Large Amplitude Vibration of a Circular Plate With Concentric Rigid Mass

Abstract

Simplified nonlinear governing differential equations proposed by Berger and extended by Nash and Modeer are applied to obtain natural frequencies of a circular plate with concentric rigid part at its center in large amplitude vibrations. A modified Galerkin technique is used to derive a nonlinear differential equation of which the solution is given in terms of elliptic functions. The small amplitude vibration is treated as a special case of large amplitude vibration, while the free, large amplitude vibration of a flat circular plate is studied as a special case of large amplitude vibration of a circular plate with a concentric mass. The numerical results show that the effect of added concentric rigid mass to a circular plate is significant.