结构复固有频率区域的区间摄动法

利用区间数学研究具有误差或有界不确定性结构参数的非比例阻尼结构复特征值 所在区域问题.将误差或有界不确定性结构参数用区间定量化,这样,具有误差或有界不确 定性结构参数的非比例阻尼结构复特征值所在区域问题便可归结为实区间矩阵的广义特征值 问题.对于小的误差或有界不确定参数,所提出的求解实区间矩阵的广义特征值问题的区间 摄动法可以给出满足工程要求的结构固有频率所在的区域.

Interval Perturbation Method for Computing Regions Containing Complex Natural Frequencies of Structures

By interval mathematics, the problem on regions containing complex eigenvalues for structures with errors or uncertain but bounded parameters was studied. These parameters were described by interval numbers. The non-proportional damping structural eigenvalue problem with errors or uncertain but bounded parameters can be transformed into the generalized eigenvalue problem of interval matrices, and the complex eigenvalues are regions containing natural frequencies of structures with errors or uncertain but bounded parameters. For small errors or uncertain but bounded parameters, the interval perturbation method was presented for computing complex interval eigenvalues of the generalized interval eigenvalue problem, and the required regions containing natural frequencies of structures may be obtained.