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

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