Application of FRF-based inverse substructuring analysis to vehicle NVH problems

A multi-coordinate FRF-based inverse substructuring approach is proposed to partition a vehicle system into two or more substructures, which are coupled at discrete interface points. The joint and free substructure dynamic characteristics are then extracted from the coupled system response spectra. Depending on the actual form of the structural coupling terms, three forms of the coupling matrix are assumed here. The most general one constitutes the non-diagonal form, and the other two simpler cases are the block-diagonal and purely diagonal representations that can be used to simplify testing process and overcome computational problems. The paper is focused on the investigation of the durability of these three formulations when the input FRFs are noise contaminated. A finite element model of a simplified vehicle system is used as the case study. In general, simulation results show that the non-diagonal and block-diagonal formulations are very sensitive to the input noise, while the purely diagonal formulation is much less noise sensitive. This is because the matrix inversion process involved in the non-diagonal and block-diagonal formulations cause the magnification of the input error. The singular value decomposition technique is then applied to address this problem. It turns out the performance of the non-diagonal and block-diagonal formulations can still be improved significantly when the input FRFs are heavily noise contaminated.