一类非光滑机械系统的Hopf分岔与混沌  

HOPF BIFURCATION AND CHAOS OF A NON-SMOOTH MECHANICAL SYSTEM

作　　者：李万祥[1] 何玮[1] 安国会[2] 罗海玉[3] 张远军[1] 

机构地区：[1]兰州交通大学机电工程学院,兰州730070 [2]河南科技学院,新乡453003 [3]天水师范学院工学院,天水741001

出　　处：《振动与冲击》2005年第6期114-116,共3页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(编号:10472096)

摘　　要：通过用四阶Runge-kutta数值积分法和Poincaré映射法对系统复杂动力学现象进行的仿真,对一类简谐激振力作用下的双边不对称复杂约束系统的动力学行为进行了分析,证实单自由度含间隙系统中存在Hopf分岔,分析了系统周期运动的Hopf分岔以及通向混沌的拟周期道路。对其分岔与混沌行为的研究为工业实际中含间隙机械系统和冲击振动系统的优化设计提供了理论依据。The dynamics of a non-symmetric oscillator with elastic two-sided amplitude constraints subject to harmonic loads is analyzed. The fourth order Runge-Kutta numerical integration method and Poincare´ map are used to detect the complex dynamical phenomena of the system. It is found that in he one-degree-of-freedom system exists Hopf bifurcation. An important field in vibration engineering is the dynamics of mechanical systems with piecewise smooth features. It is possible to optimize system parameters, of such kind of practical systems by investigation of its bifurcation and chaos property.

关 键 词：非光滑 周期运动 HOPF分岔 混沌 

分 类 号：O332[理学—一般力学与力学基础]