摘要
建立了具有双面碰撞约束的两自由度碰撞振动系统的力学模型,得到了系统的对称周期n-2运动。推导了Poincaré映射的对称性,并把映射不动点的分岔理论运用到该模型。对称周期运动对应于Poincaré映射的对称不动点。分析表明,Poincaré映射的对称性抑制了对称周期n-2运动的周期倍化分岔,Hopf-flip以及pitchfork-flip分岔,并证明了两个反对称的周期n-2运动具有相同的稳定性。数值模拟得到了对称周期n-2运动的Neimark-Sack-er分岔和音叉分岔。当Poincaré映射的雅可比矩阵有一个实特征值从+1处穿越单位圆时,一条稳定的对称的周期轨道失稳,并通过音叉分岔生成另外两条稳定的反对称的周期轨道。
A two-degree-of-freedom vibro-impact system having two-sided impact constraints is considered, and the symmetric period n--2 motion is obtained. The theory of bifurcations of the fixed point is applied to such model, and the symmetry of the Poincaré map is derived. The symmetric period n-2 motion corresponds to the symmetric fixed point of the Poincaré map. It is shown that the symmetry of the Poincaré map suppresses the period-doubling bifurcation, Hopf-flip bifurcation and pitchfork-flip bifurcation of the symmetric period n--2 motion, and it is proved that both the two antisymmetric period n--2 motions have the same stability. Pitchfork bifurcation and Hopf bifurcation of the symmetric period n-2 motion are obtained by numerical simulations. If the Jacobian matrix of the Poincaré map has a real eigenvalue crossing the unit circle at＋1, the stable symmetric periodic orbit losses its stability, and bifurcates into two stable antisymmetric periodic orbits via pitchfork bifurcation.
出处
《振动工程学报》
EI
CSCD
北大核心
2008年第4期376-380,共5页
Journal of Vibration Engineering
基金
国家自然科学基金(10472096
10772151)
西南交通大学博士创新基金资助项目
