On the ensemble variance of the energy of random plates loaded by point forces and distributed pressure fields

Abstract

Statistical energy analysis (SEA) is used to predict the dynamic behavior of structural-acoustic systems at high frequencies. SEA predicts the mean vibrational energy over an ensemble of nominally equivalent systems. For example, a collection of individual cars coming off an assemble line would make an ensemble whose mean response is predicted by SEA. Recently a prediction of the variance of the energy in the SEA ensemble has been developed. At high frequencies where small changes in the system cause shifts in natural frequency that are larger than the average spacing of the natural frequencies, the variance becomes independent of the detailed nature of the differences between the members of the ensemble. This variance of energy can then be predicted with information available in an SEA model and with some few additional parameters describing the nature of the excitations and couplings. This new formulation is applied to an ensemble of random plates loaded by point forces and distributed pressure fields. An accurate prediction of the observed variance is demonstrated.