Multi-frequency model reduction for uncertainty quantification in computational vibroacoutics

This work is devoted to the vibroacoustics of complex systems over a broad-frequency band of analysis. The considered system is composed of a complex structure coupled with an internal acoustic cavity. On one hand, the global displacements are associated with the main stiff part and on the other hand, the local displacements are associated with the preponderant vibrations of the flexible subparts. Such complex structures induce interweaving of these two types of displacements, which introduce an overlap of the usual three frequency bands (low-, medium- and high-frequency bands (LF, MF, and HF). A reduced-order computational vibroacoustic model is constructed by using a classical modal analysis with the elastic and acoustic modes. Nevertheless, the dimension of such reduced-order model (ROM) is still important when there is an overlap for each one of the three frequency bands. A multi-frequency reduced-order model is then constructed for the structure over the LF, MF, and HF bands. The strategy is based on a multilevel projection consisting in introducing three reduced-order bases that are obtained by using a spatial filtering methodology. To filter out the local displacements in the structure, a set of global shape functions is introduced. In addition, a classical ROM using acoustic modes is carried out for the acoustic cavity. Then, the coupling between the multilevel ROM and the acoustic ROM is presented. A nonparametric probabilistic modeling is then proposed to take into account the model uncertainties induced by modeling errors that increase with the frequency. The proposed approach is applied to a large-scale computational vibroacoustic model of a car.