Abstract
Galerkin's method has been used to obtain the frequencies of symmetric transverse vibrations of an elliptic plate with clamped edges and variable thickness. The procedure can be used to generate a sequence of approximations which may be truncated when the required number of frequencies have converged to the desired accuracy. The numerical values of the first four frequencies are reported correct to five significant digits for various values of the taper parameter and the ratio of the semi-axes. Mode shapes and the nodal ellipses have also been worked out for the second and third modes. The results for an elliptic plate with uniform thickness, circular plate with parabolically varying thickness and a circular plate with uniform thickness have been obtained as special cases.
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