无阻尼结构系统的特征结构配置  

EIGEN-STRUCTURE ASSIGNMENT FOR AN UNDAMPED STRUCTURAL SYSTEM

作　　者：刘皞[1] 戴华[1] 

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《振动与冲击》2008年第4期122-125,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(No.10271055)

摘　　要：无阻尼结构系统的特征结构配置问题是指选择反馈矩阵G∈Rm×n使得闭环束Qc(λ)=λMa-Ka-BG具有给定的特征值与特征向量。运用代数特征值反问题的理论与方法,研究了两类无阻尼结构系统的特征结构配置问题。对问题1,给出了求解此问题的数值算法,此方法的过程简单而且容易实现,并且能有效地改善系统的条件数;对问题2,给出了能保持系统对称性的条件和解的表达式。数值算例表明,该方法对求解此两类问题是有效的。Eigen-structure assignment problem for an undamped structural system is referred to as that a feedback matrix G∈Rm×n is chosen properly so that the quadratic pencil Qc(λ)=λMa-Ka-BG has a prescribed subset of eigenvalues and eigenvectors.By means of the theory and methods of the algebraic eigenvalue inverse problems,two eigen-structure assignment problems for an undamped structural system are studied.For problem 1,a numerical algorithm is proposed to solve this problem,the procedure of the method is very simple and easy to realize and can improve the condition number of the system.For problem 2,the condition to keep the symmetricity of the system and the expressions of the solution are given.Numerical examples show the proposed methods are effective to solve these two problems.

关 键 词：无阻尼结构系统 特征结构配置 反问题 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]