Vibration and Post-buckling of In-Plane Loaded Rectangular Plates Using a Multiterm Galerkin’s Method

Abstract

A procedure to calculate the natural frequencies of in-plane loaded, thin, slightly curved, simply supported rectangular plates is presented, with numerical results. This includes the solutions to von Karman’s static equilibrium equation and the linear shell vibration equation using Galerkin’s method. The compatibility equations are given in terms of Airy stress functions which satisfy the “shear free” and “constant normal displacement” in-plane edge conditions. This procedure is an extension to the method presented by Hui and Leissa, the difference being the use of a multiterm Fourier series representation for the initial imperfection, the static deflection and the vibratory modes.