ATTRACTOR MIGRATION CONTROL CHARACTERISTICS OF THE TWO-STAGE QUASI-ZERO STIFFNESS VIBRATION ISOLATION SYSTEM

Nonlinear vibration isolation systems commonly exhibit the coexistence of multiple stable attractors, with different vibration isolation effects when operating on different attractors. To ensure that the nonlinear vibration isolation system is in the optimal state, this study focuses on the attractor migration control characteristics of a two-stage quasi-zero stiffness vibration isolation system (TQZS VI). First, the dynamic model of the TQZS VI system is established, and the global bifurcation characteristics and attractor coexistence characteristics are revealed using parameter continuation tracking methods and parallel cell mapping methods. Under different excitation force amplitudes, the TQZS VI system exhibits significant bifurcation characteristics, including periodic motion (period-1, period-2, period-3, etc.) and chaotic motion. Then, based on the theory of attractor migration control, a sliding mode variable structure-based attractor migration control method is proposed using a classical exponential approach law. This method does not require the establishment of a nonlinear control term, and the target orbit function transfer domain has globality. Finally, the migration control term for the TQZS VI system is constructed using the proposed attractor migration control method, revealing the migration control characteristics between different target orbits and attractors. The results show that the sliding mode variable structure-based attractor migration control method can effectively control the motion state of the TQZS VI system, providing a new approach for state control and noise reduction in nonlinear vibration isolation systems.