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

Abstract

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.

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

“…Figures 4 and 5 are devoted to the comparison of solutions at the first and the second orders of approximation respectively between the cases of a half-space with/without slab. The results for the half-space without slab were recently published by the same authors 20 . According to these figures, we concluded that the presence of the bonded slab yields faster attenuation of the solution with depth.…”

“…Body forces and heat sources are disregarded. The dimensionless equations of plane thermoelasticity for a transversely isotropic material within the theory of extended thermodynamics to be considered are expressed in 19 , 20 . They involve the equations of motion, the equation of energy, the evolution laws for the heat flux components and the generalized Hooke’s laws differentiated w.r.t.…”

“…The system of governing equations to be considered here below in dimensionless form is given in 20 . It is formulated within the theory of extended thermodynamics and involves eight first-order partial differential equations: Two equations of motion, the equation of energy, two evolution laws for the heat flux components and three constitutive relations for the identically non-vanishing stress components (these are differentiated w.r.t.…”

“…Ahmed et al 18 , 19 considered a linear, two-dimensional initial-boundary-value problem of heat wave propagation in a thick slab of anisotropic thermal conductor within the dual-phase-lag model. Lately, Youssef et al 20 investigated the nonlinear Rayleigh wave propagation in a half-space of a thermoelastic material within dual-phase-lag, with temperature dependent thermal conductivity using Poincaré small parameter expansion.…”

“…The present work is an extension of 20 to the case of a layered thermoelastic medium consisting of a thick layer rigidly bonded to a half-space, with temperature dependent thermal conductivity for both. The main difference between the present work and the above reference consists of considering a layered medium with an interface, instead of a single half-space.…”