The Comparison of the Vibration Response Variance of a Plate Subjected to Uniformly Distributed Excitation and Diffused Sound Field Excitation

Abstract

The response of a structure subjected to diffused sound field excitation at high frequencies can be predicted by Statistical Energy Analysis (SEA), in which the mean energy level of the structure can be obtained. In addition to the mean energy level, the variance of the response is necessary in order to predict the tolerance limit of the response for a conservative design purpose. The theoretical variance prediction model for the case of the diffuse sound field excitation has been developed based on the assumption that the diffused sound field excitation can be regarded as a uniformly distributed point force excitation (rain-on-the-roof excitation). This model yields the ensemble variance of the vibration response taken over the structures with random parameters. In this paper, the group of plate structures with random natural frequencies is generated by Gaussian random Young's moduli of the plates, of which responses are numerically calculated by modal analyses for diffused sound field excitation and rain-on-the-roof excitation. The ensemble variances of the response to these two excitations are compared to the variance value predicted by the theoretical model. The result from the comparison shows good agreement between the prediction method and the numerical results, and the applicability of the prediction method to diffuse sound field excitation case is also discussed.