The study of the effects of thermal environment on Free Vibration analysis of two-dimensional Functionally Graded Rectangular plates on Pasternak elastic foundation

This paper is the study of the effects of thermal environment on vibration analysis of a two-dimensional functionally graded rectangular plate on Pasternak elastic foundation. The natural frequencies of the plate are calculated by using the Rayleigh–Ritz method based on minimizing the total energy of the plate.analysis procedure is. The transverse displacement of the plate based on the third-order shear deformation plate theory(TSDT) is approximated by a set of admissible trial functions which is required to satisfy the clamped (CL) and simply supported geometric boundary conditions. For verifying the accuracy of this method, results are compared with those reported in the literature. As we seeit is shown a good conformance is derived from the obtained results and the exact solution. In the numerical results, the effects of volume fraction coefficients, thickness ratios ,aspect ratios of the FG plates, foundation stiffness parameters, temperature and boundary conditions on the natural frequencies are examined and discussed in detail.