Numerical solution for frequencies and mode shapes of elliptical plate half of whose boundary is simply supported and the rest free

Free transverse vibrations of elliptical and circular plates of variable thickness with half of the boundary is simply supported and the rest is completely free have been computed till the first four frequencies converge to at least four significant digits. The thickness of the plate is taken varying linearly with space coordinates. Computations have been carried out by using the famous Rayleigh–Ritz method. Results are reported for various values of the taper parameters. Almost all the results reported here are entirely new. A table has been prepared to indicate the trend of convergence of the results with increasing the order of approximation. Comparison has been made with known results in special cases. For the sake of completeness, results for the cases when the entire boundary is simply supported or completely free are also reported. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases using tools of Computer Graphics and Turbo C++.