Nonlinear model updating of frictional structures through frequency-energy analysis

Recently, some researchers have suggested using frequency-energy representations of nonlinear normal modes (NNMs) for nonlinear model updating of conservative systems. The current work investigates this idea for frictional structures. The studied structure undergoes friction under variable normal contact force. Based on the invariance principle, the NNM-branch extension of the experimental structure's first linear mode was obtained in a new way: The frequency-energy plot (FEP) was approximated by measuring the instantaneous frequencies and total energy of the system's nonlinear decaying response. The wavelet-bounded empirical mode decomposition (WBEMD) method was used to obtain the first isolated frequency component of the experimental signals. On the other hand, theoretical FEPs were computed for every candidate nonlinear model's equivalent conservative system. To do this, the extended periodic motion concept (EPMC) was used while introducing the multi-harmonic balance (MHB) equations into a continuation algorithm. The proposed model updating method considers the overlapping of such FEPs as a measure of similarity between dynamic behaviors of design model and the real structure. Finally, after performing sensitivity analysis for the named criterion, the updated nonlinear model was verified against the experimental data. This survey concludes that the new technique is capable of successfully updating the nonlinear finite element model of the structures that contain frictional contact undergoing variable normal force. Therefore, it can be used for bladed-disk systems, in which frictional contacts serve as energy dissipators. The proposed method's applicability is restricted to a certain band of system's mechanical energy starting from linear regimes of motion. By increasing this energy level, the occurrence of first strong modal interactions would prevent the decomposition of response to isolated frequency components.