单自由度碰撞振动系统的奇异非混沌动力学和多稳态共存  

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

作　　者：吴鑫 李高磊 乐源[1] WU Xin;LI Gaolei;YUE Yuan(School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学力学与工程学院,成都610031

出　　处：《振动与冲击》2022年第2期45-52,86,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11672249,11732014)。

摘　　要：基于一类单自由度受拟周期激励的具有悬臂结构碰撞振动系统,通过数值模拟研究了系统在参数α变化下的奇异非混沌动力学及多稳态共存现象。采用相敏感函数、奇异连续谱、有理数频率逼近、状态变量的傅里叶变换部分和在复平面上的路径等工具刻画了系统在特定参数范围内出现的奇异非混沌吸引子(strange nonchaotic attractors,SNAs)的奇异性。通过最大Lyapunov指数验证了SNAs非混沌特性。发现了系统存在分形和阵发两种通向SNAs的路径,揭示了这两种路径的演化过程和规律特征。结合系统状态变量的时间序列,分析了系统暂态及稳态SNAs与拟周期吸引子的共存、稳态SNAs与混沌吸引子的共存情况,进一步揭示了SNAs的多稳态共存现象及转换规律。该研究可为含悬臂结构的碰撞振动系统的优化设计提供理论依据。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.

关 键 词：碰撞振动系统 奇异非混沌动力学 分形路径 阵发路径 多稳态共存 

分 类 号：O322[理学—一般力学与力学基础]