强共振情况下冲击成型机的亚谐与Hopf分岔  

SUBHARMONIC AND HOPF BIFURCATIONS OF AN IMPACT-FORMING MACHINERY IN A STRONG RESONANCE CASE

作　　者：罗冠炜[1] 谢建华[2] 

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

出　　处：《力学学报》2003年第5期592-598,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10172042;100725051);教育部博士点基金(20010613001)

摘　　要：通过理论分析与数值仿真研究了双质体冲击振动成型机的周期运动在强共振条件下的亚谐分岔与Hopf分岔,证实了此系统的1/1周期运动在强共振(λ40=1)条件下可以分岔为稳定的4/4周期运动及概周期运动.讨论了冲击映射的奇异性,分析了冲击振动系统的'擦边'运动对强共振条件下周期运动及全局分岔的影响.An impact-forming machinery with double masses is considered. Dynamics of the system are studied with special attention to subharmonic and Hopf bifurcations of period 1 single-impact motion in a strong resonance case. The Poincare map of period 1 single-impact motion of the vibro-impact system is established. Bifurcation values and intersecting conditions of the period motion with one impact, in the strong resonance case, are determined. A center manifold theorem technique is applied to reduce the Poincare map to a two-dimensional one, which is put into normal form by theory of normal forms. By theory of subharmonic and Hopf bifurcations of fixed points in .R2-strong resonance, local dynamical behavior of the vibro-impact system, near by the points of resonance, may be analyzed. The theoretical analyses are verified by the results from simulation. The singularity of the Poincare map of the vibro-impact system, caused by the motion with grazing contact, is analyzed by numerical simulation. The influence of the motions with grazing contact on global bifurcations of period 1 single-impact motion, in the strong resonance case, is elucidated.

关 键 词：冲击振动系统 “擦边”运动 强共振 冲击成型机 亚谐 HOPF分岔 冲击映射 碰撞振动 奇异性 

分 类 号：O32[理学—一般力学与力学基础] TH113.1[理学—力学]