Free vibration and buckling analysis of clamped rectangular plates of variable thickness by the Galerkin method

Abstract

The problem of free vibration and buckling of isotropic clamped rectangular plates of variable thickness is investigated. The fourth order differential equation is solved by using Galerkin's variational method. The thickness of the plate varies linearly along the x axis and this variation is taken to be symmetric with respect to the middle surface. The parameters considered herein, for buckling and free vibration behaviour of rectangular plates of variable thickness, are the plate aspect ratios, taper parameters and load ratios. Simplicity and quick convergence is the advantage of the method in comparison with other much more laborious numerical methods which require extensive computer facilities.