Rayleigh surface waves problem in linear thermoviscoelasticity with voids

In this paper, we study the propagation of the Rayleigh surface waves in a half-space filled by an exponentially functionally graded thermoviscoelastic material with voids. We take into consideration the dissipative character of the porous thermoviscoelastic models upon the propagation waves and study the damped in time wave solutions. The propagation condition is established in the form of an algebraic equation of tenth degree whose coefficients are complex numbers. The eigensolutions of the dynamical system are explicitly obtained in terms of the characteristic solutions. The concerned solution of the Rayleigh surface wave problem is expressed as a linear combination of the five analytical solutions, while the secular equation is established in an implicit form. The explicit secular equation is obtained for an isotropic and homogeneous thermoviscoelastic porous half-space, and some numerical simulations are given for a specific material.