一类对称约束碰振系统周期运动分析  

ANALYSIS ON PERIODIC MOTIONS OF A LINEAR VIBRO-IMPACT SYSTEM WITH SYMMETRIC TWO-SIDED CONSTRAINTS

作　　者：李健[1] 张思进[1] 孙丹[1] 

机构地区：[1]湖南大学力学与航空航天学院,长沙410082

出　　处：《动力学与控制学报》2007年第3期255-259,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金(10402011)资助项目~~

摘　　要：针对一类具有对称约束的单自由度线性系统,以定相位面为Poincaré截面建立起Poincaré映射,讨论了此类周期运动的稳定性问题.并基于胞映射的思想,引入拉回积分等分析手段,得到了该碰振系统对称双碰周期1的吸引子与吸引域,分析了吸引域随参数的变化规律.最后发现了吸引域的变化和系统分岔图中出现跳跃现象之间的联系.An undamped model for the response of one DOF（degree-of-freedom） systems having two-sided amplitude constraints was proposed. Firstly, the Poincare map of the period-n motions was set up for the system by using fixed phase plane as Poincare section, and the stability of periodic motions was also discussed. Then a numerical simulation was carried out, and it was shown that our conclusions were valid. Moreover, the phenomenon of multi-solutions＇ coexistence in this system was found through the numerical simulation. Finally, a means of pullback integral is introduced into the impact process based on the cell-mapping method, from which the coexist- ent attractors of the symmetric double-impact period-1 motions were derived, and it was found that the variation of domains of attraction was related to the leap phenomenon after comparing with Poincare map figures.

关 键 词：碰振系统 对称约束 Poincar6映射  吸引子  吸引域 

分 类 号：O313.4[理学—一般力学与力学基础]