Benchmark solution for transverse vibration of annular Reddy plates

Abstract

The exact closed-form solution for freely vibrating annular thick plates is presented on the basis of the Reddy's higher-order shear deformation plate theory. Several combinations of classical boundary conditions including, free, soft simply supported, hard simply supported and clamped, are applied at the inner and outer edges of annular plates. Hamiltonian and minimum potential energy principles are employed to derive the equations of dynamic equilibrium and natural boundary conditions of the plate. To validate the accuracy and effectiveness of the present formulation, direct comparisons are made between our results and those from the literature. In parametric studies, the first eight natural frequencies of annular plates with different combinations of boundary conditions are tabulated for various values of the inner–outer radius ratios and thickness–radius ratios. A set of three-dimensional vibration mode shapes along with their corresponding contour plots are presented to illustrate transverse displacements of annular thick plates. Since the results of the present exact solution are the closest to those of exact three-dimensional elasticity solution, they can serve as a reliable benchmark for checking the accuracy of future numerical and analytical solutions.