عنوان مقاله [English]
In this research, an exact solution for free vibration analysis of thick transversely isotropic simply supported rectangular plates on the Pasternak foundation presented by using displacement potential function method. By means of proposed displacement potential functions for dynamic problems by Eskandari-Ghadi, the differential governing equations in terms of displacements are converted to two linear partial differential equations of second and forth order. This differential equations are solved based on the separation of variables method and satisfying exact boundary conditions. In order to validate, the obtained results are compared with other available analytical works for isotropic and transversely isotropic plates, and it indicated remarkable agreement. Having no simplifying assumptions for the strain or stress distribution in the plate thickness, the obtained results in this paper are applicable to any arbitrary plate thickness with no limitation on its thickness ratio such as thin, moderately thick and thick plates. Thus, the obtained results of present work can be used as a benchmark solution for other analytical and numerical studies. To investigate the effect of various parameters on the vibrational plate response, the precise non-dimensional frequencies are obtained for different ranges of thickness ratio, aspect ratio, elastic foundation coefficients and mechanical characteristics of plates. It is observed that with increasing thickness ratio and aspect ratio of the plate, the non-dimensional natural frequencies of plate decrease and increase, respectively. In addition, comparative results of isotropic and transversely isotropic plates show that the shear modulus in transverse direction has important influence on the vibrational behavior of rectangular plates. It has been shown that when the value of the thickness ratio increases, the sensitivity of non-dimensional frequency response to values of foundation stiffness coefficients decreases. In addition, it can be conducted that the effect of shearing layer of elastic foundation coefficient value increases by increasing the thickness ratios of plates.