FREE VIBRATION ANALYSIS OF TRANSVERSE ISOTROPIC THICK RECTANGULAR PLATES ON TWO-PARAMETER PASTERNAK FOUNDATION

In this research, an exact solution for free vibration analysis of thick transversely isotropic simply supported rectangular plates on the Pasternak foundation was proposed using the displacement potential function method. By means of the proposed displacement potential functions for dynamic problems by Eskandari-Ghadi, the differential governing equations in terms of displacements were converted into two linear partial differential equations of second and forth order. These differential equations were solved based on the separation of variables method and satisfying exact boundary conditions. In order to validate the results, the obtained results were 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 were 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 the 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 were obtained in different range of thickness ratios, aspect ratios, elastic foundation coefficients, and mechanical characteristics of plates. It was observed that with increasing thickness ratio and aspect ratio of the plate, the non-dimensional natural frequencies of plate decreased and increased, respectively. In addition, comparative results of isotropic and transversely isotropic plates showed that shear modulus in transverse direction would have significant influence on the vibrational behavior of rectangular plates. It was shown that when the value of the thickness ratio increased, the sensitivity of non-dimensional frequency response to values of foundation stiffness coefficients decreased. In addition, it can be conducted that the effect of the shearing layer of elastic foundation coefficient value increased by increasing the thickness ratios of plates.