Surface waves problem in a thermoviscoelastic porous half-space

• The surface waves problem is studied for a thermoviscoelastic model for porous materials with dissipation energy.
• The secular equation is explicitly obtained for an isotropic thermoviscoelastic porous half space.
• The thermal and viscous dissipation energies influence the attenuation in time and in deep of the half space for the surface wave solutions.
• Numerical simulation reveals that there can exist more than one solution of the surface wave propagation problem.
• The present analysis leads to surface wave solutions with finite internal energy, instead to that with infinite energy existent in the literature.

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.