非线性能量阱系统吸引子迁移控制

针对非线性能量阱系统多值性导致系统存在多个不同拓扑特性的吸引子，提出了一种基于吸引子迁移控制方法的非线性减振策略。首先，分析了大参数范围内激励力幅值对系统全局性态的影响；其次，提出了一种改进型的并行多自由度胞映射法，对典型参数下的共存吸引子及其吸引域进行研究；最后，通过迁移控制方法实现了不同振幅吸引子之间的跃迁。仿真结果表明：非线性能量阱系统在多个典型参数区间内呈现了多稳定吸引子共存现象，并行多自由度胞映射算法具有较高效率和精度，通过开环加线性闭环算法可使非线性能量阱系统由大振幅吸引子迁移至小振幅吸引子，从而实现减振降噪。

A Study of Attractor Migration Control for Nonlinear Energy Sink System

Aimed at the problem that the coexistent attractors with different topological properties remain in the nonlinear energy sink (NES) system caused by the multi value character, a nonlinear vibration reduction strategy based on the attractor migration control method is proposed. Firstly, the influence of excitation force amplitude on the global behavior of the NES system in the large parameter range is analyzed. Secondly, an improved parallelized multi degrees of freedom cell mapping (PMDCM) method is proposed to study the coexistent attractors and their basins under typical parameters. Finally, the attractor transitions with different amplitudes are realized by means of migration control. The simulation results show that the NES system in several typical parameter range presents multi stable coexistent attractors phenomenon, the PMDCM method has higher efficiency and precision, and the NES system can be migrated from large amplitude attractors to small amplitude attractors by using open plus nonlinear closed loop (OPNCL), reducing vibration and noise.