一类两自由度干摩擦系统倍化分岔与混沌的数值模拟  

The Numerical Simulation of Period Doubling Bifurcation and Chaos in a Two Degree of Freedom Dry Friction System

作　　者：余本嵩[1] 谢建华[2] 徐慧东[2] 

机构地区：[1]南京航空航天大学航空宇航学院．南京210016 [2]西南交通大学应用力学与工程系,成都610031

出　　处：《力学季刊》2009年第1期97-100,共4页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金项目(10772151)

摘　　要：本文利用Runge-Kutta数值积分法对一类两自由度干摩擦系统进行了数值仿真。文中列出了该系统中质块与传送带间处于黏附与滑移两种不同状态时质块的运动方程,同时给出了两种状态间的转换条件,在此基础上对系统进行数值模拟。通过不断变化传送带的速度对该系统的动力行为进行了分析,证实此系统存在稳定的周期运动及倍化分岔,得到了该系统周期运动的倍化分岔通向混沌的路径。对此系统分岔与混沌行为的研究为生产实践中的干摩擦现象的优化配置提供了理论依据。The numerical simulation for a two degree of freedom dry friction system with the help of Runge-Kutta numerical integration method was carried out. It lists masses＇ motion equations, corresponding to two different states, namely, stick and slip state were listed, which are between masses and conveyor in the system. Meanwhile the transfer conditions between the two states were given, it carry out the numerical simulation of the system by means of the motion equations and transfer conditions. The dynamic behaviors of the system were analyzed by changing the speed of the conveyor continuously, and the existence of stable periodic motions and the period-doubling bifurcation of the system were confirmed. The path of the period-doubling bifurcation of the system＇s periodic motions was obtained that leading to the chaos. The study about the behaviors of bifurcation and chaos in the system provides a theoretical basis for the optimized configuration about the practical production concerned with dry friction phenomenon.

关 键 词：干摩擦 周期运动 倍化分岔 混沌 

分 类 号：O313[理学—一般力学与力学基础]