一类n自由度碰撞振动系统的余维二分岔分析  

Co-dimensional-two Bifurcation Analysis of a Kind of n Degree-of-freedom Impact Vibration Systems

作　　者：李松涛 李群宏[2] LI Songtao;LI Qunhong(Fundamentals Department,Naval Engineering University,Wuhan 430033,China;College of Mathematics and Information Science,Guangxi University,Nanning 530004,China)

机构地区：[1]海军工程大学基础部,湖北武汉430033 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《枣庄学院学报》2025年第2期12-24,共13页Journal of Zaozhuang University

基　　金：国家自然科学基金(11872154)。

摘　　要：利用解析和数值的方法分别讨论对n自由度单侧刚性碰撞振动系统擦边周期轨道附近的动力学行为,推导出关于m周期1次碰撞运动发生SN分岔和PD分岔的存在条件,进一步得出系统出现余维二分岔点的条件。为了验证理论是否具有普适性与正确性,以四自由度单侧刚性碰撞振动系统作为例,得到系统同时发生SN分岔、PD分岔和GR分岔的条件。在余维二分岔点附近,通过Lyapunov指数图和局部分岔图分析发现在一定的参数范围内,系统交替出现了周期运动与混沌运动的现象。理论分析与数值仿真相吻合,从而验证结论。This paper uses analytical and numerical methods to separately discuss the dynamic behavior near the grazing periodic orbit of a class of n-degree-of-freedom vibro-impact systems with unilateral rigid constraint.After analysis,the existence conditions of saddle-node bifurcation and period-doubling bifurcation for periodic motion with a collision in m-period are derived,and the conditions for the occurrence of a co-dimension-two bifurcation point in the system are further derived.To verify the universality and correctness of the theory,a four-degree-of-freedom unilateral rigid constraint system is used as an example to obtain the conditions for simultaneous occurrence of saddle-node bifurcation,period-doubling bifurcation and grazing bifurcation.Near the co-dimension-two bifurcation points,Through the analysis of Lyapunov exponent diagram and local bifurcation diagram,it was found that within a certain parameter range,the system alternates between periodic and chaotic motion.Therefore,theoretical analysis is consistent with numerical simulation,which verifies the conclusion.

关 键 词：不连续映射 余维二擦边分岔 局部分岔图 LYAPUNOV指数 

分 类 号：O322[理学—一般力学与力学基础]