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In this paper, a new energy-density field approach is proposed for lowmedium-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. INTRODUCTION Vibroacoustic design of automotive vehicles is becoming a more and more complex task due to the increasing demand of acoustic comfort. Thus, car makers are forced to increase the quality of the design process while keeping its cost within affordable limits. However, in the current design process, the complexity of an automotive vehicle structure as well as the numerous noise sources lead to consider a very large number of Frequency Response Functions (FRF), making the analysis a very exhausting process. Moreover, the existence of modeling uncertainties (data and model errors) as well as product uncertainties increases the difficulty of analyses. In a context of development costs reduction, the need for more robust and simplified models becomes a necessity. In the past years, statistical methods such as the Statistical Energy Analysis (SEA) [1] and its derivations were adopted by the automotive industry as a powerful tool for the analysis of vibroacoustic behavior of complex structures in the high-frequency range. These methods are very efficient because they synthesize the dynamical behavior of a structure in a few robust quantities such as exchanged power or energies. Unfortunately, they do not apply in the lowand medium-frequency ranges, due to some specific assumptions or pre-requisites such as space and frequency homogeneity of responses. Recently developed probabilistic vibroacoustic models now allow investigating the ensemble statistical properties of the dynamic responses of any industrial product (including design diversity as well as manufacturing uncertainties). In the present work an energy density field approach based on a probabilistic computational model is proposed. The use of a probabilistic model is essential since it allows a statistical analysis even when space or frequency responses statistics are not relevant. This permits the application of energy approaches in the lowand mediumfrequency ranges and hopefully the rise of interesting properties. In the first part of the paper, the general structuralacoustic problem of a vehicle at low frequencies is presented, along with current modeling tools. Then, the application of the nonparametric probabilistic approach is introduced, leading to the construction of independent realization of the system dynamic responses (FRF). In a third part, a novel energy density field approach is proposed. The method requires a projection on specific local coordinates, which are introduced in a fourth part. Finally, numerical results are presented, showing immediate benefits of the proposed energy method on an automotive vehicle case. VIBROACOUSTIC PROBLEM ANALYSIS Figure1: Vibroacoustic system modeling The vibroacoustic problem of an automotive vehicle is modeled by a structure coupled with its internal acoustic cavity [2]. Surface or volume forces are applied to the structure and acoustic sources are placed inside the internal acoustic cavity. Such a system is shown in Fig.1. The analysis of the system consists in studying the FRFs between various excitation and observation points. For any structural problem, for example, the linear dynamic response may be written:

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