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Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes

E. Jacquelin, O. Dessombz, J.-J Sinou, S. Adhikari, M.I. Friswell, Michael Friswell, Sondipon Adhikari

Procedia Engineering, Volume: 199, Pages: 1104 - 1109

Swansea University Authors: Michael Friswell, Sondipon Adhikari

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DOI (Published version): 10.1016/j.proeng.2017.09.212

Abstract

Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate...

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Published in: Procedia Engineering
ISSN: 1877-7058
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa35312
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last_indexed 2018-02-09T05:26:20Z
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spelling 2017-09-18T12:11:38.9180458 v2 35312 2017-09-18 Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2017-09-18 FGSEN Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate model based on a polynomial chaos expansion (PCE) can be built as an alternative to MCS. However, some previous studies have shown poor convergence properties around the deterministic eigenfrequencies. In this study, an extended Pade approximant approach is proposed not only to accelerate the convergence of the PCE but also to have a better representation of the exact frequency response, which is a rational function of the uncertain parameters. A second approach is based on the random mode expansion of the response, which is widely used for deterministic dynamical systems. A PCE approach is used to calculate the random modes. Both approaches are tested on an example to check their efficiency. Journal Article Procedia Engineering 199 1104 1109 1877-7058 Random dynamical systems; polynomial chaos expansion; multivariate Pade approximants; random modes 31 12 2017 2017-12-31 10.1016/j.proeng.2017.09.212 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2017-09-18T12:11:38.9180458 2017-09-18T12:09:01.4956971 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised E. Jacquelin 1 O. Dessombz 2 J.-J Sinou 3 S. Adhikari 4 M.I. Friswell 5 Michael Friswell 6 Sondipon Adhikari 7 0035312-18092017121127.pdf jacquelin2017(2).pdf 2017-09-18T12:11:27.7470000 Output 719748 application/pdf Version of Record true 2017-09-18T00:00:00.0000000 false eng
title Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
spellingShingle Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
Michael Friswell
Sondipon Adhikari
title_short Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
title_full Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
title_fullStr Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
title_full_unstemmed Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
title_sort Steady-state response of a random dynamical system described with Padé approximants and random eigenmodes
author_id_str_mv 5894777b8f9c6e64bde3568d68078d40
4ea84d67c4e414f5ccbd7593a40f04d3
author_id_fullname_str_mv 5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
author Michael Friswell
Sondipon Adhikari
author2 E. Jacquelin
O. Dessombz
J.-J Sinou
S. Adhikari
M.I. Friswell
Michael Friswell
Sondipon Adhikari
format Journal article
container_title Procedia Engineering
container_volume 199
container_start_page 1104
publishDate 2017
institution Swansea University
issn 1877-7058
doi_str_mv 10.1016/j.proeng.2017.09.212
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 Designing a random dynamical system requires the prediction of the statistics of the response, knowing the random model of the uncertain parameters. Direct Monte Carlo simulation (MCS) is the reference method for propagating uncertainties but its main drawback is the high numerical cost. A surrogate model based on a polynomial chaos expansion (PCE) can be built as an alternative to MCS. However, some previous studies have shown poor convergence properties around the deterministic eigenfrequencies. In this study, an extended Pade approximant approach is proposed not only to accelerate the convergence of the PCE but also to have a better representation of the exact frequency response, which is a rational function of the uncertain parameters. A second approach is based on the random mode expansion of the response, which is widely used for deterministic dynamical systems. A PCE approach is used to calculate the random modes. Both approaches are tested on an example to check their efficiency.
published_date 2017-12-31T03:43:54Z
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score 11.012678

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