Coupled thermopiezoelectric behaviour of a one-dimensional functionally graded piezoelectric medium based on C–T theory

Abstract

In this article, the transient thermopiezoelectric behaviour of a one-dimensional (1D) functionally graded piezoelectric medium subjected to a moving heat source is investigated. The formulation is given based on the Chandrasekhariah and Tzou (C–T) generalized thermoelasticity theory to consider the details of energy transport in the material in comparison with the Lord–Shulman (L–S) generalized theory. All material properties are taken to vary exponentially along the length of the medium except for phase lags, the relaxation time, and the specific heat, which are taken to be constant. The governing partial differential equations are given in the three coupled fields of displacement, temperature, and electric potential based on the C–T theory. Using Laplace transform to eliminate the time dependency of the problem, an analytical method is presented to obtain the coupled fields in the Laplace domain. The solutions are then derived in time domain by employing the fast Laplace inversion technique. Numerical results are shown to display the effects of discontinuities on the temperature and stress distribution, non-homogeneity index and the phase-lag constants of heat flux and temperature gradient on the wave propagation of temperature and stress fields based on the dual-phase-lag model of the C–T. Furthermore, the results are compared between the C–T and L–S thermoelasticity theories. Finally, the results are validated with those reported in the literature.