中文摘要：

以两自由度碰撞振动系统为研究对象,数值仿真了系统1/n周期运动经周期倍化分岔和Hopf分岔向混沌转迁的路径。使用微幅阻尼控制策略,对系统的分岔行为和混沌进行了控制,控制信号是根据质块M1的运动方向来改变阻尼系数而得到的。在此基础上引入反馈控制方法,即在Poincaré截面里,选择变量β＊=2π或4π作为期望目标,动态地调节控制参数,把系统的多碰周期运动、概周期运动和混沌有效地控制到单碰周期轨道。仿真结果表明,输入的控制信号u=γ｜x1｜是一个微幅阻尼信号,达到控制的目标只消耗少量的能量。

英文摘要：

A two-degree-of-freedom impact oscillator is considered. Routes from doubling-periodic bifurcations and Hopf bifurcations of period-n single-impact motions to chaotic motions are illustrated by numerical simulation.Bifurcation behavior and chaotic motions are suppressed by using a small- amplitude damping control law. The control signal is obtained by varying the damping coefficient according to the velocity direction of mass M1. Choosing the variable β＊= 2π or 4π in Poincaré section as the desired target,the control parameter is dynamically adjusted by applying the feedback control technique. The multi-impact periodic motions,quasi-periodic motions and chaotic behavior in the system are effectively controlled to the single-impact periodic motion. Numerical results show that the control input u = γ ｜x1｜ is a small-amplitude damping signal,it is necessary to apply a small quantity of energy to the control implementation.