用试验数据修正振动系统的双对称阻尼矩阵与刚度矩阵  

Bisymmetric Damping and Stiffness Matrices Calibration With Test Data of Vibration Systems

作　　者：周硕[1] 韩明花[1] 孟欢欢[1] 

机构地区：[1]东北电力大学理学院,吉林吉林132012

出　　处：《应用数学和力学》2014年第6期697-711,共15页Applied Mathematics and Mechanics

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

摘　　要：讨论用试验数据修正振动系统的双对称阻尼矩阵与刚度矩阵问题.依据特征方程、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,研究了该问题解的存在性与唯一性,提出了修正阻尼矩阵与刚度矩阵的一个新方法.利用双对称矩阵的性质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.用该方法修正的阻尼矩阵与刚度矩阵不仅满足二次特征方程,而且是唯一的双对称矩阵.The problem of bisymmetric damping and stiffness matrices calibration with test data of vibration systems was discussed. Based on the eigen equation as well as bisymmetry of the damping and stiffness matrices, existence and uniqueness of the solution to the problem was studied by means of the theory and method for the inverse algebraic quadratic eigenvalue prob- lem. A new method for the calibration of damping and stiffness matrices was presented. Accord- ing to the properties of bisymmetric matrices, the bisymmetric solution to the matrix equation was studied. The general expression of the bisymmetric solution was obtained. Moreover, the related optimal approximation problem of any related matrix was addressed and the solution given. The damping and stiffness matrices calibrated with the method not only satisfy the quad- ratic eigen equation, but also are the unique bisymmetric matrix solution. A numerical example proves efficiency of the present method.

关 键 词：结构模型 反问题 修正 阻尼矩阵 刚度矩阵 双对称矩阵 

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