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This study deals with the propagation of a semi-infinite crack influenced by SH-wave propagation in an initially stressed dry sandy (ISDS) strip. The Fourier integral transforms (FIT) and Wiener–Hopf (WH) approach are used to solve the model analytically. For the cases of concentrated force of constant intensity (CF) and constant load (CL), the stress intensity factor (SIF) is calculated. The effects of sandiness, crack speed/length, and initial stress on the SIF in ISDS strip are numerically elucidated and graphically demonstrated. Comparison of the SIF analysed for differently configured strips influenced by distinct cases of initial stresses is one of the novel features of this study. [ABSTRACT FROM AUTHOR]

In the present model, we have analyzed the dynamic stress concentration of a semi-infinite smooth moving punch on the shear wave propagation in an initially stressed dry sandy strip. For the analytical solution of the problem, the Wiener–Hopf technique and two-sided Fourier integral transforms have been used. The expression of dynamic stress concentration for the force of a constant intensity has been determined in closed-form. Noticeable effects of the speed of the moving punch, horizontal initial stress, vertical initial stress, and sandiness parameter on the dynamic stress concentration in an initially stressed dry sandy strip have been unraveled and depicted by numerical computations and graphical demonstrations. Further, the expression of dynamic stress concentration for the case of constant load has been deduced from the obtained expression of dynamic stress concentration. Comparison of dynamic stress concentration performed for different cases of initial stresses and differently configured strips serve as one of the major highlights of the present problem. Moreover, for the sake of validation, the obtained results for constant load have been matched with the pre-established results as a particular case of the problem. [ABSTRACT FROM AUTHOR]

• Scattering of SH wave on an irregular surface of the piezomagnetic stratum-substrate structure is studied. • The expressions of frequency relation and group velocity of SH wave is derived in closed form for both MO and MS cases. • The expressions of mechanical displacement and magnetic potential are derived for three different shaped irregularities. • Validation of the derived results of both cases is found in well agreement with the classical Love wave equation. • The impact of material properties is depicted on the phase velocity and group velocity of SH wave for both MO and MS cases. The present paper investigates the scattering phenomenon of horizontally polarized Shear wave on an irregular surface of the piezomagnetic stratum lying over a piezomagnetic substrate. The expressions of frequency relation and group velocity of scattered Shear wave on the considered piezomagnetic stratum-substrate structure are deduced for magnetically open and magnetically short cases by inducing appropriate boundary conditions. A closed form expressions of reflected mechanical displacement and reflected magnetic potential function related to stratum and substrate are also determined for three different shaped irregularities (rectangular shaped, parabolic shaped and triangular shaped) by employing perturbation technique and residue theorem for both magnetically open and short cases. The efficacy of piezomagnetic coupling parameter, vertical irregular parameter due to presence of surface irregularities is portrayed on the phase velocity, group velocity, reflected mechanical displacement and reflected magnetic potential function related to the stratum for both magnetically open and short conditions graphically. A comparative study is also made to examine the impact of different shaped irregularities on the reflected mechanical displacement and reflected magnetic potential function of the stratum. [ABSTRACT FROM AUTHOR]

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-stressed fibre-reinforced stratum and pre-stressed dry sandy viscoelastic substrate. Method of separation of variables has been adopted as the solution technique for the problem. Closed form of dispersion equation for the propagation of shear wave in the layered structure has been deduced analytically and the obtained result has been found in agreement with the classical case. The effect of various parameters, viz. wave number, width ratio, bonding parameter, initial stress, sandiness parameter and shear viscosity on the phase velocity of shear wave has been studied through numerical computations and graphical illustrations. Some remarkable results regarding the propagation behavior of shear wave in the considered 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. [ABSTRACT FROM AUTHOR]

This study deals with the deduction of the stress intensity factor (SIF) for the propagation of rectilinear semi-infinite noncentrally located interfacial crack influenced by propagating SH-waves in the framework of two different dry sandy layers composed of a strip under various loading conditions. Two-sided Fourier integral transform, Liouville's, and Abel's theorem along with the Wiener–Hopf technique serve as a salient feature of the adopted mathematical treatment. The analysis has been carried out for constant loading (CL) and stress-free (SF) cases under nonharmonic loading (NHL), and for constant amplitude of vibration (CAV) and SF cases under harmonic loading (HL). Moreover, the expression of SIF for the static crack has been obtained under various conditions of NHL and HL as a limiting case. The effects of various existing parameters, viz., dry sandiness ratio, width ratio, sandiness parameter of upper and lower layers, inhomogeneity parameter on the SIF for the previously mentioned cases along with comparative analysis for differently configured dry sandy elastic strips have been investigated numerically as well as graphically. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

During the occurrence of earthquake, the shear wave propagates in the rocks present inside/at the Earth’s crust. The propagation of shear wave may lead to the progression of punch present inside the rock medium. As a result of this, substantial stress accumulated at the vicinity of propagating punch inside rock medium which significantly affects the stability of various geological and human-made structure and, hence, may cause failure of structure. Therefore, the analysis of stress concentration at the vicinity of punch moving due to shear wave propagation has become prominent in the area of seismology. In the present paper, an analytical perspective has been employed to discuss the influence of velocity of moving punch associated with the propagation of shear wave on developed dynamic stress concentration (DSC) in three types of pre-stressed vertical transversely isotropic (VTI) poroelastic media viz. granite (an igneous rock); sandstone (a sedimentary rock); and marble (a metamorphic rock). The closed form expression of DSC for the force of constant intensity has been derived with the aid of Weiner-Hopf technique along with Galilean and two-sided Fourier integral transformations. The noticeable influence of different affecting parameters (viz. velocity of moving punch associated with the shear wave propagation, horizontal compressive/tensile initial stresses, vertical compressive/tensile initial stress, porosity, and anisotropy parameter) on dynamic stress concentration has also been reported. Numerical computation and graphical illustrations have been carried out for the aforementioned three different types of porous rocks to investigate the profound impact of affecting parameters on DSC. Moreover, some noteworthy peculiarities have also been derived from the obtained expression of dynamic stress concentration. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to theoretically analyze the propagation of Love-type wave in an irregular piezoelectric layer superimposed on an isotropic elastic substrate.Design/methodology/approach The perturbation technique and Fourier transform have been applied for the solution procedure of the problem. The closed-form expressions of the dispersion relation have been analytically established considering different type of irregularities, namely, rectangular and parabolic for both the cases of electrically open and short conditions.Findings The study reveals that the phase velocity of Love-type wave is prominently influenced by wave number, size of irregularity, piezoelectric constant and dielectric constant of an irregular piezoelectric layer. Numerical simulation and graphical illustrations have been effectuated to depict the pronounced impact of aforementioned affecting parameters on the phase velocity of Love-type wave. The major highlight of the paper is the comparative study carried out for rectangular irregularity and parabolic irregularity in both electrically open and short conditions. Classical Love wave equation has been recovered for both the electrical conditions as the limiting case when both media are elastic and interface between them is regular.Practical implications The consequences of the study can be utilized in the design of surface acoustic wave devices to enhance their efficiency, as the material properties and the type of irregularities present in the piezoelectric layer enable Love-type wave to propagate along the surface of the layer promoting the confinement of wave for a longer duration.Originality/value Up to now, none of the authors have yet studied the propagation of Love waves in a piezoelectric layer overlying an isotropic substrate involving both parabolic and rectangular irregularities. Further, the comparative study of rectangular irregularity and parabolic irregularity for both the cases of electrically open and short conditions elucidating the latent characteristics is among the major highlights and reflects the novelty of the present study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

This article deals with the propagation of SH-wave in a vertically heterogeneous viscoelastic layer lying over a micropolar elastic half-space. Dispersion and damping equations are obtained analytically in closed form. Phase and damped velocities are computed numerically and depicted by means of a graph to exhibit the substantial effect of heterogeneity, viscoelasticity (internal friction), and micropolar parameter. As a special case of the problem, it is found that deduced dispersion relation is well in agreement to the classical-Love wave equation and damping equation vanishes identically for the isotropic case. Influence of micropolarity present in the medium of half-space is highlighted through comparative study. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A mathematical model is developed in which the effect of imperfect bonding between the constituents of layer and half-space on the phase velocity and damped velocity of SH-wave is discussed. The model consists of a micropolar elastic half-space bonded imperfectly with a heterogeneous viscoelastic layer. The dispersion equation and damping equation of SH-wave propagation in the said model is obtained in the closed form analytically. The effects of imperfect bonding, internal friction, heterogeneity, micropolarity, and complex interface stiffness parameters highlighted through numerical computation and graphical demonstrations. Standard Love-wave equation and dispersion equation as well as damping equation for perfectly bonded micropolar half-space with heterogeneous viscoelastic layer is obtained as a special case of the problem. Through comparative study of homogeneity with heterogeneity in the layer; imperfect bonding of layer and half-space with their welded (perfect) contact; and presence of micropolarity in half-space with its absence in half-space are compared meticulously. [ABSTRACT FROM PUBLISHER]

The present paper investigates the propagation of horizontally polarised shear wave in distinct vertically heterogeneous double layers overlying an isotropic half-space under horizontal initial stress. The vertical heterogeneity in the uppermost layer is caused due to quadratic variation only in rigidity, whereas vertical heterogeneity in the sandwiched layer is caused due to exponential variation in rigidity and density both. The closed form of velocity equation is obtained which leads to the dispersion equation as its real part and damping equation as its imaginary part. The validation of dispersion relation with the classical case is made by using Debye asymptotic expansion which is the major highlight of this study. The significant effect of the width ratio of the layers, heterogeneity parameters of both the layers and horizontal compressive/tensile initial stress on the phase velocity and damped velocity of SH-wave have been traced out. The comparative study and some important peculiarities have been revealed by means of graphical illustrations. [ABSTRACT FROM AUTHOR]

This paper investigates the propagation of crack due to horizontally polarized shear waves in a magnetoelastic self-reinforced medium. The methodology includes the Weiner-Hopf technique. The effects of reinforcement and magnetic field on the propagation of the crack have been studied. The stress intensity factor at the crack tip for a concentrated force of a constant intensity has been calculated and depicted by means of graphs for various cases. It is observed that self-reinforcement increases the stress intensity factor whereas magnetoelastic coupling parameter has the reverse impact. It is remarkable to state that the stress intensity factor decreases with the increase in the length of crack. Also, the comparative study has been made through graphs to find the effect of reinforcement over the reinforced-free case on the stress intensity factor. Moreover, some important peculiarities have been observed in graphs. [ABSTRACT FROM AUTHOR]

The present paper discusses the dispersion equation for horizontally polarized shear waves (SH waves) in a non-homogeneous self-reinforced layer over a semi infinite self-reinforced medium with an irregularity. The dispersion equation has been obtained in closed form. In the isotropic case, when non homogeneity and irregularity are absent, the dispersion equation reduces to standard SH wave equation. The dispersion curves have been presented by means of graphs for different sizes of irregularity and different values of non-homogeneity parameters. The influence of depth of irregularity and non-homogeneity parameters on phase velocity has been studied. [ABSTRACT FROM PUBLISHER]

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. • Propagation of shear wave in an initially stressed composite structure under the influence of an impulsive source. • Structure is composed of a transversely isotropic porous layer over a dry sandy stratum and functionally graded substrate. • Bonding between the interfaces of the layers and semi-infinite medium are considered to be imperfect. • Green's function along with Fourier's transform has been employed to establish the closed form of dispersion equation. • Obtained results are found in well agreement with pre-established and classical results through particular cases. [ABSTRACT FROM AUTHOR]

• Dispersion characteristics of shear wave propagation in an anisotropic dry sandy spherical layered structure is studied. • Structure is composed of isotropic sandy medium covered by a concentric transversely isotropic sandy layer of finite width. • Analytical treatment with contour integration and Fourier-Legendre Expansion theorem is used to achieve dispersion relation. • Debye Asymptotic Expansion is employed to obtain exact closed form dispersion relation and matched with classical result. • Numerical computations are carried out to illustrate the influence of affecting parameters on dispersion curves graphically. 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. [ABSTRACT FROM AUTHOR]