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An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum

Ghosh, Debraj and Ghanem, Roger (2012) An invariant subspace-based approach to the random eigenvalue problem of systems with clustered spectrum. In: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 91 (4). pp. 378-396.

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Official URL: http://dx.doi.org/10.1002/nme.4276

Abstract

The repeated or closely spaced eigenvalues and corresponding eigenvectors of a matrix are usually very sensitive to a perturbation of the matrix, which makes capturing the behavior of these eigenpairs very difficult. Similar difficulty is encountered in solving the random eigenvalue problem when a matrix with random elements has a set of clustered eigenvalues in its mean. In addition, the methods to solve the random eigenvalue problem often differ in characterizing the problem, which leads to different interpretations of the solution. Thus, the solutions obtained from different methods become mathematically incomparable. These two issues, the difficulty of solving and the non-unique characterization, are addressed here. A different approach is used where instead of tracking a few individual eigenpairs, the corresponding invariant subspace is tracked. The spectral stochastic finite element method is used for analysis, where the polynomial chaos expansion is used to represent the random eigenvalues and eigenvectors. However, the main concept of tracking the invariant subspace remains mostly independent of any such representation. The approach is successfully implemented in response prediction of a system with repeated natural frequencies. It is found that tracking only an invariant subspace could be sufficient to build a modal-based reduced-order model of the system. Copyright (C) 2012 John Wiley & Sons, Ltd.

Item Type: Journal Article
Additional Information: Copyright for this article belongs to WILEY-BLACKWELL
Keywords: random eigenvalue;polynomial chaos;repeated eigenvalues;clustered eigenvalues
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 30 Jul 2012 05:44
Last Modified: 30 Jul 2012 05:44
URI: http://eprints.iisc.ernet.in/id/eprint/44852

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