摘要
应用映射的中心流形和范式方法,研究了冲击振动落砂机高维映射在其Jacobian矩阵的一对复共轭特征值±i穿越复平面单位圆周情况下的分岔:应用中心流形理论将Poincaré映射化为二维映射,并得到了1∶4强共振下的范式映射,从而讨论了映射在1∶4强共振点附近的分岔图重组过程,定性分析了冲击振动落砂机在1∶4强共振点及其附近的动力学特性。数值仿真结果也表明:冲击振动落砂机在1∶4强共振点附近存在周期运动的Neimark-Sacker分岔和一些复杂分岔,如周期4轨道的Ton型和Tout型相切分岔。
The local bifurcation of an inertial shaker, concerning one complex conjugate pair of eigenvalues ±i of the Jacobian matrix of the mapping escaping the unit circle simultaneously, is investigated by using the center manifold theorem technique and normal form method of the mapping. A center manifold theorem technique is applied to reduce the Poincare mapping to a two-dimensional one, and the normal form mapping associated with 1 ： 4 strong resonance is obtained. Thusly, the changing process of the bifurcation diagrams of the mapping near 1 ： 4 strong resonance point is discussed. The local dynamical behavior of an inertial shaker near 1 ： 4 strong resonance point is investigated by using qualitative analysis. The results from numerical simulation also illustrate that Neimark-Sacker bifurcation of periodic-impact motions and some complicated bifurcations, e.g., Ton and Tout types of tangent bifurcations of period-4 orbits, are found to exist in the inertial shaker near 1 ：4 strong resonance point.
出处
《工程力学》
EI
CSCD
北大核心
2008年第8期194-199,211,共7页
Engineering Mechanics
基金
国家自然科学基金项目(10572055
50475109)
甘肃省自然科学基金项目(3ZS062-B25-007
3ZS042-B25-044)
关键词
冲击振动
强共振
中心流形
范式
分岔
混沌
vibro-impact
strong resonance
center manifold
normal form
bifurcation
chaos
