两点碰撞振动系统的周期运动与分叉  

PERIODIC MOTION AND BIFURCATION OF A VIBRO-IMPACT SYSTEM WITH TWO MOTION LIMITING CONSTRAINTS

作　　者：林梅[1] 丁旺才[1] 武俊虎[1] 

机构地区：[1]兰州交通大学机电工程学院,兰州730070

出　　处：《动力学与控制学报》2006年第1期16-21,共6页Journal of Dynamics and Control

基　　金：国家自然科学基金(10472096);甘肃省自然科学基金资助项目(3ZS042-B25-019)~~

摘　　要：建立了两自由度两点碰撞振动系统的动力学模型,给出了碰撞振动系统产生粘滞的条件,分析了系统存在的粘滞运动.采用打靶法,利用变步长逐次迭代逼近的方法求解系统的不稳定的周期碰撞运动,即Poincar啨截面上的不动点.通过对两自由度两点碰撞振动系统进行数值模拟显示了系统在一定参数条件下存在周期倍化分叉和Hopf分叉,同时通过数值模拟的方法得到了以两自由度两点碰撞振动系统Poincar啨截面上的不变圈表示的拟周期响应,并进一步分析了随着分岔参数的变化,两自由度两点碰撞振动系统周期运动经拟周期分叉和周期倍化分叉向混沌的演化路径.The dynamical model of a two-degree-of-freedom vibro-impact system with two motion limiting constraints was established, whose sticking conditions were given. The analysis shows that there exist sticking motions. According to the shooting method, the unstable periodic motion of vibro-impact, i.e. the fixed point of Poincare section, was solved by the method of varied step and gradual iteration. Hopf bifurcation and period-doubling bifurcation were analyzed under certain parameters by numerical simulation, At the same time the quasi-periodic responses of the system represented by invariant circles in the projected Poincare section of two-degree-of-freedom system with two motion limiting constraints were obtained by numerical simulations. As the controlling parameter varied further, the routes of the two-degree-of-freedom system with two motion limiting constraints to chaos via quasi-period bifurcation and period-doubling bifurcation were investigated respectively.

关 键 词：碰撞振动 两点碰撞 周期运动 POINCARE映射 分叉 混沌 

分 类 号：O322[理学—一般力学与力学基础] TH112[理学—力学]