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.
出处
《工程力学》
EI
CSCD
北大核心
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)
关键词
碰撞振动
Poincar6映射
稳定性
HOPF分岔
周期倍化分岔
混沌
Bifurcation (mathematics)
Chaos theory
Computer simulation
Degrees of freedom (mechanics)
Differential equations
Impact resistance
Stability
