A continuum three-dimensional vibration analysis of thick rectangular plates

Abstract

This paper presents a continuum three-dimensional Ritz formulation for the vibration analysis of homogeneous, thick, rectangular plates with arbitrary combinations of boundary constraints. This model is formulated on the basis of the linear, three-dimensional, small deformation elasticity theory to predict the vibratory responses of these thick rectangular plates. The displacement fields in the transverse and in-plane directions are expressed by sets of orthogonally generated polynomial functions. These shape functions are intrinsically a product of a class of orthogonal polynomial functions and a basic function which are chosen to satisfy the essential geometric boundary conditions at the outset. Sets of frequency data for plates with various aspect ratios and thickness ratios have been presented. These data are used to examine the merits and limitations of the classical plate theory and Mindlin plate theory by direct comparisons. Finally, using the three-dimensional continuum approach, sets of first known deformed mode shapes have been generated thus helping to understand the vibratory motion. Furthermore, these results may also serve as the benchmark to further research into the refined plate theories.