Approximate Analysis of the Forced Vibration Response of Plates

Abstract

An approximate method is presented for the forced vibration analysis of plates. It is applicable in excitation frequency ranges close to resonances. A displacement shape for the plate in the resonance region is assumed, which is either an exact or approximate representation for the corresponding free vibration mode shape. The response amplitude is determined from a proper energy balance. The method is demonstrated for two types of plates—simply supported rectangular and clamped circular—subjected to uniform transverse exciting pressure. Special considerations are indicated for cases when degenerate or closely spaced resonant frequencies are present. Both viscous and material damping are treated. Numerical comparisons between approximate and exact forced vibration solutions are made to demonstrate the accuracy of the method.