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Multi-Frequency Model Reduction for Uncertainty Quantification in Computational Vibroacoustics of Automobiles
ISSN: 0148-7191, e-ISSN: 2688-3627
To be published on June 03, 2020 by SAE International in United States
Event: 11th International Styrian Noise, Vibration & Harshness Congress: The European Automotive Noise Conference
This paper deals with the vibroacoustics of complex systems over a broad frequency band of analysis. The system under consideration is composed of a complex structure coupled with an internal acoustic cavity, such as the one encountered in automotive industry. The complex structure is defined by a complex geometry, constituted of heterogeneous materials and of two types of structural levels: a stiff main part and numerous flexible sub-parts. In such a structure, the vibroacoustics model is represented by the usual global-displacements elastic modes associated with the main part, and by numerous local elastic modes, which correspond to the preponderant vibrations of the flexible sub-parts. However, in the framework of automobile vibroacoustic modeling, the main difficulty is the interweaving of the global displacements with the numerous local displacements, which introduce an overlap of the usual three frequency domains (low- (LF), medium- (MF), and high frequency (HF)). In the automotive industry, computational vibroacoustic models are used for predicting the internal noise levels. However, the dimension of computational vibroacoustic models is very high. In this paper, a computational model with 19 million of degrees-of-freedom (DOFs) for the structural part and 1 million of DOFs for the coupled acoustic cavity is considered. Such a high dimension brings some computational challenges that are mostly overpassed by introducing a reduced-order computational vibroacoustic model (ROM) constructed with a classical modal analysis. Nevertheless, the dimension of such ROM is still very important when the frequency band of analysis overlaps the LF, MF and HF domains. Consequently, a multi-level reduced-order model - for the structure [1, 2] is constructed over the LF, MF, and HF frequency bands. The strategy is based on a multi-level projection consisting in introducing three reduced-order bases (ROBs) that are obtained by using a filtering methodology of local displacements. The filtering method requires the introduction of a set of global shape functions that define a subspace for projecting the mass matrix of the structure yielding a matrix for which the null space is made up of local displacements that need to be filtered out. In addition, a classical ROM using acoustic modes is carried out for the acoustic cavity. Then, the coupling between the multi-level reduced order model and the acoustic reduced-order model is presented. A nonparametric probabilistic modeling [3, 4] is then proposed in order to take into account the model uncertainties induced by modeling errors that increase with the frequency. A numerical application is presented, which consists in a realistic computational vibroacoustic model of a car (structure coupled with an internal acoustic cavity).