Volume 3, Issue 1
A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics

Adv. Appl. Math. Mech., 3 (2011), pp. 65-86.

Published online: 2011-03

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• Abstract

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.

• Keywords

Inverse eigenvalue problem, structural dynamic model updating, quadratic pencil, iteration method.

15A24, 65F18, 65H17

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@Article{AAMM-3-65, author = {}, 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 = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m0943}, url = {http://global-sci.org/intro/article_detail/aamm/157.html} }
TY - JOUR T1 - A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 65 EP - 86 PY - 2011 DA - 2011/03 SN - 3 DO - http://doi.org/10.4208/aamm.09-m0943 UR - https://global-sci.org/intro/article_detail/aamm/157.html KW - Inverse eigenvalue problem, structural dynamic model updating, quadratic pencil, iteration method. AB -

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.

Jiaofen Li & Xiyan Hu. (1970). A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics. Advances in Applied Mathematics and Mechanics. 3 (1). 65-86. doi:10.4208/aamm.09-m0943
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