Abstract
Characteristic orthogonal polynomials in two variables have been generated over the annular region occupied by a circular or elliptic plate satisfying the essential boundary conditions. These are used to express the displacement in the transverse vibration of the plate. The Rayleigh-Ritz method is then applied to study the fundamental mode of vibration. Comparison has been made with the known results for circular annular plates in some cases. The results for the elliptic annular plate are entirely new and are not available elsewhere. All the results are summarized in tables covering various combinations of the boundary conditions.
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