Elastic and thermal effects upon the propagation of waves with assigned wavelength

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.