含双侧非线性约束机械振动系统的低频动力学特性  

LOW⁃FREQUENCY DYNAMIC CHARACTERISTICS OF A MECHANICAL VIBRATION SYSTEM UNDER BILATERAL NONLINEAR RESTRAINTS

作　　者：文智华 朱喜锋[1,2] 王剑锋 WEN ZhiHua;ZHU XiFeng;WANG JianFeng(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;Key Laboratory of System Dynamics and Reliability of Rail Transport Equipment of Gansu Province,Lanzhou 730070,China;Department of Railway Locomotive and Car,Baotou Railway Vocational and Technical College,Baotou 014060,China)

机构地区：[1]兰州交通大学机电工程学院,兰州730070 [2]甘肃省轨道交通装备系统动力学与可靠性重点实验室,兰州730070 [3]包头铁道职业技术学院铁道机车车辆系,包头014060

出　　处：《机械强度》2023年第3期555-561,共7页Journal of Mechanical Strength

基　　金：甘肃省科技计划(20JR5RA424)资助。

摘　　要：通过4阶Runge-Kutta数值算法,对一类两自由度含双侧非线性约束振动系统进行了研究,分析了该系统在低频激励下p/1周期运动的动力学特性、相互转迁规律以及间隙与周期共存区的对应规律,并结合胞映射法研究了周期运动共存区不同吸引子及吸引域的分布规律。结果表明,系统的周期运动之间主要通过Grazing分岔和Saddle-node分岔进行转迁,由于转迁过程不可逆,使得相邻运动之间存在周期运动共存区,且随着间隙增大,系统的周期共存区范围逐渐减小。A type of two⁃degree⁃of⁃freedom vibration system with bilateral nonlinear constraints is established.Through the fourth⁃order Runge⁃Kutta numerical algorithm,the dynamic characteristics of the p/1 periodic motion of the system under low frequency excitation,the law of mutual transition and the corresponding law of the coexistence zone of gap and period are analyzed.The cell mapping method is used to study the distribution law of different attractors and attracting domains in the coexistence area of periodic motion.The results show that the periodic motions of the system are mainly transferred through Grazing bifurcation and Saddle⁃node bifurcation.Due to the irreversible transition process,there is a coexistence zone of periodic motion between adjacent motions.As the gap increases,the range of the coexistence zone of periodic motion of the system gradually decreases.

关 键 词：颤碰 非线性约束 分岔 共存吸引子 

分 类 号：O322[理学—一般力学与力学基础]