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Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems

E. Jacquelin, Sondipon Adhikari, J.-J. Sinou, Michael Friswell

Journal of Engineering Mechanics, Volume: 141, Issue: 4

Swansea University Authors: Sondipon Adhikari, Michael Friswell

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DOI (Published version): 10.1061/(ASCE)EM.1943-7889.0000856

Abstract

The first two moments of the steady-state response of a dynamical random system are determined through a polynomial chaos expansion (PCE) and a Monte Carlo simulation that gives the reference solution. It is observed that the PCE may not be suitable to describe the steady-state response of a random...

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Published in: Journal of Engineering Mechanics
ISSN: 0733-9399 1943-7889
Published: 2015
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URI: https://cronfa.swan.ac.uk/Record/cronfa20474
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spelling 2021-01-14T13:12:56.5349228 v2 20474 2015-03-17 Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems 4ea84d67c4e414f5ccbd7593a40f04d3 Sondipon Adhikari Sondipon Adhikari true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2015-03-17 FGSEN The first two moments of the steady-state response of a dynamical random system are determined through a polynomial chaos expansion (PCE) and a Monte Carlo simulation that gives the reference solution. It is observed that the PCE may not be suitable to describe the steady-state response of a random system harmonically excited at a frequency close to a deterministic eigenfrequency: many peaks appear around the deterministic eigenfrequencies. It is proved that the PCE coefficients are the responses of a deterministic dynamical system—the so-called PC system. As a consequence, these coefficients are subjected to resonances associated to the eigenfrequencies of the PC system: the spurious resonances are located around the deterministic eigenfrequencies of the actual system. It is shown that the polynomial order required to obtain some good results may be very high, especially when the damping is low. These results are shown on a multidegree-of-freedom (DOF) system with a random stiffness matrix. A 1-DOF system is also studied, and new analytical expressions that make the PCE possible even for a high order are derived. The influence of the PC order is also highlighted. The results obtained in the paper improve the understanding and scope of applicability of PCE for some structural dynamical systems when harmonically excited around the deterministic eigenfrequencies. Journal Article Journal of Engineering Mechanics 141 4 0733-9399 1943-7889 30 4 2015 2015-04-30 10.1061/(ASCE)EM.1943-7889.0000856 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2021-01-14T13:12:56.5349228 2015-03-17T09:29:02.6938200 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised E. Jacquelin 1 Sondipon Adhikari 2 J.-J. Sinou 3 Michael Friswell 4
title Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
spellingShingle Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
Sondipon Adhikari
Michael Friswell
title_short Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
title_full Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
title_fullStr Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
title_full_unstemmed Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
title_sort Polynomial Chaos Expansion and Steady-State Response of a Class of Random Dynamical Systems
author_id_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3
5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 4ea84d67c4e414f5ccbd7593a40f04d3_***_Sondipon Adhikari
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Sondipon Adhikari
Michael Friswell
author2 E. Jacquelin
Sondipon Adhikari
J.-J. Sinou
Michael Friswell
format Journal article
container_title Journal of Engineering Mechanics
container_volume 141
container_issue 4
publishDate 2015
institution Swansea University
issn 0733-9399
1943-7889
doi_str_mv 10.1061/(ASCE)EM.1943-7889.0000856
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 0
active_str 0
description The first two moments of the steady-state response of a dynamical random system are determined through a polynomial chaos expansion (PCE) and a Monte Carlo simulation that gives the reference solution. It is observed that the PCE may not be suitable to describe the steady-state response of a random system harmonically excited at a frequency close to a deterministic eigenfrequency: many peaks appear around the deterministic eigenfrequencies. It is proved that the PCE coefficients are the responses of a deterministic dynamical system—the so-called PC system. As a consequence, these coefficients are subjected to resonances associated to the eigenfrequencies of the PC system: the spurious resonances are located around the deterministic eigenfrequencies of the actual system. It is shown that the polynomial order required to obtain some good results may be very high, especially when the damping is low. These results are shown on a multidegree-of-freedom (DOF) system with a random stiffness matrix. A 1-DOF system is also studied, and new analytical expressions that make the PCE possible even for a high order are derived. The influence of the PC order is also highlighted. The results obtained in the paper improve the understanding and scope of applicability of PCE for some structural dynamical systems when harmonically excited around the deterministic eigenfrequencies.
published_date 2015-04-30T03:24:13Z
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score 11.037056

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