含间隙强非线性扭振系统的分岔行为研究

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振动与冲击 ›› 2012, Vol. 31 ›› Issue (21) : 62-67.

论文

含间隙强非线性扭振系统的分岔行为研究

时培明1 韩东颖2 蒋金水1 朱占龙1 陈浩1

作者信息 +

Study on Bifurcation of a Strongly Nonlinear Torsional Vibration System with Backlash

SHI Peiming1 HAN Dongying 2 JIANG Jinshui1 ZHU Zhanlong1 Chen Hao1

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文章历史 +

摘要

建立了含间隙旋转机械强非线性扭振系统的动力学方程。应用MLP法求解谐波激励下强非线性系统的解析近似解，并运用MLP法与多尺度法结合的方法得到该系统的分岔响应方程。采用奇异性理论研究了系统在非自治情形下的分岔特性，得到不同参数下系统的分岔形态。最后通过具体算例，利用数值模拟的方法得到系统在强非线性项参数变化下的分岔行为，发现随着系统参数变化系统发生周期运动、倍周期运动以及混沌等多种运动形态的复杂动力学行为。研究结果为分析间隙引起的旋转机械传动系统扭振特性提供一定的理论指导和参考。

Abstract

The dynamic equation of a rotating machinery 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 machinery caused by backlash.

导出引用

时培明韩东颖蒋金水朱占龙陈浩. 含间隙强非线性扭振系统的分岔行为研究[J]. 振动与冲击, 2012, 31(21): 62-67

SHI Peiming HAN Dongying JIANG Jinshui ZHU Zhanlong Chen Hao . Study on Bifurcation of a Strongly Nonlinear Torsional Vibration System with Backlash[J]. Journal of Vibration and Shock, 2012, 31(21): 62-67