【摘要】 与光滑动力系统不同,擦边分岔是非光滑动力系统中的一种特殊分岔行为.局部不连续映射是研究非光滑动力系统擦边分岔的一种有力工具.对一类单侧弹性碰撞悬臂振动系统进行了擦边分岔分析.首先建立了系统对应的局部不连续映射(ZDM)和全局Poincaré映射,进而在其他参数固定,碰撞间隙g为分岔参数时利用数值仿真的方法分别对原系统和对应的Poincaré映射进行擦边分岔分析,得到了该系统的两种不同类型的擦边分岔行为:周期1到周期2运动和周期1到混沌,这两种擦边分岔与刚性碰撞系统的情况是不相同的.由分析可知,对于含高阶非线性项的非光滑动力系统的擦边分岔,同样可以利用局部不连续映射的方法进行研究.更多还原

【Abstract】 Grazing bifurcation is a special bifurcation behavior of non-smooth dynamical systems.In the present paper,grazing bifurcations of a cantilever system with one-sided impact is investigated.Firstly,the local discontinuity mapping and Poincarémapping of the vibrating system are developed.Secondly,numerical simulation with the impacting clearance as the bifurcation parameter are carried out to obtain two types of grazing bifurcations of the system,which are different from those of rigid impact systems.Finally,it is further shown that the local discontinuity mapping can be also used to investigate grazing bifurcation of non-smooth dynamical systems with high order nonlinear terms.更多还原