Efficacy of Orthogonal Polynomial Displacement Functions in Dynamic Analysis of Rectangular Plates

Abstract

In this paper, the derivation of orthogonal polynomial displacement functions based on static deflection profiles for rectangular plates with various boundary conditions was carried out. The completeness characteristics for appropriate shape functions were taken into consideration; and the derived polynomial shape functions satisfied the homogeneous boundary conditions. Furthermore, the efficacy of the derived polynomial shape functions in dynamic analysis of rectangular plates was determined by using the derived polynomial shape functions to determine the fundamental frequencies of rectangular plate with various boundary conditions in Ritz method. The numerical values for the fundamental frequencies of rectangular plates as computed were compared with the results from previous work in literature; and it was discovered that 76.19% of the boundary conditions of rectangular plates showed good convergence to results in literature. Equally observed, the set of boundary conditions containing two or more free edges conditions exhibited poor convergence to exact results. Nonetheless, the mean percentage difference between the present study’s results and those results from the previous work in literature is 12.581, which in view of statistical interpretation is in close agreement with results in literature.