非线性约束下机械振动系统的低频动力学特性  

Low frequency Dynamic Characteristics of Mechanical Vibration System under Nonlinear Constraints

作　　者：朱喜锋[1,2] 文智华 王剑锋 马硕[1] ZHU Xi-feng;WEN Zhi-hua;WANG Jian-feng;MA Shuo(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou730070,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,内蒙古包头014060

出　　处：《兰州交通大学学报》2021年第6期89-95,共7页Journal of Lanzhou Jiaotong University

基　　金：甘肃省科技计划资助(20JR5RA424)。

摘　　要：以一类两自由度含非线性约束机械振动系统为研究对象,通过4阶变步长Runge Kutta数值算法,分析了该系统在低频激励下p/1周期运动的动力学特性及其相互转迁规律,研究了Grazing分岔和saddle node分岔在p/1周期运动中的频率迟滞特性.研究结果表明,随着激振频率减小,Grazing分岔会使p/1周期运动的碰撞次数逐步增加直至发生颤碰运动.最后,结合胞映射法研究了周期运动共存区内吸引域的分布情况及其转迁规律.Taking a type of two degree of freedom vibration system with nonlinear constraints as the research object,through the fourth order Runge Kutta numerical algorithm,the transition law of p/1 periodic motion of the system under low frequency excitation is analyzed,and the grazing bifurcation and saddle are revealed,in which the frequency hysteresis characteristics of node in p/1 periodic motion is studied.The results show that the grazing bifurcation will gradually increase the number of collisions of the p/1 periodic motion until the chattering motion occurs.Finally,combined with the cell mapping method,the distribution of the attraction domain and its transition law in the polymorphic coexistence area of periodic motion are studied.

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]