一类刚弹混合碰撞系统的动力学分析

Analysis on a Kind of Rigid-Elastic Hybrid Collision System

为了研究动力系统中同时含有刚性碰撞过程和弹性碰撞过程时的系统特性,本文给出了一类新的既含有刚性碰撞又含有弹性碰撞过程的碰撞振动模型。通过建立全局Poincaré映射的方法解析的分析了此碰撞振动系统的一周期一碰及一周期n碰的周期运动条件。数值仿真模拟了系统的周期碰撞运动现象,并得到了随参数发生变化时,系统出现的分岔现象,且利用数值仿真的方法对系统中的共存吸引子进行了初步研究。

In order to study the system characteristics of a dynamic system with both rigid and elastic colli-sions, a new type of collisional vibration model with both rigid and elastic collisions is presented in this paper. A global Poincarémapping method is used to analyze the conditions of one-collision- one-period and n-collisions-one-period motion vibration system. The numerical simulation simu-lates the system’s periodic collision movement phenomenon, and obtains the bifurcation phe-nomenon that occurs when the parameters change with the system. The numerical simulation method is used to study the coexistence attractors in the system.