TRANSVERSE VIBRATION OF SIMPLY SUPPORTED ELLIPTIC AND CIRCULAR PLATES USING BOUNDARY CHARACTERISTIC ORTHOGONAL POLYNOMIALS IN 2 VARIABLES

The first four frequencies and mode shapes have been computed for elliptical and circular plates of uniform thickness with simply supported edges by employing orthogonal polynomials in the Rayleigh-Ritz method. In general, this is found to give better results than traditional methods. Successive approximations have been worked out to ensure convergence. Comparisons have been made with existing results in some cases. Calculations have been done for several values of b a; i.e., the ratio of the semi-major and semi-minor axes. Mode shapes have been used to obtain three-dimensional plots of plates in displaced configurations. © 1992.