In-Plane Vibration Analysis of Annular Plates Considering All Combinations of Edge Conditions

The Ritz method is applied to an in-plane vibration analysis to obtain accurate frequencies of isotropic annular plates. The method is formulated in a manner that allows all combinations of free boundary conditions, two types of supported (constraining only either radial or circumferential displacement) boundary conditions, and clamped boundary conditions. Admissible functions for the two displacement components are chosen as products of trigonometric functions in the circumferential coordinate and special algebraic polynomials in the radial coordinate, enabling all possible boundary-condition combinations to be satisfied. In the numerical study, after the solution’s accuracy is verified through convergence and comparison tests, extensive and accurate frequency parameters are presented to cover all combinations of the four in-plane boundary conditions along the outer and inner edges of the annular plates.