随机干扰对两自由度碰撞振动系统的倍化分岔的影响

针对一类含单侧刚性约束的两自由度碰振系统确定Poincaré映射截面,用四阶Runge-Kutta法数值仿真了系统的倍化分岔及其向混沌的转迁过程,并讨论了随机干扰对系统倍化分岔的影响.结果表明:该系统周期运动经倍化分岔向混沌转迁的途径中,包含了倍化序列、Neimark-Sacker分岔、擦边分岔,随机干扰会导致周期运动由确定的单线扩散为带状,当确定系统的多周期运动相轨线距离较近时,可能会因为随机干扰导致的扩散而重叠,随机干扰还会造成擦边运动的提前.

The Effect of Stochastic Disturbance on Doubling Bifurcation of A Two-DOF Vibro-impact System

The Poincar＆#233;mapping of a two DOF vibro-impact system section is determined.Period doubling bifurcation and the way to the chaos are simulated numerically with four-stage Runge-Kutta,and the effect of the dynamic behavior of vibro-impact system under stochastic disturbance is studied.Numerical simulations show that ways to the chaos from period doubling bifurcation include period doubling cascade,Neimark-Sacker bifurcation and grazing bifurcation.The stochastic disturbance leads the phase line spreading into ribbon,the phase overlaps while coming closed because of the stochastic disturbance,and the stochastic disturbance will lead to advance grazing bifurcation.