三自由度碰撞振动系统的周期运动稳定性与分岔  

STABILITY AND BIFURCATIONS OF PERIODIC MOTION IN A THREE-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

作　　者：丁旺才[1] 谢建华[1] 李国芳[2] 

机构地区：[1]西南交通大学应用力学与工程系,四川成都610031 [2]兰州交通大学机电与动力工程学院,甘肃兰州730070

出　　处：《工程力学》2004年第3期123-128,共6页Engineering Mechanics

基　　金：国家自然科学基金资助项目(10072051);教育部高等学校博士学科点专项科研基金资助项目(20010613001)

摘　　要：建立了三自由度碰撞振动系统的动力学模型,推导出系统n-1周期运动的六维Poincar映射,根据映射Jacobi矩阵的特征值来分析n-1周期运动的稳定性。数值模拟了1-1周期运动的Hopf分岔和周期倍化分岔,进一步分析了当分岔参数变化时碰撞振动系统周期运动经拟周期分岔和周期倍化分岔向混沌的演化路径,其中有的路径是非常规的。A three-degree-of-freedom vibro-impact system was considered. Based on the solutions of differential equations between impacts, impact conditions and match conditions of periodic motion, the six-dimension Poincare maps of n-1 periodic motion were established. The stability of the periodic motion was determined by computing eigenvalues of Jacobian matrix of the maps. If some eigenvalues are on the unit circle, bifurcation occurs as controlling parameter varies. By numerical simulation, Hopf bifurcation and period-doubling bifurcation of 1-1 periodic motion were analyzed. As controlling parameter varies further, the routes from periodic motion to chaos via quasi-periodic bifurcation and period-doubling bifurcation were investigated, respectively. One of the routes is found to be non-typical.

关 键 词：碰撞振动 Poincar6映射 稳定性 HOPF分岔 周期倍化分岔 混沌 

分 类 号：O322[理学—一般力学与力学基础]