Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables

Abstract

A set of characteristic orthogonal polynomials in two variables is used as deflection functions to obtain the natural frequencies and mode shapes of polygonal plates by the Rayleigh-Ritz method. The set of orthogonal polynomials is constructed by employing the Gram-Schmidt orthogonalization procedure. The first six natural frequencies are numerically evaluated for triangular plates of different configurations by using these orthogonal functions and the corresponding mode shapes are plotted. Results are compared with those obtained previously by other methods.