Nonlinear Rayleigh wave propagation in thermoelastic media in dual-phase-lag

A model of generalized thermoelasticity within dual-phase-lag is used to investigate nonlinear Rayleigh wave propagation in a half-space of a transversely isotropic elastic material. It is assumed that the coefficient of heat conduction is temperature-dependent, a fact that plays an important role in the coupling behaviour analysis of thermoelastic and piezo-thermoelastic solids. Taking such a dependence into account becomes a necessity at higher temperatures and in nano-structures, when the material properties can no longer be considered as constants. Normal mode analysis is applied to find a particular solution to the problem under consideration. A concrete case is solved under prescribed boundary conditions and tentative values of the different material coefficients. The results are discussed to reveal the effect of temperature dependence of the heat conduction coefficient, as well as the thermal relaxation times, on nonlinear Rayleigh wave propagation. All quantities of practical interest are illustrated in two-and three-dimensional plots. The presented results may be useful in the detection of the second harmonic amplitudes through measurements related to the propagating heat wave.