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A reduced modal subspace approach for damped stochastic dynamic systems

S. Kasinos, A. Palmeri, M. Lombardo, Sondipon Adhikari

Computers & Structures, Volume: 257, Start page: 106651

Swansea University Author: Sondipon Adhikari

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DOI (Published version): 10.1016/j.compstruc.2021.106651

Abstract

A novel method for characterising and propagating system uncertainty in structures subjected to dynamic actions is proposed, whereby modal shapes, frequencies and damping ratios constitute the random quantities. The latter, defined in the modal subspace rather than the full geometrical space, reduce...

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Published in: Computers & Structures
ISSN: 0045-7949
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa58106
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spelling 2021-10-22T17:15:15.7235381 v2 58106 2021-09-27 A reduced modal subspace approach for damped stochastic dynamic systems 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2021-09-27 FGSEN A novel method for characterising and propagating system uncertainty in structures subjected to dynamic actions is proposed, whereby modal shapes, frequencies and damping ratios constitute the random quantities. The latter, defined in the modal subspace rather than the full geometrical space, reduce the number of the random variables and the size of the dynamic problem. A numerical procedure is presented for their identification by calibrating their probabilistic definition in line with the geometrical space. A high-order perturbation technique is proposed for the multi-fidelity response quantification by means of an ad hoc extension of the conventional perturbation method. The approach involves a set of auxiliary deterministic differential equations to be adaptively solved with the piecewise exact method, and moment-cumulant relationships are employed to approximate high-order moments. Finally, a polynomial chaos expansion approach is adopted to complement the second-moment analysis for spectral quantification with the modal subspace reduction. Demonstrated on a multi-storey steel frame with semi-rigid connections and a simply supported bridge subjected to a moving load, the proposed variants exhibit improved performance with respect to the conventional second-order and improved perturbation, as well as increased flexibility, enabling the analyst to decide, on-demand, the level of fidelity, balancing accuracy and computational effort. Journal Article Computers & Structures 257 106651 Elsevier BV 0045-7949 High-order perturbation, Modal analysis, Polynomial chaos expansion, Random vibration, Stochastic finite element method, Uncertainty quantification 1 12 2021 2021-12-01 10.1016/j.compstruc.2021.106651 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-10-22T17:15:15.7235381 2021-09-27T11:04:42.3526592 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised S. Kasinos 1 A. Palmeri 2 M. Lombardo 3 Sondipon Adhikari 4 58106__21023__b9f8ee9cad13484e8a57c7f724a6f76e.pdf 58106.pdf 2021-09-28T09:22:56.8901007 Output 1134925 application/pdf Accepted Manuscript true 2022-09-17T00:00:00.0000000 ©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 A reduced modal subspace approach for damped stochastic dynamic systems
spellingShingle A reduced modal subspace approach for damped stochastic dynamic systems
Sondipon Adhikari
title_short A reduced modal subspace approach for damped stochastic dynamic systems
title_full A reduced modal subspace approach for damped stochastic dynamic systems
title_fullStr A reduced modal subspace approach for damped stochastic dynamic systems
title_full_unstemmed A reduced modal subspace approach for damped stochastic dynamic systems
title_sort A reduced modal subspace approach for damped stochastic dynamic systems
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Sondipon Adhikari
author2 S. Kasinos
A. Palmeri
M. Lombardo
Sondipon Adhikari
format Journal article
container_title Computers & Structures
container_volume 257
container_start_page 106651
publishDate 2021
institution Swansea University
issn 0045-7949
doi_str_mv 10.1016/j.compstruc.2021.106651
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
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 A novel method for characterising and propagating system uncertainty in structures subjected to dynamic actions is proposed, whereby modal shapes, frequencies and damping ratios constitute the random quantities. The latter, defined in the modal subspace rather than the full geometrical space, reduce the number of the random variables and the size of the dynamic problem. A numerical procedure is presented for their identification by calibrating their probabilistic definition in line with the geometrical space. A high-order perturbation technique is proposed for the multi-fidelity response quantification by means of an ad hoc extension of the conventional perturbation method. The approach involves a set of auxiliary deterministic differential equations to be adaptively solved with the piecewise exact method, and moment-cumulant relationships are employed to approximate high-order moments. Finally, a polynomial chaos expansion approach is adopted to complement the second-moment analysis for spectral quantification with the modal subspace reduction. Demonstrated on a multi-storey steel frame with semi-rigid connections and a simply supported bridge subjected to a moving load, the proposed variants exhibit improved performance with respect to the conventional second-order and improved perturbation, as well as increased flexibility, enabling the analyst to decide, on-demand, the level of fidelity, balancing accuracy and computational effort.
published_date 2021-12-01T04:14:22Z
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score 11.03559

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