Surface waves problem in a thermoviscoelastic porous half-space

Abstract

In this paper we analyze the surface Rayleigh waves in a half space filled by a linear thermoviscoelastic material with voids. We take into account the effect of the thermal and viscous dissipation energies upon the corresponding waves and, consequently, we study the damped in time wave solutions. The associated characteristic equation (the propagation condition) is a ten degree equation with complex coefficients and, therefore, its solutions are complex numbers. Consequently, the secular equation results to be with complex coefficients, and therefore, the surface wave is damped in time and dispersed. We obtain the explicit form of the solution to the surface wave propagation problem and we write the dispersion equation in terms of the wave speed and the thermoviscoelastic homogeneous profile. The secular equation is established in an implicit form and afterwards an explicit form is written for an isotropic and homogeneous thermoviscoelastic porous half-space. Furthermore, we use numerical methods and computations to solve the secular equation for some special classes of thermoviscoelastic materials considered in the literature.