Three-dimensional vibration of rectangular plates : Effects of thickness and edge constraints

A continuum three-dimensional Ritz formulation is presented for the free vibration analysis of homogeneous, isotropic, thick, rectangular plates. The method is applied specifically to investigate the effects of boundary constraints and thickness ratios on the vibration responses of these plates. A general switching of transverse vibratory motions to surface-parallel modes at the higher thickness ratio is manifested vividly through three-dimensional deformed mode shape plots. The present formulation is based on the linear, three-dimensional, small-strain elasticity energy principle. In the solution process, sets of self-generating polynomial shape functions are used to derive the governing eigenvalue equation. In essence, these functions comprise a class of orthogonal polynomial functions and a basic function which is chosen to satisfy the essential geometric boundary conditions at the outset. They are found very suitable for the computationally intensive task of 3-D modelling due to the ease of generation and numerical implementation. Several numerical examples have been computed to demonstrate the accuracy and efficiency of the method. The influences of plate thickness and boundary constraints on the overall vibratory characteristics of thick plates are also discussed in detail. © 1995 Academic Press. All rights reserved.