TRANSVERSE VIBRATION OF A QUARTER OF AN ELLIPTIC PLATE WITH VARIABLE THICKNESS

Rayleigh-Ritz method has been used to find the first three frequencies and mode shapes for free flexural vibration of a plate in the form of a quadrant of an ellipse with linear and quadratic thickness variations. The results for a quarter of a circular plate with uniform thickness have been obtained as a special case and comparison has been made with results already available. By taking various combinations of clamped, simply-supported and completely-free edges we get twenty-seven different cases. Tables are given for the first three frequencies for different values of parameters. Mode shapes have also been plotted in some cases. The convergence of results is indicated by working out approximations of various orders.