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Codimension two bifurcation and chaos of a vibro-impact forming machine associated with 1：2 resonance case

ISSN号：0567-7718
期刊名称：《力学学报：英文版》
时间：0
分类：O34[理学—固体力学;理学—力学]
作者机构：[1]School of Mathematics, Physics and Software Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China, [2]Department of Engineering Machanics Southwest Jiaotong University, Chengdu 610031, China
相关基金：The project supported by the National Natural Science Foundation of China （10572055, 50475109） and the Natural Science Foundation of Gansu Province Government of China （3ZS051-A25-030（key item）） The English text was polished by Keren Wang.

作者： Guanwei Luo, Jianning Yu, Jianhua Xie

关键词：振动, 碰撞, 共振, 余维数, 分歧, Vibration, Impact , 1：2 resonance, . Codimension two bifurcation

中文摘要：

与两倍群众形成机器的 vibro 影响被考虑。颤动的系统的部件与对方一起碰撞。如此的模型与影响部件在机械系统的动力学的研究起一个重要作用。与形成影响的系统的状态联系的 Poincar é节，就立即在影响以后，被选择，并且时期 n 单个影响的运动和它的扰乱的地图被导出经分解。一个中心歧管定理技术被使用把 Poincar é地图归结为一张二维的地图，和与 codimension 联系的正常形式地图 1:2 回声的二分叉被获得。正常形式地图展开被分析。形成影响的系统的动态行为，在 codimension 的点附近二分叉，被使用质的分析和数字模拟调查。在 codimension 的点附近，在那里的二分叉存在与时期一单个影响的运动联系的不仅 Neimark 麻袋分叉，而且时期二双影响运动的 Neimark 麻袋分叉。在分叉点附近，单个影响的周期的轨道的固定的点的不同形式的转变被表明，并且到混乱的从周期的影响运动的不同线路也被讨论。

英文摘要：

A vibro-impact forming machine with double masses is considered. The components of the vibrating system collide with each other. Such models play an important role in the studies of dynamics of mechanical systems with impacting components. The Poincaré section associated with the state of the impact-forming system, just immediately after the impact, is chosen, and the period n single-impact motion and its disturbed map are derived analytically. A center manifold theorem technique is applied to reduce the Poincaré map to a two-dimensional map, and the normal form map associated with codimension two bifurcation of 1：2 resonance is obtained, Unfolding of the normal form map is analyzed. Dynamical behavior of the impact-forming system, near the point of codimension two bifurcation, is investigated by using qualitative analyses and numerical simulation. Near the point of codimension two bifurcation there exists not only Neimark-Sacker bifurcation associated with period one single-impact motion, but also Neimark-Sacker bifurcation of period two double-impact motion. Transition of different forms of fixed points of single-impact periodic orbits, near the bifurcation point, is demonstrated, and different routes from periodic impact motions to chaos are also discussed.

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