An innovative series solution for dynamic response of rectangular Mindlin plate on two-parameter elastic foundation, with general boundary conditions

Abstract

In this paper, a new analytical approach is proposed for free vibration and buckling analysis of a rectangular Mindlin plate resting on the Winkler–Pasternak foundation of varying stiffness. According to Mindlin theory, there are three independent governing differential equations. Thus, three Fourier series expansions along with auxiliary polynomial functions are employed to represent the plate's deflection and rotation angle functions. The process of making a set of equations is then completed satisfying the corresponding equilibrium equations and boundary conditions. The proposed method incorporates general elastic supports for all plate's edges, and subsequently can deal with all possible boundary conditions including classical ones as well as uniform or non-uniform elastic constraints. The natural frequencies and buckling loads of several examples are determined to merely show the accuracy of the presented approach.