Free vibration of arbitrarily shaped plates with concentric ring elastic and/or rigid supports

Abstract

In the work reported in this paper the problem of free vibration of arbitrarily shaped plates with an arbitrary number of concentric ring supports, elastic and/or rigid, has been considered. A general analytical method is presented. In this analysis, the reaction forces of concentric ring supports, elastic and/or rigid, are regarded as the unknown external forces acting on the plate; the analytical solution of dynamic response of the plate is given, and the unknown integral constants in the solution are obtained by utilizing the Fourier expansion collocation method. The frequency equation which is a determinant whose order is equal to the number of the concentric ring supports, is obtained by using the linear relationships between the displacements of the plate at the supports and the reaction forces of the supports. The eigenfrequencies can be given by the searching root method of determinants. To verify the present method, numerical calculations are carried out for a clamped circular plate with a concentric ring, elastic support, and the results obtained are compared with ones obtained by other methods.