Transverse vibration of a circular plate with arbitrary thickness variation

Rayleigh-Ritz method has been employed to obtain approximations to frequencies and mode shapes of circular plates with variable thickness. The boundary is either clamped, simply supported or completely free. The main distinguishing feature of the present investigations is that the thickness approximation is done by measuring thickness at a suitable set of sample points and then using interpolation to get the approximating polynomial. Thus, unlike other methods already available in literature where either linear or quadratic variation of thickness has been examined, here one can have a polynomial of arbitrary degree depending upon the number and locations of the sample points. The results have been tabulated in a large number of cases and three-dimensional mode shapes have been plotted for some selected cases. Comparison has been made with available results. A short tables are also given to depict the rate of convergence with the order of approximation.