The method of annular finite elements with variable thickness is applied for analyzing the lateral vibration of thin annular and circular plates. The material of the plates may be of isotropic or polar orthotropic and the plate thickness may vary arbitrarily with the radius. Natural frequencies and mode shapes of the axisymmetric and nonaxi-symmetric modes are obtained. The numerical convergence of the method has been tested and comparisons have been made with the results obtained in other studies. It has been proved that the convergence of this method is very rapid and obtained results are very accurate.

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