摘要
为了研究强非线性条件下相对转动扭振系统的扭转振动,建立了非线性刚度、非线性阻尼和外扰激励作用下的扭振方程,通过MLP法求解出系统的近似解析解,结合多尺度法分析了各参数对系统幅频特性的影响,最后通过数值仿真的方法研究了激励幅值变化导致系统出现的复杂动力学行为,利用分岔图、最大Lyapunov指数图和Poincare截面图描述了系统由稳定到混沌的演变过程,为该类系统的稳定及失稳研究提供了理论依据。
For the research on torsional vibration of a strongly nonlinear relative-rotation dynamical system, the torsional vibration equation of system with nonlinear stiffness, nonlinear damping and external excitation is established. The approximate solution of system is solved with the method of modified Lindstedt-Poincare. Besides, combining the method of multiple scales, the influence of amplitude-frequency property caused by parameters is analyzed. Last, the complex dynamics behavior of system caused by the change of excitation amplitude is studied through numerical simulation, and the evolution process of system from stability to chaos is described by the use of bifurcation diagram, maximum Lyapunov index figure and Poincare section graph. This provides a theoretical basis for the stability and instability research of system.
出处
《燕山大学学报》
CAS
北大核心
2016年第2期142-149,共8页
Journal of Yanshan University
基金
国家自然科学基金资助项目(61104040
51575472)
河北省人力保障人才工程项目(A201500109)
关键词
扭振系统
强非线性
近似解
混沌
relatively rotation system
strongly nonlinear
approximate solution
chaos
