Free and forced in-plane vibration of rectangular plates

Abstract

A mathematical model is developed for the prediction of the forced response of finite plates to in-plane point force excitations. The model illustrates the nature of the coupling between in-plane longitudinal and in-plane shear waves and the resonant characteristics of the in-plane vibrational behavior of finite flat plates. The predicted resonance frequencies and mode shapes are compared against the finite element results and good agreement is found. The mode shapes of the in-plane vibration are depicted for frequencies below and above the first resonance frequency. It is illustrated by example that the input power due to in-plane force excitation at the in-plane resonance frequencies is at the same level as that due to out-of-plane force excitations at the flexural resonances in the same frequency band. The participation of the longitudinal and in-plane shear waves in transmitting the vibrational power and the resulting circulatory pattern of structural intensity is also presented.