Nonlinear Rayleigh wave propagation in a layered half-space in dual-phase-lag

Abstract

We investigate nonlinear Rayleigh wave propagation in a layered thermoelastic medium composed of a slab rigidly bonded to the surface of a half-space under prescribed external thermal boundary conditions within the dual-phase-lag theory. The heat conduction coefficient for both the slab and the matrix have a linear dependence on temperature. Our aim is to assess the effect of temperature dependence of the heat conductivity, as well as the thermal relaxation times, on the process of wave propagation in the layered medium. Poincaré expansion of the solution in a small parameter and the generation of higher harmonics allow to evaluate the coefficient of this nonlinear coupling in the slab through heat wave propagation measurement. For the used numerical values, the results show that some characteristics of the problem, e.g. the temperature, heat flux and one stress component suffer jumps at the interface, while the other stress components are continuous there. The jump in the heat flux is noticeable only in the first order of nonlinearity. The existence of jumps at the interface may be of interest for measurements. Comparison with the case of the half-space showed that the presence of the slab contributes to faster damping of the solution with depth in the half-space.