BIFURCATION OF A SHAFT WITH HYSTERETIC-TYPE INTERNAL FRICTION FORCE OF MATERIAL  

作　　者：丁千 陈予恕 

机构地区：[1]Department of Mechanics, Tianjin University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2003年第6期638-645,共8页应用数学和力学（英文版）

基　　金：theNationalNaturalScienceFoundationofChina (1 9990 51 0 ;1 0 2 72 0 78) ;theNationalKeyBasicResearchSpacialFoundationofChina (1 9980 2 0 3 1 6)

摘　　要：The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steady_state responses was also determined.Lastly, the bifurcations of both normal motion (synchronous whirl) and self_excited motion (non_synchronous whirl) were investigated using the method of singularity. The study shows that by a rather large disturbance, the stability of the shaft can be lost through Hopf bifurcation in case the stability condition is not satisfied. The averaged self_excited response appears as a type of unsymmetrical bifurcation with high orders of co_dimension. The second Hopf bifurcation, which corresponds to double amplitude_modulated response, can occur as the speed of the shaft increases. Balancing the shaft carefully to decrease its unbalance level and increasing the external damping are two effective methods to avoid the appearance of the self_sustained whirl induced by the hysteretic internal friction of material.The bifurcation of a shaft with hysteretic internal friction of material was analysed. Firstly, the differential motion equation in complex form was deduced using Hamilton principle. Then averaged equations in primary resonances were obtained using the averaging method. The stability of steady_state responses was also determined.Lastly, the bifurcations of both normal motion (synchronous whirl) and self_excited motion (non_synchronous whirl) were investigated using the method of singularity. The study shows that by a rather large disturbance, the stability of the shaft can be lost through Hopf bifurcation in case the stability condition is not satisfied. The averaged self_excited response appears as a type of unsymmetrical bifurcation with high orders of co_dimension. The second Hopf bifurcation, which corresponds to double amplitude_modulated response, can occur as the speed of the shaft increases. Balancing the shaft carefully to decrease its unbalance level and increasing the external damping are two effective methods to avoid the appearance of the self_sustained whirl induced by the hysteretic internal friction of material.

关 键 词：SHAFT hysteretic_type internal friction of material Hopf bifurcation non_synchronous whirl 

分 类 号：O322[理学—一般力学与力学基础]