Propagation of thermal waves in a functionally graded thick plate

The aim of the present contribution is concerned with the interactions of thermoelastic displacements, temperatures and stresses for the three-phase-lag and Green-Naghdi heat equations in a functionally graded transversely isotropic plate subjected to a spatially varying heat source. The upper surface of the plate is stress free with prescribed surface temperature while the lower surface of the plate rests on a rigid foundation and is thermally insulated. The governing equations for displacement and temperature fields are obtained in the Laplace-Fourier transform domain by applying Laplace and Fourier transform techniques. The inversion of double transform has been done numerically. The numerical inversion of Laplace transform is done by using a method based on the Fourier Series expansion technique. The solution to the analogous problem for isotropic material is obtained by taking suitable nonhomogeneity parameters. A comparative study between isotropic material and transversely isotropic material is also shown. In absence of nonhomogeneity, the results corresponding to Green-Naghdi II, Green-Naghdi III and 3P lag models agree with the results of the existing literature.