摘要
研究非对称刚度转轴的参激共振和分叉。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激振动方程 ,再用平均法求得平均方程 ,分叉响应方程和定常解。讨论了横截面的不对称性 ,外阻尼和非线性对幅频响应曲线的影响 ,最后用奇异性理论分析定常解的稳定性和分叉。
The parametrical resonance and stability in a rotating shaft with an asymmetrical stiffness is analyzed. By means of the Hamilton's principle the nonlinear differential equations of motion of the shaft are derived in the rotating coordinate system. Transforming the equations of motion from rotating coordinate system into stationary coordinate system and introducing a complex variable, the motion equation in complex variable forms in which the stiffness coefficient varies periodically as time, is obtained. By applying the method of averaging, the averaged equation and the amplitude-frequency response equation are obtained. According to the theory of singularity, the stability and bifurcation of the steady-state solutions are analyzed.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2001年第6期43-48,共6页
Journal of Mechanical Engineering
基金
国家'九五'攀登基金资助!项目 (PD95 2 190 1)
关键词
非对称刚度转轴
参激共振
稳定性
分叉
平均法
Shaft with unsymmetrical stiffness Parametrical resonance Stability Bifurcation Method of averaging
