Strange nonchaotic dynamics and multistable coexistence phenomena of a single-degree-of-freedom vibro-impact system

Based on a single-degree-of-freedom vibro-impact system with cantilever structure under quasiperiodic forced excitation, the strange nonchaotic dynamics and multistable coexistence phenomena of the system with parameter changes were studied by numerical simulation. The singularity of the strange nonchaotic attractors (SNAs) in a specific parameter range of the system was characterized using such tools as the phase sensitivity function, singular continuous spectrum, rational frequency approximations, and the path of the partial Fourier sum of state variables in complex plane. The nonchaotic properties of SNAs were verified by the method of top Lyapunov exponents. The fractal and intermittency routes to SNAs were discussed, and the evolutions and regularities of these routes were revealed. The coexistence of transient SNAs and quasiperiodic attractors, stable SNAs and quasiperiodic attractors, as well as stable SNAs and chaotic attractors was analyzed by using the time series of system state variables. Furthermore, the multistable coexistence and transition rules of SNAs were revealed. The research provides a theoretical basis for the optimal design of vibro-impact systems with cantilever structures. © 2022, Editorial Office of Journal of Vibration and Shock. All right reserved.