An Integrated Kirchhoff Element by Galerkin Method for Free Vibration Analysis of Plates on Elastic Foundation

Abstract

Plates resting on elastic foundations have many engineering applications, especially in the area of structural engineering. Conventionally these foundation systems can be analyzed using regular plate bending element and discrete soil springs. The present work aims an element formulation which is suitable for dynamic analysis of such elastic foundation systems without the use of explicit discrete soil springs. The scope of the work includes free vibration analysis of an isotropic rectangular plate on elastic foundation with various boundary conditions for different thickness and varying properties of foundation. In this paper, finite element modelling has been done for a rectangular isotropic plate by using a four nodded Kirchhoff rectangular element having three degrees of freedom per node, combined with Winkler model of elastic foundation. Here the formulation has been carried out by integrating the properties of the rectangular plate with properties of elastic foundation using Galerkin weighted residual approach instead of the common methods in use like potential energy approach. Numerical modelling has been carried out by developing a MATLAB code and the results of free vibration analysis obtained are in good agreement with the results reported in earlier studies.