一类二自由度碰撞振动系统的余维二擦边分岔研究

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振动与冲击 ›› 2020, Vol. 39 ›› Issue (20) : 113-120.

论文

伍帅，徐洁琼，王子汉，袁泉

作者信息 +

Co-dimensional-two grazing bifurcation of two-degree-of-freedom vibro-impact systems

WU Shuai，XU Jieqiong，WANG Zihan，YUAN Quan

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摘要

当擦边分岔和光滑分岔同时发生时，非光滑系统会发生一类余维二擦边分岔。一类二自由度碰撞振动系统的此类余维二擦边分岔及余维二擦边点附近的动力学行为得到研究。首先，讨论了擦边周期运动的存在性条件。利用不连续映射方法构造了1/n碰撞周期运动的全局庞加莱映射,并得出1/n碰撞周期运动的分岔条件。其次，结合擦边周期运动条件和碰撞周期运动分岔条件推导出擦边分岔和光滑分岔同时发生时满足的解析表达式，并数值分析了不同周期下系统余维二擦边分岔点的分布情况。最后，通过对比分别由全局庞加莱映射和原系统得到的余维二擦边点附近的分岔图，验证了理论分析的有效性。

Abstract

When grazing bifurcation and smooth bifurcation take place simultaneously, one kind of co-dimensional-two grazing bifurcation will occur. The co-dimensional-two bifurcation of a two-degree-of-freedom vibro-impact system and its dynamic behavior near the co-dimensional-two grazing bifurcation points were studied. Firstly, the existence conditions of grazing periodic motion were discussed. The global Poincaré mapping for the 1/n impact period motions was constructed by using the discontinuous mapping method, and the bifurcation conditions for the 1/n impact period motions were obtained. Then, an analytical expression satisfied for grazing bifurcation and smooth bifurcation was derived by combining the conditions of periodic grazing bifurcation and periodic impact bifurcation. Based on the expression, the distribution of co-dimensional-two bifurcation points of the system under different periods was analyzed by numerical simulation. Finally, the effectiveness of theoretical analysis was verified by comparing the bifurcation diagrams obtained by the global Poincaré map and the differential system.

导出引用

伍帅，徐洁琼，王子汉，袁泉. 一类二自由度碰撞振动系统的余维二擦边分岔研究[J]. 振动与冲击, 2020, 39(20): 113-120

WU Shuai，XU Jieqiong，WANG Zihan，YUAN Quan. Co-dimensional-two grazing bifurcation of two-degree-of-freedom vibro-impact systems[J]. Journal of Vibration and Shock, 2020, 39(20): 113-120

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