回转周期结构动力问题中复Hermite矩阵特征值的子空间迭代解法

A SUBSPACE ITERATION METHOD TO SOLVE COMPLEX HERMITE EIGENVALUE PROBLEM ENCOUNTED IN DYNAMIC CALCULATION OF ROTATIONALLY PERIODIC STRUCTURES

在离心压缩机叶轮及汽轮机叶片类回转周期结构的动力分析中，可根据波传动理论，将回转周期结构无阻尼自由振动从计算整个结构化简为只进行一个子结构的计算。然而由于引入复约束，此时刚度阵和质量阵变为复Ｈｅｒｍ ｉｔｅ矩阵，为求解其特征值，将传统子空间迭代方法及广义雅可比方法迭代公式进行了改进。数值计算结果表明，该方法既能达到理想的精度，又减少了计算的存贮量。

Wave propagation method has been used to solve dynamic problems of rotationally periodic structures such as centrifugal impellers and turbine blades in order to calculate just one substructure instead of the whole structure.However, stiffness matrix and mass matrix become complex Hermite matrices by introducing complex constrains. An improved subspace iteration method and corresponding general Jacobi method are presented to solve eigenvalue problem of Hermite matrices. The method use less computer storage but can reach a satisfied precision tested by calculation examples.