Multi-state dynamics and model similarity of a vibro-impact nonlinear system

Abstract

Vibro-impact (VI) can generate strong nonlinearities into mechanical systems. Despite extensive research, the chaotic and multi-state dynamics of VI systems are not fully understood, and modeling high-dimensional systems with multiple VI oscillators remains a challenge. This study analyzes a typical 3 degrees of freedom (DOF) VI system to elucidate its chaotic dynamic behavior. We propose a criterion for replacing the piece-wise VI model with a continuous one to streamline the modeling, speed up calculations, and facilitate system analysis. We investigate the similarity of the two models in terms of predicting system response and chaotic dynamics. Numerical and experimental findings show that with increased nonlinearity, a 3DOF VI system degenerates to a 2DOF system, due to the collisional and non-collisional states between the two oscillators. This results in discontinuous multi-state transmission curves and simultaneous resonance suppression. Moreover, by incorporating higher-order nonlinear functions, the continuous model's responses align more closely with the piece-wise model, albeit at a higher computational cost. While both models exhibit similar chaotic dynamics, the piece-wise model exhibits a higher degree of chaos. Reducing damping and the collision gap is recommended to maintain high prediction accuracy across a range of nonlinearities. These findings enhance the understanding of the multi-state and chaotic dynamics of VI motion and pave the way for the accurate and efficient modeling of strongly nonlinear, high-dimensional metamaterial systems.