重频结构大修改动力重分析的矩阵摄动法

Matrix Perturbation Method of Dynamical Reanalysis for Large Modified Structures with Repeated Eigenvalues

为拓展矩阵摄动法在结构重分析中的适用范围,提高重分析计算精度,针对重频结构参数大修改提出了重频结构动力重分析的矩阵摄动法。采用高次增量法将反映重频结构参数改变的质量矩阵和刚度矩阵的增量分别表示为小参数ε的一次与二次幂项之和,根据矩阵摄动理论推导得到重特征值的二阶摄动解及相应特征向量的一阶摄动解。数值算例表明,所提出方法极大提高了重频结构大修改下的动力重分析计算精度。

In order to extend the application range of the matrix perturbation method and improve the calculation precision of structural reanalysis,an improved matrix perturbation method of dynamical reanalysis is proposed for large modified structures with repeated eigenvalues.The stiffness matrix and mass matrix of a modified structure with repeated eigenvalues are expressed in the form of the power series inε.The changes in the matrices that reflect the changes of structural physical parameters are presented in a sum of the termsεandε2.The second order perturbation solution of repeated eigenvalues and the first order perturbation solution of associated eigenvectors are derived based on the matrix perturbation theory.The numerical results show that the presented method yields high precision for dynamical reanalysis of large modified structures with repeated eigenvalues.