分段线性振动机械关于外激振频率的分岔与混沌

Bifurcation and Chaos on Frequencies the Excited Forces in Nonlinear Vibration Mechanism with Piece-Wise Linearity

利用计算机仿真及Poincare映射方法研究不对称分段线性非线性机械系统的运动学特征·研究了外激振力角频率从 30rad/s以步长 0 1rad/s增加到 10 0rad/s时 ,系统的周期运动分岔和混沌运动·发现其中除了存在倍周期分岔外 ,还存在P 1到P 3的突变、P 2到P 1的倒分岔和P 3到P 1的突变·给出了全局分岔图、局部分岔图、混沌运动的Poincare映射及 3种周期运动的时间历程曲线和相平面图·对于设计此类机械系统具有指导意义·

The characteristics of motion in nonlinear vibration mechanism with piece wise linearity were analyzed by means of computer simulation and Poincare method. Bifurcation of periodic motions and chaos in the system were studied when the angular frequencies increase from change 30rad/s to 100?rad/s by steps 0 1?rad/s. There are sudden changes from P 1 to P 3,inverse bifurcation from P 2 to P 1 and sudden change from P 3 to P 1 except that double periodic bifurcation exist. The global and part bifurcation figure and Poincare mapping figure of chaos and the time history curves of 3 periodic motions were given.