Natural frequencies of rectangular plates using a set of static beam functions in Rayleigh-Ritz method

A fast converging series consisting of a set of static beam functions, which is a combination of sine series and polynomials, is developed and these functions are used as the basis functions in the Rayleigh-Ritz method to study the vibrational characteristics of thin, isotropic rectangular plates. In applications, a relatively small number of functions are required, and consequently, a modest amount of computation is necessary. The approach is very simple and straightforward. Some numerical results are given for rectangular plates with various aspect ratios and boundary conditions. Good accuracy and fast convergence of the method are demonstrated by comparisons with available results. Complicating factors (orthotropic properties, in-plane forces, etc.) can also be taken into account without formal difficulties. (C) 1996 Academic Press Limited