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The propagation of SH waves in a heterogeneous viscoelastic layer lying over a heterogeneous viscoelastic half space from a point source is examined analytically. The significance of the heterogeneity of hyperbolic and exponential variations associated with rigidity, viscosity, and density is investigated mathematically. A dispersion equation and displacement components are computed in a compact form, considering the case that displacement and stress are continuous at the interface and stress vanishes on a free surface. The acquired dispersion equation signifies the relation between phase velocity and dimensionless wavenumber. The dispersion equation is highly influenced by heterogeneous parameters of both the layer and the half space. The dispersion equation is reduced to the classical equation of the Love wave after eliminating all the heterogeneous parameters, in agreement with pre-established results. The analysis uses the technique of Fourier transformation and Green’s function. The wavenumber is supposed to be complex, as the frequency is fixed in the viscoelastic model. Graphs are presented to demonstrate the effect of heterogeneous parameters on phase and damping velocity with respect to wavenumber.

Earthquakes yield motions of massive rock layers accompanied by vibrations which travel in waves. This paper analyses the possibility of G-type wave propagation along the plane surface at the interface of two different media which is assumed to be heterogeneous and viscoelastic. The upper layer is considered to be viscoelastic and the lower half space is considered to be an initially stressed heterogeneous half space. The dispersion equation, as well as the phase and group velocities, is obtained in closed form. The dispersion equation agrees with the classical Love type wave. The effects of the nonhomogeneity of the parameters and the initial stress on the phase and group velocities are expressed by means of a graph.

Purpose The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Design/methodology/approach The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves. Findings The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form. Originality/value Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.