A hybrid modal/statistical formulation for predicting the energy response of vibroacoustic systems in the mid frequency range

International audienceThe Statistical modal Energy distribution Analysis (SmEdA) method predicts the power flow between coupled subsystems excited by random excitations from a deterministic modal description of the uncoupled subsystems. As the modes can be computed by Finite Element Method (FEM) for complex subsystems, it can be seen as an extension of FEM to the mid frequency range where the modal densities of subsystems arenot too high. Conversely, the Statistical Energy Analysis (SEA) method is a statistical approach predicting the mean power flow of a population of similar structures presenting manufacturing uncertainties. Assuming a diffuse field within each subsystem, it is dedicated to the high frequency range where modal densities of subsystems are high. However, in many applications, subsystems with low and high modal densities can coexist in the mid frequency range and in that case neither SmEdA nor SEA is well adapted. The purpose of this article is then to propose a hybrid SmEdA/SEA formulation allowing some subsystems with low modal densities to be described by SmEdA and other ones by SEA. For the SEA-described subsystems, the vibratory field of the statistical population is supposed to be diffuse. These subsystems are then characterized by sets of natural frequencies and mode shapes constructed from the Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. In another hand, the SmEdA-described subsystems are represented by their modes that can be extracted by usual computer codes. In order to couple the two models, Monte Carlo simulations are used for generating samples of the stochastic modes of the SEA- described subsystems. From the distribution of the estimated energy response of the coupled subsystems, the ensemble average and the confidence interval can finally be estimated. For validation purpose, the results of the proposed hybrid SmEdA/SEA approach are compared to the numerical results computed with the finite element method (FEM) on a population of plate-cavity systems having similar properties. A good agreement is observed whereas the computation time of the proposed approach is much less important than the one of the FEM which can be up to several days for each element of the population