Energy-density field approach for low- and medium-frequency vibroacoustic analysis of complex structures using a statistical computational model

Abstract

In this paper, an energy-density field approach applied to the vibroacoustic analysis of complex industrial structures in the low-and medium-frequency ranges is presented. This approach uses a statistical computational model. The analyzed system consists of an automotive vehicle structure coupled with its internal acoustic cavity. The objective of this paper is to make use of the statistical properties of the frequency response functions of the vibroacoustic system observed from previous experimental and numerical work. The frequency response functions are expressed in terms of a dimensionless matrix which is estimated using the proposed energy approach. Using this dimensionless matrix, a simplified vibroacoustic model is proposed.

Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances

“…This prior probability distribution is constructed by using the Maximum Entropy Principle [20] (from Information Theory [21]) for which the constraints are defined by the available information [13,14,22,15]. Since the paper [13], many works have been published in order to validate the nonparametric probabilistic approach of model uncertainties with experimental results (see for instance [23,24,25,26,27,28,15,29]), to extend the applicability of the theory to other areas [30,31,32,33,34,35,36,37,38,39,40,41], to extend the theory to new ensembles of positive-definite random matrices yielding a more flexible description of the dispersion levels [42], to apply the theory for the analysis of complex dynamical systems in the medium-frequency range, including vibroacoustic systems, [43,44,23,45,25,26,27,28,46,47,48,39], to analyze nonlinear dynamical systems (i) for local nonlinear elements [49,50,37,…”

Bayesian posteriors of uncertainty quantification in computational structural dynamics for low-and medium-frequency ranges

“…Since the paper [70], many works have been published, in particular concerning extension of the theory and its experimental validations [5,7,8,17,18,23,24,29,31,32,33,36,42,50,60,61,72,73,74,76,78,79].…”

“…1 shows a large variability of the frequency response function. Such a high sensitivity of the frequency responses to uncertainties characterizes the medium-frequency range for which a stochastic modeling of uncertainties is absolutely necessary, in particular, the model uncertainties induced by modeling errors (see [20,24,33,36,42,55,56,73,76]). …”

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

“…calculation of the frequency-dependent wave numbers (25), 2. integration of the purely acoustic boundary conditions (2)- (4) to obtain the uncoupled acoustic WBM matrix A aa , 3. integration of the vibro-acoustic velocity excitation and pressure loading terms to obtain the hybrid coupling matrices C aa and C as , 4. solution of the sparse uncoupled FE model to obtain the auxiliary matrices H and h using equations (36), 5. solution of the densly populated reduced hybrid model (35) to obtain the WB wave function contributions.…”

“…In order to incorporate these effects in the numerical models, Soize and co-workers have recently developed [31][32][33] and validated [34] a non-parametric probabilistic approach to uncertainty modelling in the context of the FEM for low-and mid-frequency vibro-acoustic predictions. In recent work [35] a simplified vibro-acoustic model for low-and mid-frequency response predictions is derived based on an energy-density field which uses this statistical model.…”