用试验数据修正质量矩阵,阻尼矩阵与刚度矩阵  

Bisymmetric Mass Matrix, Damping Matrix and Stiffness Matrix Correction Using Test Data

作　　者：郭丽杰[1] 周硕[1] 

机构地区：[1]东北电力大学理学院,吉林132012

出　　处：《系统科学与数学》2017年第2期587-600,共14页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11072085);吉林省自然科学基金(201115180)资助课题

摘　　要：讨论用试验数据修正振动系统的双对称质量矩阵,阻尼矩阵与刚度矩阵的问题.依据特征方程,质量矩阵,阻尼矩阵与刚度矩阵的双对称性,利用代数二次特征值反问题的理论和方法,研究了这个问题解的存在性与惟一性,提出了修正质量矩阵,阻尼矩阵与刚度矩阵的一个新方法.利用矩阵的奇异值分解和矩阵的Kronecker乘积研究了方程的双对称解.给出了二次特征值反问题双对称解的一般表达式,讨论了对任意给定矩阵的最佳逼近问题,并给出了问题的最佳逼近解.The problem of bisymmetric mass matrix, damping matrix and stiffness matrix correction using test data of vibration system is discussed. Based on the characteristic equation, the bisymmetry of mass, damping and stiffness matrices, the existence and uniqueness of solution to the problem is studied by means of the theory and method of the algebraic quadratic inverse eigenvalue problem. A new method of mass matrix, damping matrix and stiffness matrix correction is presented. By singular value decomposition of matrix and Kronecker product of matrices, the bisymmetric solution of matrix equation is studied. The general expression of the bisymmetric solution is obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved. The damping and stiffness matrices correctedby the method not only satisfy the quadratic characteristic equation, but also are the unique bisymmetric matrix.

关 键 词：振动系统 修正 质量矩阵 阻尼矩阵 刚度矩阵 双对称矩阵 

分 类 号：O241.6[理学—计算数学]