Methodology for model updating of mechanical components with local nonlinearities

In this work, we propose a new nonlinear model updating strategy based on global/local nonlinear system identification of the dynamics. The main objective of this study is to construct and update reduced-order models (ROM) of a dynamical system based solely on measured data. The approach relies on analyzing transient system responses (local dynamics) in the frequency-energy domain, and based on these, constructing damped frequency-energy plots - FEPs (global dynamics) under the assumption of weak damping. The system parameters are characterized and updated by matching the backbone branches of the FEPs with reduced-order model FEPs using experimental or computational data. The main advantage of this method is that the system model is updated solely based on simulation and/or experimental results. It follows that the approach is purely data-driven. By matching the frequency-energy dependences of the dynamics of the physical dynamical system and its reduced order model, we are able to identify, update and reconstruct not only the global features of the dynamics in the frequency and energy ranges of interest, but also the local dynamics, i.e., individual time series for specific initial or excitation conditions. Hence, this work paves the way toward a nonlinear model updating methodology with broad applicability. The main features of the proposed methodology are demonstrated with a system of nonlinearly coupled beams excited by a concentrated transient force.