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.
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