循环对称结构特征值问题的复数域子空间迭代法

A COMPLEX-DOMAIN SUBSPACE ITERATION METHOD FOR EIGENPROBLEM OF CYCLIC SYMMETRIC STRUCTURES

提出求解在循环对称结构固有特性问题的研究中出现的复Ｈｅｒｍｉｔｅ阵特征值问题的复数域子空间迭代法。根据Ｔｈｏｍａｓ等人提出的理论，生成循环对称结构任一子结构的复约束质量阵和复约束刚度阵。根据本文提出的办法，生成一个包含ｑ个相互质量正交归一的复向量组成的初始里兹迭代复向量组，并将原广义特征值问题的求解空间投影到由这ｑ个复向量张成的Ｋｒｙｌｏｖ空间上可很方便地在ｑ维Ｋｒｙｌｏｖ空间上进行广义复Ｈｅｒｍｉｔｅ矩阵特征值问题的求解。

Based on the subspace iteration technique,a complex-domain subspace iteration is proposed to simplify the solution of the eigenproblem of the generalized Hermite matrices arising in dyanmic analysis of cyclic symmetric structures.At first,according to the station wave theory presented by Thomas,the constrained mass and stiffness matrices are set up.Secondly,a group of q Ritz initially mass-orthorgonized complex trying vectors are formed where q =min( 2p,p+8),p denotes the number of eigenpairs desired.At last,the original generalized Hermite eigenproblem is projected onto the Krylov space by q complex vectors obtained.As the scale of the problem is greatly diminished,the q -dimensioned generalized Hermite matrices eigenproblem can be solved with considerably less CPU time and computer storage.