梁的广义特征值反问题及离散模型修正

Generalized Inverse Eigenvalue Problem and Model Updating for Discrete Beam

摘要: 本文研究当梁的总质量未知时给定两个特征对的广义特征值反问题与梁的最佳模型修正问题，给出了广义特征值反问题的通解表达式。针对梁的模型修正问题，利用最小二乘方法选取最优参数，使得新梁的物理参数与原梁物理参数的误差达到最小。

Abstract: In this paper, we study the generalized inverse eigenvalue problem and the optimal model updating problem according to two given eigenpairs, while the total mass of beam is unknown. We present the general solution of the inverse generalized eigenvalue problem. Aiming at the beam model updating problem, we use the least squares method to compute the optimal quality parameter to minimize the distance between the physical parameters of the new beam system and those of the original one.