@Article{AAMM-3-65,
author = {Li , Jiaofen and Hu , Xiyan},
title = {A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2011},
volume = {3},
number = {1},
pages = {65--86},
abstract = {<p style="text-align: justify;">In this paper we first present a CG-type method for inverse 
eigenvalue problem of constructing real and symmetric matrices $M$, 
$D$ and $K$ for the quadratic pencil $Q(\lambda)=\lambda^2M+\lambda 
D+K$, so that $Q(\lambda)$ has a prescribed subset of eigenvalues 
and eigenvectors. This method can determine the solvability of the 
inverse eigenvalue problem automatically. We then consider the least 
squares model for updating a quadratic pencil $Q(\lambda)$. More precisely, 
we update the model coefficient matrices $M$, $C$ and $K$ so 
that (i) the updated model reproduces the measured data, (ii) the 
symmetry of the original model is preserved, and (iii) 
the difference between the analytical triplet $(M, D, K)$ and the 
updated triplet $(M_{\text{new}}, D_{\text{new}}, 
K_{\text{new}})$ is minimized. In this paper a 
computationally efficient method is provided for such model updating 
and numerical examples are given to illustrate the effectiveness of 
the proposed method.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.09-m0943},
url = {http://global-sci.org/intro/article_detail/aamm/157.html}
}