直升机弹性多支点传动轴的主共振分岔分析

根据质心运动定理、Galerkin法和Dirac函数,求得非惯性移动系下直升机的倾斜弹性多支点传动轴的弯曲运动方程.在此基础上,用多尺度法求得稳态下主共振的分岔方程.分析了运动稳定性、幅频响应曲线的拓扑结构等.结果表明:弹性中间支点有限幅器的功用,能提高传动轴的运动稳定性,增大相邻阶主共振之间不分岔的频率范围.可通过减小偏心距、降低主共振的阶数、加大传动轴及中间支点处的阻尼,使传动轴主共振不分岔.

Bifurcation Analysis of Main Resonance for a Helicopter Drive Shaft with Elastic Multi-Supports

A bending motion equation of a tilting helicopter drive shaft with elastic multi-supports was derived by the theorem of motion for center of mass,Galerkin method and Dirac function.A bifurcation equation of the steady state main resonance was obtained based on the multiple scales method.The motion stability,topology structure of amplitude-frequency response curves etc.were analyzed.The results show that elastic intermediate supports plays the role of the limiters,which can improve the motion stability and increase frequency range of non-bifurcation between adjacent orders of main resonance.The bifurcation of main resonance can be removed by reducing the eccentricity and the order of main resonance and increasing damping of the driving shaft and intermediate supports.