Thickness Effect on the Dynamic Behavior of Three-Dimensional Plates by using the Ritz Method

A continuum three-dimensional Ritz formulation is presented for the free vibration analysis of homogeneous, isotropic, thick rectangular plates. The method is applied to investigate the effects of boundary constraints and thickness ratios on the vibration responses of these plates. The present formulation is based on the linear, three-dimensional, small-strain elasticity theory. The in-plane displacements and deflections are approximated by sets of self generating polynomial shape functions able to satisfy the essential geometric boundary conditions at the outset. Several numerical examples have been computed to demonstrate the accuracy and efficiency of the method. The influence of plate thickness and boundary constraints on the vibratory characteristics of thick plates is also discussed in detail.