《含间隙强非线性扭振系统的分岔行为研究(含程序)》.doc

含间隙强非线性 时培明1 刘浩然2 朱占龙1 韩东颖3 侯东晓1 (1.燕山大学电气工程学院 秦皇岛 066004; 2.燕山大学信息科学与工程学院 秦皇岛 066004; 3. 燕山大学车辆与能源学院 秦皇岛 066004) 摘要：建立了含扭系统的动力学方程关键词：传动系统 间隙 分岔 中图分类号：TH113.1 Study on Bifurcation Characheristic of a Strongly Nonlinear Torsional Vibration System with Backlash SHI Peiming1 LIU Haoran 2 ZHU Zhanlong 1 HAN Dongying 3 HOU Dongxiao 1 (1. Institude of Electrical Engineering Yanshan University, Qinhuangdao 066004; 2. Institude of Information Science and Engineering Yanshan University, Qinhuangdao 066004; 3.College of Vehicles and Energy Yanshan University, Qinhuangdao 066004) Abstract: The dynamic equation of a rotating mechinery strongly nonlinear system with backlash is established. The method of Modified Lindstedt-Poincare is employed to obtain the analytical solutions of the strongly nonlinear system under harmonic excitation. The bifurcation equation of the system is deduced by the modified Lindstedt-Poincare combined with the multiple scales. The characteristics of bifurcation of nonautonomy system are analyzed by means of singularity theory, respectively, and different topological structure of solution is obtained under different parameters. At last, the numerical simulation exhibits many different motions such as periodic motion, period-doubling motion and chaos, which describes the change of the strongly nonlinear parameter influences motion state of the system. The research results provide theory basis and reference for analyzing torsional vibration of rotating mechinery caused by backlash. Key words: Drive system Strongly nonlinear Backlash Bifurcation Chaos 0 引言 对传动系统造成了很大的影响有的意义。文献[]在曲轴传动系统扭转振动问题上利用Liapunov-Schmidt方法和奇异性理论研究了系统方程各个参数对系统分岔曲线的影响，为轴系扭振分析提供了新方法。文献[]研究了。文献[]研究了主传动机电耦联扭振系统的复杂动力学行为，重点分析了动态分岔情况及稳定性。为深入研究传动系统非线性动力学行为的全局性态提供参考。 因此本文基于Lagrange方程建立了强非线性系统的动力学方程，求出了该系统的解析近似解及其分岔响应方程。分析了此系统在不同参数下的拓扑结构。最后通过数值仿真得到了系统在强非线性项参数变化下的分岔图，得到了系统在不同参数下的多种运动状态，为研究和抑制此类强非线性系统动力学行为提供了理论参考。 1 系统动力学方程 对于两的系统，为系统集中的转动惯量，为系统的，θθ2分别为两个集中的转角，分别为两个