刚性多支点传动轴主共振分析

根据质心运动定理、Galerkin法和Heaviside函数,求得非惯性系下倾斜刚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一次近似定常解.分析了主共振的振型、最大振幅、稳定性和振幅突变性.结果表明:传动轴的弯曲运动方程是Duffing方程;主共振时,各段轴相互影响;每段轴主共振的振型与两支点轴主共振的振型相同;主共振的最大振幅在最大跨距的轴段上;主共振时,轴的振幅有可能突变,振幅突变的频率区间长度很小,其频率略小于固有频率.

Analysis of main resonance of drive shaft with rigid multi-supports

A bending motion equation of a tilting drive shaft with rigid multi-supports is derived by theorem of the motion of mass center,method of Galerkin and Heaviside function.Approximate steady-state solutions of the main resonance are obtained through multiple scales method.The shapes,maximum amplitude,stability and amplitude jump of main resonance are analyzed.The results show that the bending motion equation is the Duffing one.Every span shaft in main resonance affects each other.The shape of main resonance of every span shaft is the same as that of a shaft with two supports.The maximum amplitude of main resonance is located at the maximum span shaft.When a drive shaft is in main resonance,the amplitude jump is possible.The interval length of frequency of amplitude jump is very small,and the frequency is a little smaller than the natural frequency.