一类含非黏滞阻尼的Duffing单边碰撞系统的激变研究

Global analysis of crises in a Duffing vibro-impact oscillator with non-viscously damping

以一类含非黏滞阻尼的Duffing单边碰撞系统为研究对象,运用复合胞坐标系方法,分析了该系统的全局分岔特性.对于非黏滞阻尼模型而言,它与物体运动速度的时间历程相关,能更真实地反映出结构材料的能量耗散现象.研究发现,随着阻尼系数、松弛参数及恢复系数的变化,系统发生两类激变现象:一种是混沌吸引子与其吸引域内的混沌鞍发生碰撞而产生的内部激变,另一种是混沌吸引子与吸引域边界上的周期鞍(混沌鞍)发生碰撞而产生的常规边界激变(混沌边界激变),这两类激变都使得混沌吸引子的形状发生突然改变.

In this paper studied is the crises in the Duffing vibro-impact oscillator with non-viscously damping by the composite cell co-ordinate system method. It is assumed that the non-viscously damping depends on the past history of the velocities other than the instantaneous generalized velocities. The energy dissipation behaviors of real structural materials can be preferably represented in the non-viscously damping models. Numerical simulations show that as the damping coefficient or the relaxation parameter or the recovery coefficient is varied, there appear two kinds of crises： one is the interior crisis, which results from the collision between a chaotic attractor and a chaotic saddle on the basin boundary, and the other is the regular/chaotic boundary crisis, which is due to the collision of a chaotic attractor with a periodic/chaotic saddle on its basin boundary. All the crises result in a sudden change in size and shape of the attractor.