Analysis of the Nonlinear Multimode Systems Under the Limited Measurement Conditions

Despite advancements in the numerical methods used to simulate the complex systems, structural damping simulation remains debated due to its complexity. Hybrid models are often using the experimentally determined damping, challenging in the nonlinear dynamics, where the conventional methods fail. The Hilbert Transform assesses linear and nonlinear systems, but struggles with the polymodal signals. To address this problem, the paper proposes to combine the Hilbert Transform with the Singular Spectrum Analysis enabling mode extraction out of the limited data. The paper explores these methods for analyzing free decay in the multi-degree-of-freedom systems and introduces an algorithm for the nonlinear polymodal systems. Numerical tests using an artificial signal with the nonlinear damping demonstrate the proposed approach effectiveness in identifying modal parameters for the nonlinear systems.