Free vibration and stability analysis of isotropic rectangular plates on elastic foundation based on Levy’s approach using element based differential transformation (EDTM) and (FEM) finite element

Abstract

Element based Differential Transform method (EDTM) and Finite Element methods (FEM) are applied to analyze the free vibration and stability of isotropic Levy’s rectangular plates resting on Winkler foundation. Two opposite edges of the plate are assumed to be simply supported and the other two may be of any type of boundary conditions. To develop an analytical approach for buckling and free vibration of stepped and multi-span plates, Levy’ solution that satisfies equilibrium and compatibility conditions at the interfaces is used. In this paper, an exact buckling in-plane loads and natural frequencies are determined for many cases and compared with the published results and using other method such as FEM developed by the author.