A free vibration analysis of plates by the Rayleigh-Ritz method using Lagrange multipliers.

Abstract

A method of analyzing free vibrations of plates with arbitrary shape and boundary conditions is proposed in this report. The procedure presented is based on the Rayleigh-Ritz method using Lagrange multipliers. The deflection of plate is expressed by a double power series of x and y. Since this function, in general, does not satisfy geometrical boundary conditions, the Lagrange multiplier method is applied t fullfil them. The strain and kinetic energies are evaluated by a single integral along the edge of plates. The theoretical values obtained are compared with exact values and test results. The comparison shows that the method proposed is useful to analyze the free vibration of plates with arbitrary shape and boundary conditions.