1/2 SUBHARMONIC RESONANCE OF A SHAFT WITH UNSYMMETRICAL STIFFNESS

作     者：Xiao XiwuYang Shuzi Huang YuyingDepartment of Mechanics,Huazhong University of Scienceand Technology,Wuhan 430074, China 

作者机构：Department of Mechanics Huzahong University of Scienceand Technology Wuhan 430074 

出 版 物：《Chinese Journal of Mechanical Engineering》 (中国机械工程学报（英文版）)

年 卷 期：2003年第16卷第1期

页      面：25-27,30页

核心收录：

学科分类：08[工学] 080203[工学-机械设计及理论] 0802[工学-机械工程] 

基　　金：This project is supported by National Key Project of China(No.PD9521901) 

主　　题：Shaft with unsymmetrical stiffiless Subharmonic resonance Stability Bifurcation MMS 

摘      要：The 1/2 subharmonic resonance of a shaft with unsymmetrical stiffness is studied. By means of the Hamilton s principle the nonlinear differential equations of motion of the rotating shaft are derived in the rotating rectangular coordinate system. Transforming the equations of motion from rotating coordinate system into stationary coordinate system and introducing a complex variable, the equation of motion in complex variable form is obtained, in which the stiffness coefficient varies periodically with time. It presents a nonlinear oscillation system under parametric excitation. By applying the method of multiple scales (MMS) the averaged equation, the bifurcating response equations and local bifurcating set are obtained. Via the theory of singularity, the stability of constant solutions is analyzed and bifurcating response curves are obtained. This study shows that the rotating shaft has rich bifurcation phenomena.