摘要
对不对称转子系统的非线性振动问题进行了研究 .首先用哈密顿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 ;然后用多尺度法研究 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 .结果表明 ,刚度不对称性、质量偏心都使不稳定区增大 ,而外阻尼能使共振振幅减小 .最后用奇异性理论分析分叉响应方程和定常解的稳定性 。
The nonlinear oscillation of an unbalanced rotor system with unsymmetrical stiffness is studied. By means of the Hamilton′s principle, the nonlinear differential equations of the rotor system motion are derived in the rotating rectangular coordinate system. By introducing a complex variable, the motion equation in complex variable form where the stiffness coefficient varies periodically is obtained. This paper studies 1/2 sub harmonic resonance primary resonance of the rotor system by applying the method of multiple scales. The averaged equation and frequency response equation are obtained. The unsymmetrical stiffness, the eccentricity of mass and external damping have great influence on stability. When the asymmetry of the shaft grows, the width of unstable region does. When the eccentricity of mass center grows, the resonance amplitude and width of unstable region do. While external damping is larger, the amplitude becomes smaller. According to the theory of singularity, the stability of constant solutions is analyzed and bifurcating group and response curves are obtained
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2002年第5期81-84,共4页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
国家"九五"攀登计划资助项目 (PD95 2 190 1)
关键词
不对称转子
参数激励强迫振动
稳定性
分叉
多尺度法
非线性振动
unsymmetrical rotor
parametrically excited and forced oscillation
stability
bifurcation
multiple scales method
