迟滞型材料阻尼转轴的分岔  

Bifurcation of a Shaft With Hysteretic-Type Internal Friction Force of Material

作　　者：丁千[1] 陈予恕[1] 

机构地区：[1]天津大学力学系,天津300072

出　　处：《应用数学和力学》2003年第6期565-571,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19990510;10272078);国家重点基金研究专项经费资助项目(G1998010316)

摘　　要：　应用平均法研究迟滞型材料阻尼转轴的分岔·　首先用Hamilton原理推导出复数形式的转轴运动微分方程,然后用平均法求出各阶模态主共振时的平均方程,并分析定常解的稳定性,最后用奇异性理论分析正常运动和失稳运动响应(异步涡动)的分岔·　研究表明,一定参数条件下,转轴在通过各阶临界转速(主共振)时,可能会因受到冲击而失稳(Hopf分岔)·　正常运动响应在不平衡量较大时有滞后和跳跃现象,而失稳运动响应是一类余维数较高的非对称分岔·　由于内阻尼的非线性,响应随转速增加时还可能产生二次Hopf分岔。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：转轴 迟滞型材料阻尼 HOPF分岔 自激振动 

分 类 号：O322[理学—一般力学与力学基础]