约束矩阵方程的中心对称解及其在振动理论反问题中的应用  

Centrosymmetric Solutions of Constrained Matrix Equation and Its Application to Inverse Problem of Vibration Theory

作　　者：周硕[1] 王霖[1] 韩明花[1] 

机构地区：[1]东北电力大学理学院,吉林132012

出　　处：《应用数学和力学》2013年第3期306-317,共12页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(11072085);吉林省自然科学基金资助项目(201115180)

摘　　要：研究了中心主子矩阵约束下矩阵方程的中心对称解.利用矩阵向量化、Kronecker乘积及奇异值分解方法,得到了有解的充分必要条件及解的一般表达形式.同时,考虑了与之相关的对任意给定矩阵的最佳逼近问题.进而,给出在振动理论反问题中的应用,利用截断的主质量矩阵(或主刚度矩阵)、截断模态矩阵以及质量矩阵(或刚度矩阵)的中心主子阵,求系统的质量矩阵(或刚度矩阵).最后用两个例子说明文中方法的有效性.The centrosymmetric solutions of constrained matrix equation under a central principal submatrix constraint were studied. By using matrix to quantify, Kronecker product and singular value decomposition （SVD） method, the necessary and sufficient conditions for solvability and the general expression of solutions were obtained. Then, the expression of solution to the related optimal approximation problem was considered. Moreover, the applications in the inverse problem of vibration theory were given, by using the reduction principal mass matrix （ or principal stiffness matrix）, reduction modal matrix and central principal submatrix of the mass matrix （ or stiffness matrix）, the mass matrix （ or stiffness matrix） of the system was obtained. Finally, the proposed method was demonstrated by two examples.

关 键 词：振动理论 反问题 矩阵方程 中心主子阵约束 中心对称矩阵 最佳逼近 

分 类 号：TH123.1[机械工程—机械设计及理论] O241.6[理学—计算数学]