含双侧刚性约束碰撞振动系统的混沌控制

Chaos Control of a Two-degree-of-freedom Vibrating System with Two Rigid Constraints

建立了一类两自由度含双侧刚性约束振动系统的非对称型周期运动方程,构建了其Poincaré映射方程。数值计算结果揭示了该系统的周期运动及其通向混沌的转迁途径,给出了系统从周期运动变成混沌过程中激振频率ω的变化范围,并得到了系统的混沌运动。利用外加恒定载荷和位相法两种非反馈方法,以适当的控制强度将系统的混沌运动控制到稳定的周期轨道。

With the help of uncoupled approach of modal matrix, symmetrical periodic motion and the Poincare mapping of a two-degree-of-freedom vibrating system with two rigid constraints are derived analytically. Periodic motions of the system and their routes to chaos are also illustrated by numerical simulation. The ranges of the system excited frequency from periodic motions to chaotic motions are obtained. The chaos controlling methods by the addition of constant motor torque and the addition of phase are dissertated and analyzed numerically by the numerical solution. The chaos of the system is controlled by the two methods. The allowable range of controlling variables and the steady orbit of the system under controlling are obtained.