Energy Density Field Approach for Low- and Medium-Frequency Vibroacoustic Analysis of a Car Body Using a Probabilistic Computational Model

In this paper, a new energy-density field approach is proposed for low- medium-frequency vibroacoustic analysis of complex industrial structures, using a probabilistic computational model. The observed structure is composed of a trimmed body coupled and its internal cavity. The objective of this paper is to take advantage of some statistical properties of the frequency response functions to build a simplified vibroacoustic model. In this approach, the Frequency Response Functions (FRF) of the vibroacoustic system are expressed as the product of a dimensionless “smooth” matrix and local mobilities or impedances, depending on their type (acoustical, vibratory or vibroacoustic). The stochastic computational model of the vibroacoustic system is obtained from the reduced mean computational model and is using a nonparametric probabilistic approach. Thus, both the data uncertainties and the model uncertainties are taken into account. The stochastic equations are solved using the Monte Carlo method providing independent realizations of the dimensionless FRF of the vibroacoustic system. The confidence regions around the mean value of both the conventional FRFs and the dimensionless ones are estimated using quantiles. The mean frequency response functions are used to compute the principal local axes regarding the structural local sensitivities (direction of maximum mobility). Both types of FRFs are then projected over these principal axes. This projection provides useful information about archetypal characteristics of structural components and avoids local correlation problems. Above a selected frequency, some interesting spectral and spatial properties of the dimensionless frequency response functions appear; smooth variations allow building the expected simplified model, by gathering redundant information in the excitation and observation areas.