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A CG-Type Method for Inverse Quadratic Eigenvalue Problems in Model Updating of Structural Dynamics

Published online by Cambridge University Press:  03 June 2015

Jiaofen Li  and
Xiyan Hu
Jiaofen Li*
Affiliation:
School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China
Xiyan Hu*
Affiliation:
College of Mathematics and Econometrics, Hunan University, Changsha 410082, China
*
Corresponding author. URL: http://w3.guet.edu.cn/dept7/people/TeacherDetail.Asp?TeacherID=371 Email:lixiaogui1290@163.com
Email:xyhu@hnu.cn
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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(λ) = λ2M + λD + K, so that Q(λ) 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(λ). 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 (Mnew, Dnew, Knew) 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

15A2465F1865H17Inverse eigenvalue problemstructural dynamic model updatingquadratic penciliteration method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 1 , February 2011 , pp. 65 - 86
Copyright
Copyright © Global-Science Press 2011

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