A simple finite element analysis of axisymmetric vibration of annular and circular plates

The axisymmetric vibration of annular and circular plates, isotropic or polar orthotropic, is analysed by an axisymmetric finite element. The features of the present study are that: (i) the formulation of the finite element is based on elasticity theory and has no assumptions as in the conventional plate theory-based analysis, yet is still simple and ready for use, and (ii) the boundary conditions are satisfied exactly and the significant effect of boundary conditions on the vibration frequency is demonstrated. Comparisons with alternative solutions show the accuracy of the present approach and the inadequacy of conventional methods in dealing with the vibration of annular and circular plates with simply supported boundary conditions.

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