Statistical Energy Analysis (SEA) based approaches for the mid- and high-frequency vibro-acoustic analysis of complex systems

Abstract

This paper will present methods for predicting the statistics of the frequency response functions of complex random vibro-acoustic systems. The statistical properties include the ensemble mean, the ensemble variance, level crossing rates, extreme values, and quefrencies. The approach is based on a combination of statistical energy analysis (SEA), the finite element method, random point process theory, and random matrix theory. In the mid frequency range the finite element method is used to model components that have a low modal density, while other components are modelled as SEA subsystems. The coupling between the finite element components and the SEA subsystems is effected using the diffuse field reciprocity principle, which was developed some years ago. The blocked modes of the SEA subsystems are assumed to have natural frequency statistics that are governed by the Gaussian Orthogonal Ensemble, and this enables the statistical properties of the response to be found without any need for Monte Carlo simulations. The use of SEA leads to a relatively low number of degrees of freedom used in the model, and thus the approach is numerically efficient well suited to the design stage, where many design options may be explored.