In this paper we study the spatial behaviour for a large class of isotropic and homogeneous porous thermoelastic materials for which the constitutive coefficients are supposed to satisfy some relaxed positive definiteness conditions. By using some appropriate measures, we are able to establish results describing the spatial behaviour of transient and steady-state solutions in these enlarged classes of thermoelastic porous materials.
This paper is concerned with the linear dynamic theory of thermoelastic solids with microstructure. Existence and uniqueness theorems and general properties of regularity for the solution of initial-boundary-value problems are established.
It is well known that harmonic longitudinal elastic waves propagate without damping in time, while the heat equation leads to standing modes that decrease exponentially over time. In this article, it is shown that the elastic deformation when coupled with thermal deformation leads to the following effects on the propagation of harmonic longitudinal waves and on standing modes: (a) the harmonic longitudinal waves become damped in time; (b) the standing modes suffer a slower decrease in time in relation to the pure thermal modes; and (c) the propagation speed of harmonic longitudinal waves increases in relation to that predicted by the purely elastic theory. The dependence of the dimensionless parameters that characterize the effects described at these previous points in relation to the material and coupling characteristics is explicitly presented and then is numerically simulated and graphically illustrated. As regards the Rayleigh waves class, although a rigorous mathematical proof is not offered, the numerical results presented for a lot of common thermoelastic materials show the same effects of thermoelastic coupling as in the case of longitudinal harmonic plane waves. The present article systematically synthesizes the thermal effects on wave propagation, and it provides a reference work with regard to the thermoelastic coupling.
In this paper we study the spatial behavior of the amplitude of the steady-state vibrations in a thermoviscoelastic porous beam. Here we take into account the effects of the viscoelastic and thermal dissipation energies upon the corresponding harmonic vibrations in a right cylinder made of a thermoviscoelastic porous isotropic material. In fact, we prove that the positiveness of the viscoelastic and thermal dissipation energies are sufficient for characterizing the spatial decay and growth properties of the harmonic vibrations in a cylinder.