Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part II: Frequency analysis

Abstract

This paper deals with exact solutions for free vibration analysis of rectangular Mindlin plates when uniformly and linearly distributed in-plane loading is acting at two opposite edges simply supported. Different combinations of free, simply supported and clamped boundary conditions may be taken into account for the other two edges. The plate is resting on Winkler- and Pasternak-type foundations. In order to extract characteristic equations of the rectangular plate under in-plane loading resting on elastic foundation, the analysis procedure is based on the Mindlin plate theory considering the first-order shear deformation effect, including plate-foundation interaction. After making a comparison of results with those available in literature and confirming the excellent accuracy of the present closed-form exact solutions, the effect of foundation stiffness parameters and loading factors on the natural frequencies of the plate, constrained by different combinations of classical boundary conditions, is presented for various values of aspect ratios and thickness to length ratios. Furthermore, the effect of the above-mentioned parameters on nondimensional frequency parameter is graphically presented for a wide range of in-plane loads.