摘要
建立了一类含干摩擦对称间隙的弹性碰撞振动系统的动力模型,分析并推导了系统运动中黏着、滑动和碰撞运动的衔接关系及判断条件.研究系统在周期外力作用下且外激励频率远小于系统固有频率的动力学响应.分析了两尺度效应下含干摩擦系统的簇发振荡模式,通过转换相图揭示了系统穿越分界面时产生的簇发振荡行为;并分析了一类含干摩擦对称性系统通向混沌的分岔机制.计算了系统的最大李雅普诺夫指数,并以最大李雅普诺夫指数为判据,分析了系统的稳定性.结果表明:超低频区系统呈现为周期陷窝形式分布,激励频率在周期陷窝中心两侧蔓延过程中,会伴随着擦边分岔的出现,碰撞次数依次减少;系统在两频域尺度效应耦合作用下,表现为簇发振荡运动;在低频区,系统通过叉式分岔,形成一对反对称周期运动,随着激励频率的减小,通过序列倍化分岔转迁为一对反对称混沌运动,再通过激变分岔转迁为单个对称混沌运动.
With dry friction symmetrical clearance,a dynamic model of a class of elastic impact vibration system was established in this paper.Meanwhile,the cohesion relations and judging conditions of adhesion,sliding and collision motions in the system motion were also analyzed.Under periodic external force,the dynamic response of the system was studied,and the frequency of external excitation was considered to be much lower than the natural frequency of the system.Under two-scale effect,the mode of bursting oscillations of the system with dry friction was analyzed,and by the phase diagram when it crosses the interface,the behavior of cluster oscillation of the system was revealed.The bifurcation mechanism of a class of system with dry friction symmetry to chaos was analyzed and the system was calculated.The maximum Lyapunov exponent of the system was calculated,and the stability of the system with the maximum Lyapunov exponent as the criterion was analyzed.The results show that the ultra-low frequency system is distributed in the form of periodic dimples.During the dual spread of the periodic dimple center,the frequency of collisions will decrease along with the occurrence of edge rubbing bifurcations.Under the coupling effect of scale effect in the two frequency domains,bursting oscillations motion is exhibited by the system.The system will be related to the scale effect in the two frequency domains.In the low frequency range,a pair of anti-symmetric periodic motions through pitchfork bifurcation is formed by the system.With the decrease of excitation frequency,the system is transformed into a pair of anti-symmetric chaotic motions by period doubling bifurcation,and then into a single symmetric chaotic motion by means of radical bifurcation.
作者
吴丹
丁旺才
WU Dan;DING Wangcai(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2020年第3期46-51,共6页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家自然科学基金资助项目(11732014,11462011)
兰州交通大学青年基金资助项目(2017014).
关键词
干摩擦
弹性碰撞
簇发振荡
分岔
李雅普诺夫指数
dry friction
soft impact
bursting oscillations
bifurcation
Lyapunov exponent
