一类非线性约束下单自由度碰撞系统的动力学特性  

Dynamics characteristic of a class of single-degree-of-freedom collision system under nonlinear constraint

作　　者：马成 朱喜锋[1,2] 郑冬 付文斌 MA Cheng;ZHU Xifeng;ZHENG Dong;FU Wenbin(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)

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

出　　处：《机械强度》2025年第3期82-89,共8页Journal of Mechanical Strength

基　　金：甘肃省科技计划项目(20JR5RA424)。

摘　　要：研究了一类单自由度含非线性项以及单侧新型非线性约束机械碰撞振动系统模型,利用变步长4阶RungeKutta数值算法以及多参数协同仿真,分析该系统在低频激励下的p/1周期运动的动力学特性,以及擦边分岔与鞍结分岔在p/1周期运动中的频率迟滞特性,发现两种不同的运动会同时存在,揭示了相邻周期运动之间转迁不可逆。最后研究了间隙的改变对系统的多态共存区的影响,随着间隙的增大,部分周期运动共存区段减小并向低频区段过渡。A single-degree-of-freedom mechanical collision vibration system model with nonlinear terms and unilateral new nonlinear constraints was studied.The dynamics characteristics of the p/1 periodic motion of the system under lowfrequency excitation were analyzed by using the variable-step fourth-order Runge-Kutta numerical algorithm and multiparameter co-simulation.And the frequency hysteresis characteristics of the grazing bifurcation and saddle-node bifurcation in the p/1 periodic motion were analyzed.It was found that two different motions will exist at the same time,revealing the irreversibility of the transition between adjacent periodic motions.Finally,the influence of the change of the gap on the multistate coexistence region of the system was studied.As the gap increases,the coexistence region of partial periodic motion decreases and transits to the low-frequency region.

关 键 词：非线性约束 分岔 多参数协同 吸引子共存 

分 类 号：O322[理学—一般力学与力学基础]