惯性式冲击振动落砂机周期运动的Hopf分叉  

Hopf Bifurcation of Periodic Motions in the Inertial Shaker

作　　者：谢建华[1] 郑小武[1] 

机构地区：[1]西南交通大学应用力学与工程系,成都610031

出　　处：《振动工程学报》1999年第3期297-303,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金

摘　　要：研究了惯性式冲击振动落砂机由周期运动失稳而产生 Ｈｏｐｆ 分叉的问题。首先利用中心流形定理将该模型的 Ｐｏｉｎｃａｒé映射简化成两维的，然后根据平面 Ｒ２ 上映射的 Ｈｏｐｆ分叉定理研究此系统 Ｈｏｐｆ 圈的存在性，最后通过数值模拟获得由 Ｐｏｉｎｃａｒé截面上不变圈所表示的系统拟周期响应。The Hopf bifurcation problems in a kind of inertial shakers due to destabilization of its periodic motions are studied. Firstly, the Center Manifold theorem is applied to reduce the Poincarē map of the model to a two dimensional one. Then the theory of Hopf bifurcation of maps in R 2 is applied to investigate the existence of Hopf circle of the system. Finally, the quasi periodic response of the system, represented by an invariant circle in the Poincarē section,is obtained through numerical simulations.

关 键 词：冲击 振动 落砂机 稳定性 周期运动 HOPF分叉 

分 类 号：TG231.7[金属学及工艺—铸造] O322[理学—一般力学与力学基础]