摘要
建立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。
The dynamic equation of a strongly nonlinear rotating machinery system with backlash was established. The method of modified Lindstedt-Poincare was employed to obtain the analytical approximate solutions to the strongly nonlinear system under harmonic excitation. The bifurcation equation of the system was deduced with the modified Lindstedt-Poincare method combined with the multiple scales. The characteristics of bifurcation of the nonautonomous system were analyzed by means of the singularity theory, respectively, and the different topological structures of the solution were obtained with different parameters. At last, the numerical simulation exhibited many different motions, such as, periodic motion, period-doubling motion and chaos, it was shown that the change of the strongly nonlinear parameters influences the motion state of the system. The results provided a theoretic basis and reference for analyzing torsional vibration of a rotating machinery caused by backlash.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第21期62-67,共6页
Journal of Vibration and Shock
基金
国家自然科学基金项目(51005196)
河北省自然科学基金项目(F2010001317)
高等学校博士学科点专项科研基金(20101333120004)
关键词
扭振系统
强非线性
间隙
分岔
混沌
torsional vibration system
strongly nonlinear
backlash
bifurcation
chaos
