USE OF 2-DIMENSIONAL ORTHOGONAL POLYNOMIALS FOR VIBRATION ANALYSIS OF CIRCULAR AND ELLIPTIC PLATES

A general numerical method is developed to estimate the natural frequencies and the mode shapes for transverse vibration of circular and elliptical plates. A set of orthogonal plate functions is used as the admissible functions in the Rayleigh-Ritz approach to approximate the eigenvalues and eigenvectors. New starting functions are proposed which are used in a recurrence formula to generate the higher terms in the set of orthogonal plate functions to approximate the mode shapes for circular and elliptical plates. These functions are general and easily formed for circular and elliptical plates having classical boundary conditions. Several numerical examples are solved to demonstrate the applicability and the accuracy of the new proposed plate functions. © 1992.