A simple formula for predicting resonant frequencies of a rectangular plate with uniformly restrained edges

Abstract

This paper provides empirical formulas for rapidly calculating the resonant frequencies of an orthotropic, rectangular plate with its edges constrained by elastic supports. In particular, the classical boundary condition with guided supports at its edges is considered. Other boundary conditions, such as the guided–free edges, guided–clamped edges and guided–free support edges have also been included in the present study. Simple and closed form empirical formulas have been derived to allow straightforward computations of the modal resonant frequencies. The empirical formulas are based on the analytical results obtained from the Rayleigh–Ritz method. However, the coefficient is determined empirically from the results obtained by other more accurate computational scheme, e.g. finite element method. The method is further generalized to predict the resonant frequencies for general boundary conditions of a square, orthotropic plate.