Clamped plates considered as three-dimensional solids: A method to find arbitrary precision frequencies

Abstract

In this paper, the plate is assumed as a regular prism of arbitrary aspect ratio and thickness with four consecutive faces clamped. By increasing the thickness from zero, one may model the thin, moderately thick and thick plate successively. By means of WEM, the frequency parameters are obtained for the transverse modes of vibration with arbitrary precision. Other modes (such as the "breathing'' ones) might be easily considered. Also, a finite-element model using "brick'' elements was solved for comparison.