Nonlinear Propagation of Coupled First- and Second-Sound Waves in Thermoelastic Solids

We study coupled nonlinear first- and second-sound propagation along equilibrium and nonequilibrium states of a thermoelastic system undergoing small perturbations. We apply a nonlinear constitutive equation for the Cauchy stress and a nonlinear heat-transport equation ruling the evolution of the heat flux. Both of them account for relaxational and nonlinear effects, as well as for the coupling between strain tensor and heat flux. The speeds of thermomechanical waves are obtained, and we show that they depend on whether the waves are travelling along, or against, a superimposed constant heat flux.