结构动力模型更新中带有子矩阵约束的逆特征值问题∗

摘要

In the dynamic analysis of structure, the data obtained by the finite element model and the vibration test do not match very well. Thus, it is necessary to update the existing dynamic model based on the model test data. In this paper, we investigate an inverse eigen-value problem for symmetric matrices with submatrix constraints in structural dynamic model updating. By the basis vectors of subspace, the constrained problem is transformed into a un-constrained problem. Using this method, a sufficient and necessary condition for the solvability and the expression for the general solution of the problem are presented. Based on the above conclusions, we then consider an optimal approximation problem, get the solvability condition of the problem and derive an explicit formula for the optimal approximation solution.%　　在结构动力分析中，由有限元模型得到的数值解往往与振动测试得到的值不一致，从而依据测量值更新现有的模型是很有必要的。本文研究了结构动力模型更新中的一类带有子矩阵约束的对称矩阵的逆特征值问题。方法借助于子空间的基将约束问题转化为非约束问题。给出了该逆特征值问题有解的充分必要条件和通解的表达式。基于逆特征值的结论，又讨论了一最佳逼近问题，得到了此问题可解的条件，并给出了最佳逼近解的表示。