horizontally polarized shear wave (SH-wave) in an initially stressed inhomogeneous poroelastic strip. The expression of stress intensity factor for the force of constant intensity has been determined in closed form. The emphatic impact of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive or tensile initial stress, vertical compressive or tensile initial stress, heterogeneity parameter, porosity parameter and anisotropy parameter on the stress intensity factor in an initially stressed inhomogeneous poroelastic strip has been depicted by means of graphs. In order to solve the problem, Wiener–Hopf technique specified by Matczynski has been employed. Moreover, some special cases have been deduced from the procured expression of stress intensity factor for the force of constant intensity.

Heterogeneity, being a trivial feature inside the earth or in a geostructure, makes a strong basis for its consideration in the study of geomechanics. Inclusion of the concept of heterogeneity along with irregularity in the medium brings a novelty to the existing literature related to the study of the moving load. The present study investigates the effects of linear and exponential heterogeneity on the dynamic response due to a normal load moving with constant velocity on a rough irregular heterogeneous isotropic half-space in a comparative approach. Expressions for both normal and shear stresses for either case of heterogeneity have been established in closed form. Substantial effects of the affecting parameters such as depth, irregularity factor, maximum depth of irregularity, frictional coefficient, linear heterogeneity parameter and exponential heterogeneity parameter on normal and shear stresses for both the cases of heterogeneity have been observed. Numerical computation has been carried out...

This study investigates the effect of a semi-infinite smooth moving punch due to shear wave propagation in initially stressed, magnetoelastic, transversely isotropic material. The Wiener–Hopf technique has been employed to determine the closed form expression of dynamic stress concentration due to punch with a load of constant intensity. The substantial effects of magnetoelastic coupling parameters, horizontal and vertical compressive/tensile initial stress, and anisotropy on dynamic stress concentrations has been remarkably traced out. Numerical computations and graphical illustrations, along with comparative study, have been executed for three distinct models: when the strip is comprised of Zinc, Beryl material having hexagonal symmetry, and simply isotropic material.

An analytical solution has been attained to establish the closed form expression of stress intensity factor at the tip of a semi-infinite crack, dynamically propagating in an initially stressed transversely isotropic poroelastic strip due to Love-type wave for the case of concentrated force of constant intensity as well as for the case of constant load. The study presents the sound effect of various affecting parameters viz. speed of the crack, length of the crack, horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter on the stress intensity factor. In order to delineate the effects of these aforementioned parameters on the stress intensity factor graphically, numerical simulations have been accomplished. One of the major highlight of the paper is the comparative study carried out for horizontal compressive/tensile initial stress, vertical compressive/tensile initial stress, porosity parameter and anisotropy parameter with the case when the strip is isotropic, non-porous and free from initial stresses. Wiener–Hopf technique and the Fourier integral transform has been effectuated for the procurement of the closed form expression (exact solution) of stress intensity factor.

This paper aims to study the propagation of surface wave in two initially stressed heterogeneous magnetoelastic transversely isotropic media lying over a transversely isotropic half-space under the action of gravity. Heterogeneities of both the layers are caused due to exponential variation in elastic parameters. Dispersion relation is obtained in closed form by using Whittaker's asymptotic expansion. Magnetoelastic coupling parameters, heterogeneity, horizontal compressive initial stress and gravity parameters have remarkable effect on the phase velocity of surface wave. The obtained dispersion relation is found to be in well agreement with the classical Love-wave equation. Comparative study and graphical illustration has been made to exhibit the outcomes.

A physically realistic mathematical problem has been modelled to discuss the reflection and refraction phenomena of three-dimensional (3-D) plane waves. The considered composite structure comprises of water layer of finite width lying between isotropic and ice substrate has been considered. The mathematical analysis pertaining to this problem has been addressed analytically. The closed form expressions for reflection and refraction coefficients of different reflected and refracted waves are derived. Mathematical expressions for the energy share associated with the various waves are also enlisted in a very concise form in connection with the reflection and refraction coefficients. The effects of various polar and azimuthal angles have been exhibited on the reflection and refraction coefficients. The energy conservation law is established to validate this model. Numerical examples and computations have been performed to illustrate the results of this model graphically. Further, as a particular case of the present problem, the deduced results are compared and validated with the pre-established classical results.