TRANSVERSE VIBRATION OF THICK RECTANGULAR-PLATES .1. 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 se ries of four papers. These papers will present comprehensive sets of a ccurate vibration frequencies for thick rectangular plates subjected t o: 21 boundary conditions involving all possible combinations of clamp ed, simply supported and free edges (part I); oblique internal line su pports (part II); internal ring supports (part III) and in-plane isotr opic pressure (part IV). In this study, sets of mathematically complet e two-dimensional polynomials are assumed in the displacement and rota tional functions to approximate the appropriate mode shapes. The energ y function derived using Mindlin's plate theory is minimized using the Rayleigh-Ritz procedure which leads to the governing eigenvalue equat ions. In this part (part I), sets of reasonably accurate vibration fre quencies are presented for a wide range of aspect ratios a/b and relat ive thickness ratios t/b for each boundary condition. The present resu lts, where possible, are compared with other existing established valu es.