Transverse vibration of thick rectangular plates—I. Comprehensive sets of boundary conditions

Abstract

Recently, comprehensive research work has been carried out on the free vibration analysis of thick rectangular plates. Due to its practical importance, a vast array of research results will be presented in a series of four papers. These papers will present comprehensive sets of accurate vibration frequencies for thick rectangular plates subjected to: 21 boundary conditions involving all possible combinations of clamped, simply supported and free edges (part I); oblique internal line supports (part II); internal ring supports (part III) and in-plane isotropic pressure (part IV). In this study, sets of mathematically complete two-dimensional polynomials are assumed in the displacement and rotational functions to approximate the appropriate mode shapes. The energy function derived using Mindlin's plate theory is minimized using the Rayleigh-Ritz procedure which leads to the governing eigenvalue equations. In this part (part I), sets of reasonably accurate vibration frequencies are presented for a wide range of aspect ratios a b and relative thickness ratios t b for each boundary condition. The present results, where possible, are compared with other existing established values.