Vibration Analysis of Simply Supported Rectangular Plates Constrained by Rotational Edge Springs

Abstract

Comprehensive and accurate numerical results are presented for natural frequencies of thin isotropic, simply supported rectangular plates additionally constrained by rotational elastic springs on the edges. For complete coverage of combination, the number of all the combinations in boundary conditions of simply supported, rotationally constrained and clamped is calculated by Polya counting theory, and all sets of frequency parameters are tabulated for the lowest five modes. The Ritz method, along with displacements assumed in special polynomial form with boundary index, is used to include the strain energy stored in the rotational springs. Convergence and comparison studies are made to demonstrate accuracy of  tabulated results, and the frequency parameters are listed for the fifteen sets of boundary conditions and various spring stiffness of the square plates. Some results are also presented for rectangular plates.