Free transverse vibration of elliptical plates of variable thickness with half of the boundary clamped and the rest free

First four frequencies have been computed for an elliptical plate half of whose boundary ( y ⩾ 0 ) is clamped and the other half is free. The thickness of the plate is taken varying linearly with space coordinates. The Rayleigh–Ritz method has been used to obtain successive approximations utill convergence is achieved up to at least four significant figures. Results are tabulated for various values of the taper parameters. Three-dimensional mode shapes and the associated contour lines have been plotted in some selected cases. A table showing the rate of convergence with increasing order of approximation is given. Comparison has been made with known results in special cases. For the sake of completeness, results for the cases when the entire boundary is clamped or completely free are also reported.