碰撞振动系统强共振下的两参数动力学分析  

Dynamics analysis of two|parameter family in a case of strong resonance of vibro|impact system

作　　者：丁旺才[1] 谢建华[2] 李万祥[1] 

机构地区：[1]兰州交通大学机电工程学院,甘肃兰州730070 [2]西南交通大学应用力学与工程系,四川成都610031

出　　处：《计算力学学报》2004年第6期658-664,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10072051);教育部高等学校博士学科点专项科研基金(20010613001);兰州交通大学青篮人才工程基金资助项目.

摘　　要：建立了两自由度碰撞振动系统的动力学模型及其周期运动的Poincaré映射,当Jacobi矩阵存在一对共轭复特征值在单位圆上并满足强共振(λ40=1)条件时,通过中心流型-范式方法将四维映射转变为二维范式映射。理论分析了系统两参数开折的局部动力学行为,扩展了单参数分岔理论,给出了n-1周期运动产生Hopf分岔和次谐分岔的条件。数值仿真验证了所得出的理论,证明系统在共振点附近存在稳定的Hopf分岔不变环面和次谐分岔4-4周期运动。A two-degree-of-freedom vibro-impact system is considered. The dynamical model and Poincare maps are established. When a pair of complex conjugate eigenvalues of the Jacobi matrix cross the unit circle and satisfy the condition of a strong resonance, the four-dimensional map can be reduced to a two-dimensional one by the center manifold theorem, which is put into normal form by the theory of normal forms. The two-parameter unfoldings of local dynamical behavior are investigated by theoretical methods, which develop the theory of one-parameter family. The conditions of Hopf bifurcation and subharmonic bifurcation from n-1 periodic impact motion are put forward. And numerical calculations prove the theorem is credible. Numerical simulation results indicate that there exist the invariant torus from Hopf bifurcation and the 4-4 periodic impact motion from subharmonic bifurcation as two controlling parameters varying near the critical point.

关 键 词：碰撞振动 POINCARÉ映射 强共振 HOPF分岔 次谐分岔 

分 类 号：O322[理学—一般力学与力学基础]