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Anti-controlling Hopf-Hopf interaction bifurcations on Poincaré map of a three-degree-of-freedom vibro-impact system with clearance
Author(s): 
Pages: 952-959
Year: Issue:  6
Journal: Journal of Vibration Engineering

Keyword:  nonlinear vibrationHopf-Hopf interaction bifurcationcritical criteria of mapanti-controlling bifurcationvibro-impact system;
Abstract: 对一类含间隙碰撞振动系统Poincaré映射的Hopf-Hopf交互分岔进行了反控制研究.首先,基于碰撞振动系统建立了六维Poincaré映射,由于六维映射相应雅克比矩阵的特征值没有解析的表达式,这使得由特征值特性描述的传统临界分岔准则在确定控制增益中具有很大的局限性.针对这个局限性,建立了包含特征值分布条件、横截条件和非共振条件的显式临界准则.所建立的准则与传统的分岔准则等价,但并不依赖雅克比矩阵特征值的直接计算.然后,针对碰撞的不连续特性导致的隐式Poincaré映射在闭环系统控制设计中的困难,发展了一种基于原碰撞系统的线性反馈控制方法.最后,数值分析给出了在指定的参数点所设计的映射Hopf-Hopf交互分岔的环面解,进一步验证了理论分析的正确性.
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