Free vibration analysis of all round clamped thin isotropic rectangular plate by Ritz Direct Variational Method

Abstract

This paper developed polynomial comparison functions for the free vibration analysis of clamped thin rectangular plates using the Ritz Direct Variational Method. The polynomials were derived systematically from a predefined formula, which could generate any number of trial functions for any set of plate’s classical boundary conditions. The method was implemented by means of a Mathematica computer programme developed by the authors. The frequency parameters so obtained agreed excellently with those available in the literature. The numerical values of the frequency parameters increased with the aspect ratio irrespective of the mode considered. In addition, the study showed that the more the number of polynomial coordinate functions in the shape function, the better the accuracy of the results. The convergence study corroborated the fact that a one-term approximation yields sufficient accuracy. The convergence was best for square plates, even though acceptable percentages of convergence were obtained for the other side ratios.