摘要
研究不对称转子系统的参激强迫振动。先用 Hamilton原理导出运动微分方程 ,这是刚度系数周期性变化的参数激励和强迫激励振动方程 ,再用多尺度法研究 1/2亚谐共振 -主共振 ,求得平均方程 ,分叉响应方程和定常解 ,讨论了刚度不对称性 ,质量偏心以及外阻尼对幅频响应的影响。刚度不对称性 ,质量偏心都能增大不稳定区 ,而外阻尼能使共振振幅减小 .最后用稳定性理论分析分叉响应方程和定常解的稳定性。
In this paper, the parametrically excited and forced oscillations of an unbalanced rotor system with unsymmetrical stiffness is studied. By means of the Hamilton's principle the nonlinear differential equations of motion of the rotor system are derived in the rotating rectangular coordinate system. Introducing a complex variable we obtain the equation of motion in complex variable form in which the stiffness coefficient varies periodically. This paper studies 1/2 subharmonic resonance primary resonance of the rotor system using the method of multiple scales. The unsymmetrical stiffness, the eccentricity of center of mass and external damping have great influence on stability. When asymmetry of the shaft increases, the width of unstable region increases.As the eccentricity of the center of mass increases, the resonance amplitude and width of unstable region increase. While external damping is larger, the amplitude becomes smaller. Using the theory of singularity, the stability of stationary solutions is analyzed.
出处
《振动工程学报》
EI
CSCD
北大核心
2002年第3期315-318,共4页
Journal of Vibration Engineering
基金
国家"九五"攀登项目资助课题 (编号 :PD95 2 190 1)
关键词
不对称转子
强迫振动
稳定性
多尺度法
参数激励振动
rotor
unsymmetrical rotor
forced oscillation
stability
method of multiple scales
