Taiwanese Journal of Mathematics

A NEW EIGENVALUE EMBEDDING APPROACH FOR FINITE ELEMENT MODEL UPDATING

Yunfeng Cai and Shufang Xu

Full-text: Open access

Abstract

This paper concerns the eigenvalue embedding problem (EEP) of updating a symmetric finite-element model so that a few troublesome eigenvalues are replaced by some chosen ones, while the remaining large number of eigenvalues and eigenvectors of the original model do not change. Based on the theory established in [2], by sufficiently utilizing the inherent freedom of the EEP, an expression of the parameterized solution to the EEP is derived. This expression is then used to develop a novel numerical method for solving the EEP, in which the parameters in the solutions are optimized in some sense. This method not only utilizes the freedom of the EEP but also removes the limitation of the method proposed in [6]. The results of our numerical experiments show that the present algorithm is feasible and efficient, and can outperform the iterative method in [3] and the method in [6].

Article information

Source
Taiwanese J. Math., Volume 14, Number 3A (2010), 911-932.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405874

Digital Object Identifier
doi:10.11650/twjm/1500405874

Mathematical Reviews number (MathSciNet)
MR2667724

Zentralblatt MATH identifier
1210.15010

Subjects
Primary: 15A18: Eigenvalues, singular values, and eigenvectors 65F18: Inverse eigenvalue problems 93B55: Pole and zero placement problems

Keywords
finite element model updating inverse quadratic eigenvalue problem vibrating system numerical method

Citation

Cai, Yunfeng; Xu, Shufang. A NEW EIGENVALUE EMBEDDING APPROACH FOR FINITE ELEMENT MODEL UPDATING. Taiwanese J. Math. 14 (2010), no. 3A, 911--932. doi:10.11650/twjm/1500405874. https://projecteuclid.org/euclid.twjm/1500405874


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