自同步振动系统的稳定性与分岔

用偏心转子相位差角微分方程代替双激振器反向回转式自同步振动系统的运动方程，讨论了系统的平衡点稳定性和分岔特性。首先，根据振动系统的运动方程推导出关于偏心转子相位差角的微分方程。然后，基于该方程建立了同步运动的必要性条件，应用Lyapunov稳定性理论，讨论系统的平衡点稳定性及其分岔特性，最后，结合仿真，考察了系统质量、刚度参数和激振器参数的影响规律。

Stability and Bifurcation of Self-Synchronous Vibration System

Stability and bifurcation of vibration system are discussed using differential equation of phase difference angle of two eccentric rotors to replace dynamic equations of a self-synchronous vibration system.Firstly,The differential equation of the phase difference angle is deduced based on the dynamic equations of the vibration system.Then,the(necessary) conditions of synchronous motion are established.The stability and the bifurcation of the equilibrium points of the system are discussed using Lyapunov theories.Finally, the effects of the mass and stiffness parameters of the system and exciter parameters are investigated with numerical simulations.