Neimark-Sacker-pitchfork bifurcation of the symmetric period fixed point of the Poincar¨¦ map in a three-degree-of-freedom vibro-impact system

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• 作者：Yuan Yue ; ^{yueyuan2011@home.swjtu.edu.cn} ; Jianhua Xie
• 关键词：Symmetric three-degree-of-freedom vibro-impact system ; Poincaré ; map ; symmetric fixed point ; Neimark&ndash ; Sacker-pitchfork bifurcation
• 刊名：International Journal of Non-Linear Mechanics
• 出版年：2013
• 出版时间：January, 2013
• 年：2013
• 卷：48
• 期：Complete
• 页码：51-58
• 全文大小：903 K

文摘

A three-degree-of-freedom vibro-impact system with symmetric two-sided rigid constraints is considered. Since the symmetric period n?2 motion of the vibro-impact system corresponds to the symmetric fixed point of the Poincar¨¦ map of the vibro-impact system, we investigate bifurcations of the symmetric period n?2 motion by researching into bifurcations of the associated symmetric fixed point. The Poincar¨¦ map of the system has symmetry property, and can be expressed as the second iteration of another unsymmetric implicit map. Based on both the Poincar¨¦ map and the unsymmetric implicit map, the center manifold technique and the theory of normal forms are applied to deduce the normal form of the Neimark-Sacker-pitchfork bifurcation of the symmetric fixed point. By numerical analysis, we obtain the Neimark-Sacker-pitchfork bifurcation of the symmetric fixed point of the Poincar¨¦ map in the vibro-impact system.