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Random matrix eigenvalue problems in structural dynamics: An iterative approach

Sondipon Adhikari, S. Chakraborty

Mechanical Systems and Signal Processing, Volume: 164, Start page: 108260

Swansea University Author: Sondipon Adhikari

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DOI (Published version): 10.1016/j.ymssp.2021.108260

Abstract

Uncertainties need to be taken into account in the dynamic analysis of complex structures. This is because in some cases uncertainties can have a significant impact on the dynamic response and ignoring it can lead to unsafe design. For complex systems with uncertainties, the dynamic response is char...

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Published in: Mechanical Systems and Signal Processing
ISSN: 0888-3270
Published: Elsevier BV 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa57554
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spelling 2021-09-09T14:28:35.6226004 v2 57554 2021-08-09 Random matrix eigenvalue problems in structural dynamics: An iterative approach 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-08-09 FGSEN Uncertainties need to be taken into account in the dynamic analysis of complex structures. This is because in some cases uncertainties can have a significant impact on the dynamic response and ignoring it can lead to unsafe design. For complex systems with uncertainties, the dynamic response is characterised by the eigenvalues and eigenvectors of the underlying generalised matrix eigenvalue problem. This paper aims at developing computationally efficient methods for random eigenvalue problems arising in the dynamics of multi-degree-of-freedom systems. There are efficient methods available in the literature for obtaining eigenvalues of random dynamical systems. However, the computation of eigenvectors remains challenging due to the presence of a large number of random variables within a single eigenvector. To address this problem, we project the random eigenvectors on the basis spanned by the underlying deterministic eigenvectors and apply a Galerkin formulation to obtain the unknown coefficients. The overall approach is simplified using an iterative technique. Two numerical examples are provided to illustrate the proposed method. Full-scale Monte Carlo simulations are used to validate the new results. Journal Article Mechanical Systems and Signal Processing 164 108260 Elsevier BV 0888-3270 Random eigenvalue problem, Iterative methods, Galerkin projection, Statistical distributions, Stochastic systems 1 2 2022 2022-02-01 10.1016/j.ymssp.2021.108260 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-09-09T14:28:35.6226004 2021-08-09T09:57:00.5237339 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Sondipon Adhikari 1 S. Chakraborty 2 57554__20578__79c8fb4fab1e4a5c9126d7eb4b364b54.pdf 57554.pdf 2021-08-09T10:35:13.3379901 Output 2019221 application/pdf Accepted Manuscript true 2022-08-05T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title Random matrix eigenvalue problems in structural dynamics: An iterative approach
spellingShingle Random matrix eigenvalue problems in structural dynamics: An iterative approach
Sondipon Adhikari
title_short Random matrix eigenvalue problems in structural dynamics: An iterative approach
title_full Random matrix eigenvalue problems in structural dynamics: An iterative approach
title_fullStr Random matrix eigenvalue problems in structural dynamics: An iterative approach
title_full_unstemmed Random matrix eigenvalue problems in structural dynamics: An iterative approach
title_sort Random matrix eigenvalue problems in structural dynamics: An iterative approach
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 Sondipon Adhikari
S. Chakraborty
format Journal article
container_title Mechanical Systems and Signal Processing
container_volume 164
container_start_page 108260
publishDate 2022
institution Swansea University
issn 0888-3270
doi_str_mv 10.1016/j.ymssp.2021.108260
publisher Elsevier BV
college_str Faculty of Science and Engineering
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hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description Uncertainties need to be taken into account in the dynamic analysis of complex structures. This is because in some cases uncertainties can have a significant impact on the dynamic response and ignoring it can lead to unsafe design. For complex systems with uncertainties, the dynamic response is characterised by the eigenvalues and eigenvectors of the underlying generalised matrix eigenvalue problem. This paper aims at developing computationally efficient methods for random eigenvalue problems arising in the dynamics of multi-degree-of-freedom systems. There are efficient methods available in the literature for obtaining eigenvalues of random dynamical systems. However, the computation of eigenvectors remains challenging due to the presence of a large number of random variables within a single eigenvector. To address this problem, we project the random eigenvectors on the basis spanned by the underlying deterministic eigenvectors and apply a Galerkin formulation to obtain the unknown coefficients. The overall approach is simplified using an iterative technique. Two numerical examples are provided to illustrate the proposed method. Full-scale Monte Carlo simulations are used to validate the new results.
published_date 2022-02-01T04:13:23Z
_version_ 1763753909096022016
score 11.012678

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