高维复杂碰撞振动系统的概周期环面分岔与混沌  

QUAI-PERIODIC TORUS BIFURCATION AND CHAOS OF HIGHDIMENSIONAL COMPLICATED VIBRO-IMPACT SYSTEM

作　　者：成龙[1] 李万祥[1] 彭珊[1] 

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《机械强度》2013年第5期594-598,共5页Journal of Mechanical Strength

摘　　要：建立了一类三自由度含间隙碰撞振动系统的力学模型,推导了系统周期运动的解析解及Poincaré映射。基于六维Poincaré映射方法研究了系统的Hopf-flip余维二分岔和倍化分岔。在Hopf-flip余维二分岔中先发生Flip分岔后发生Hopf分岔,并展现了由环面倍化和"贝壳形"概周期吸引子向混沌演化的两种非常规路线。其后分析了系统周期运动经倍化分岔向混沌的演化的过程中,存在着十分复杂的非常规转迁过程和精彩的动力学行为。The mechanical model of a three-degree-of-freedom vibro-impact system with clearance is established, analytical solution and Poincare mapping of the periodic motion in the system are deduced. Based on the six-dimensional Poincare mapping method, the Hopf-flip codimension two bifurcation and doubling bifurcation are studied. During the process of Hopf-flip codimension two bifurcation, doubling bifurcation firstly takes place, and then the Hopf bifurcation occurs, two kinds of unconventional routes from torus doubling and ＂shell＂ quasi-periodic attractor to chaos are unfolded. Afterwards, in the process of periodic motion of the system via doubling bifurcation to chaos, there exists extremely complicated unconventional process and excellent dynamics behavior.

关 键 词：POINCARÉ映射 非常规混沌演化 环面分岔 

分 类 号：TH113.1[机械工程—机械设计及理论] O322[理学—一般力学与力学基础]