Frequency analysis of annular plates with inner and outer edges elastically restrained and resting on Winkler foundation

The present paper deals with exact analysis of free lateral vibrations of annular plates with inner and outer edges elastically restrained and resting on Winkler type elastic foundation. Exact solution is obtained from the formulation based on the classical plate theory assumptions. The frequencies of the annular plate are computed for various values of elastic rotational and translational restraints, foundation restraint and radius of an annular plate and the results for the first three modes of the plate vibrations are presented in both graphical and tabular form suitable for use in design. The effect of varying values of rotational and translational restraints, foundation restraint and radius of the annular plate on the vibration behavior of annular plates is studied in detail. The exact frequencies of vibration presented in non-dimensional form can serve as benchmark values for researchers to validate their numerical methods when applied for such annular plate problems.