颤振分析中的特征值排序问题  

Eigenvalue Sorting Problem in Flutter Analysis

作　　者：谢长川[1] 胡薇薇[2] 杨超[1] 

机构地区：[1]北京航空航天大学气动弹性研究室,北京100083 [2]北京信息控制研究所,北京100037

出　　处：《数学的实践与认识》2007年第18期141-146,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10432040;10502003);新世纪优秀人才支持计划资助项目(NCET-04-0170)

摘　　要：颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.The V-g and V-f locus, i. e, root locus depending on the parameters of the system, are important to determine the critical speed in flutter analysis. In almost all the general software and programs, the ＇data branch crossing＇ phenomena would be happened frequently. It leads to the inconvenience in the determination of the critical flutter speed and the coupling type of the system. By the implicit function theorem, the continuation of the eigenvalues depending on the parameters of the system can be established, except the equal multiple eigenvalues. According to the continuation of the vector value function, the sorting algorithm and the program have been given out to solve the ＇data branch crossingr problem. A numerical example is presented to prove the efficiency of the method, which can simplify the data postprocessing of the flutter analysis.

关 键 词：特征值 连续性 同胚 排序 

分 类 号：V215.34[航空宇航科学与技术—航空宇航推进理论与工程]