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Polynomial chaos-based extended Padé expansion in structural dynamics

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

International Journal for Numerical Methods in Engineering

Swansea University Authors: Michael Friswell, Sondipon Adhikari

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DOI (Published version): 10.1002/nme.5497

Abstract

The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa32201
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spelling 2017-03-02T09:01:51.4633733 v2 32201 2017-03-01 Polynomial chaos-based extended Padé expansion in structural dynamics 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 2017-03-01 FGSEN The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially around the eigenfrequencies of the dynamical system. In the present study, a new approach based on Padé approximants to obtain moments and pdf of the dynamic response in the frequency domain is proposed. A key difference between the direct polynomial chaos representation and the Padé representation is that the Padé approach has polynomials in both numerator and denominator. For frequency response functions, the denominator plays a vital role as it contains the information related to resonance frequencies, which are uncertain. A Galerkin approach in conjunction with polynomial chaos is proposed for the Padé approximation. Another physics-based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Padé approach. It is shown that both methods give accurate results even if a very low degree of the polynomial expansion is used. The methods are demonstrated for two degree-of-freedom system with one and two uncertain parameters. Journal Article International Journal for Numerical Methods in Engineering 0029-5981 31 12 2017 2017-12-31 10.1002/nme.5497 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2017-03-02T09:01:51.4633733 2017-03-01T15:55:32.1058590 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 0032201-02032017090101.pdf jacquelin2017.pdf 2017-03-02T09:01:01.9170000 Output 1938479 application/pdf Accepted Manuscript true 2018-02-07T00:00:00.0000000 false eng
title Polynomial chaos-based extended Padé expansion in structural dynamics
spellingShingle Polynomial chaos-based extended Padé expansion in structural dynamics
Michael Friswell
Sondipon Adhikari
title_short Polynomial chaos-based extended Padé expansion in structural dynamics
title_full Polynomial chaos-based extended Padé expansion in structural dynamics
title_fullStr Polynomial chaos-based extended Padé expansion in structural dynamics
title_full_unstemmed Polynomial chaos-based extended Padé expansion in structural dynamics
title_sort Polynomial chaos-based extended Padé expansion in structural dynamics
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 International Journal for Numerical Methods in Engineering
publishDate 2017
institution Swansea University
issn 0029-5981
doi_str_mv 10.1002/nme.5497
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 The response of a random dynamical system is totally characterized by its probability density function (pdf). However, determining a pdf by a direct approach requires a high numerical cost; similarly, surrogate models such as direct polynomial chaos expansions are not generally efficient, especially around the eigenfrequencies of the dynamical system. In the present study, a new approach based on Padé approximants to obtain moments and pdf of the dynamic response in the frequency domain is proposed. A key difference between the direct polynomial chaos representation and the Padé representation is that the Padé approach has polynomials in both numerator and denominator. For frequency response functions, the denominator plays a vital role as it contains the information related to resonance frequencies, which are uncertain. A Galerkin approach in conjunction with polynomial chaos is proposed for the Padé approximation. Another physics-based approach, utilizing polynomial chaos expansions of the random eigenmodes, is proposed and compared with the proposed Padé approach. It is shown that both methods give accurate results even if a very low degree of the polynomial expansion is used. The methods are demonstrated for two degree-of-freedom system with one and two uncertain parameters.
published_date 2017-12-31T03:39:25Z
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score 11.037056

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