一类对称约束碰振系统的余维二擦边分岔的存在条件

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摘要类似光滑系统的余维二分岔的分类方法，余维二擦边分岔被划分为三种类型，分别是擦边点退化、退化环擦边（非双曲）以及两个擦边事件同时发生。本文分析了一个二自由度对称约束的碰撞振动系统，得到了该系统第二类余维二擦边分岔的存在条件。首先，考虑双侧擦边周期运动，理论推导出双侧擦边周期运动的存在性条件。利用不连续映射方法，得出1/1/n碰撞周期运动发生鞍结分岔和倍周期分岔的解析表达式。然后，结合双擦边周期运动的存在性条件和1/1/n碰撞周期运动的分岔条件，推导出发生余维二擦边分岔时满足的解析表达式，并以周期1运动为例，给出了余维二擦边分岔点的分布。

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	徐洁琼
	陈慧莹
	伍帅
	袁泉

关键词 ：对称约束碰振系统, 不连续映射方法, 余维二擦边分岔

Abstract：similar to the approach used to classify co-dimension-two bifurcations in smooth systems, co-dimension-two grazing bifurcations can be put into one of the following three types: degenerate gazing point, grazing of degenerate cycles, simultaneous occurrence of two grazings. This paper obtained the existence condition of the second type co-dimension-two grazing bifurcation for a two-degree-of-freedom vibro-impact system with symmetric constraints. First, considering the periodic motion of the double-sided grazing, the existence condition of the periodic motion of the double-sided grazing was deduced theoretically. Using the discontinuous mapping method, the analytical expressions of saddle-node bifurcation and period doubling bifurcation for 1/1/n impact periodic motion are derived. Then, combining the existence condition of the grazing periodic motion and the bifurcation condition of the 1/1 /n impact periodic motion, the analytical expression of co-dimensional-two grazing bifurcation was obtained, and The distribution of co-dimensional-two bifurcation points is analyzed for period one motion.

Key words： Vibro-impact system with symmetric constraints the discontinuous mapping method；co-dimensional-two grazing bifurcation

收稿日期: 2020-08-31 出版日期: 2022-03-15

引用本文:

徐洁琼，陈慧莹，伍帅，袁泉. 一类对称约束碰振系统的余维二擦边分岔的存在条件[J]. 振动与冲击, 2022, 41(5): 273-279.
XU Jieqiong, CHEN Huiying, WU Shuai, YUAN Quan. Existence conditions of co-dimension-2 grazing bifurcation for a class of symmetrically constrained vibro-impact systems. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(5): 273-279.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2022/V41/I5/273

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