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Continuation analysis of a nonlinear rotor system

Mehmet Selim Akay, Alexander Shaw Orcid Logo, Michael Friswell

Nonlinear Dynamics, Volume: 105, Issue: 1, Pages: 25 - 43

Swansea University Authors: Alexander Shaw Orcid Logo, Michael Friswell

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DOI (Published version): 10.1007/s11071-021-06589-8

Abstract

Nonlinearities in rotating systems have been seen to cause a wide variety of rich phenomena; however, the understanding of these phenomena has been limited because numerical approaches typically rely on “brute force” time simulation, which is slow due to issues of step size and settling time, cannot...

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Published in: Nonlinear Dynamics
ISSN: 0924-090X 1573-269X
Published: Springer Science and Business Media LLC 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57260
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first_indexed 2021-07-02T09:10:45Z
last_indexed 2021-12-03T04:17:19Z
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spelling 2021-12-02T11:21:38.5548601 v2 57260 2021-07-02 Continuation analysis of a nonlinear rotor system 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2021-07-02 AERO Nonlinearities in rotating systems have been seen to cause a wide variety of rich phenomena; however, the understanding of these phenomena has been limited because numerical approaches typically rely on “brute force” time simulation, which is slow due to issues of step size and settling time, cannot locate unstable solution families, and may miss key responses if the correct initial conditions are not used. This work uses numerical continuation to explore the responses of such systems in a more systematic way. A simple isotropic rotor system with a smooth nonlinearity is studied, and the rotating frame is used to obtain periodic solutions. Asynchronous responses with oscillating amplitude are seen to initiate at certain drive speeds due to internal resonance, in a manner similar to that observed for nonsmooth rotor–stator contact systems in the previous literature. These responses are isolated, in the sense that they will only meet the more trivial synchronous responses in the limit of zero damping and out of balance forcing. In addition to increasing our understanding of the responses of these systems, the work establishes the potential of numerical continuation as a tool to systematically explore the responses of nonlinear rotor systems. Journal Article Nonlinear Dynamics 105 1 25 43 Springer Science and Business Media LLC 0924-090X 1573-269X Rotordynamics; Bifurcation; Continuation; Internal resonance; Nonlinearity 1 7 2021 2021-07-01 10.1007/s11071-021-06589-8 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2021-12-02T11:21:38.5548601 2021-07-02T10:08:37.1734203 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Mehmet Selim Akay 1 Alexander Shaw 0000-0002-7521-827X 2 Michael Friswell 3 57260__20539__1cbe7fb695e14926aa24a8b14d15d4a1.pdf 57260.pdf 2021-08-04T14:43:45.7153488 Output 2329224 application/pdf Version of Record true © The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License true eng http://creativecommons.org/licenses/by/4.0/
title Continuation analysis of a nonlinear rotor system
spellingShingle Continuation analysis of a nonlinear rotor system
Alexander Shaw
Michael Friswell
title_short Continuation analysis of a nonlinear rotor system
title_full Continuation analysis of a nonlinear rotor system
title_fullStr Continuation analysis of a nonlinear rotor system
title_full_unstemmed Continuation analysis of a nonlinear rotor system
title_sort Continuation analysis of a nonlinear rotor system
author_id_str_mv 10cb5f545bc146fba9a542a1d85f2dea
5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Alexander Shaw
Michael Friswell
author2 Mehmet Selim Akay
Alexander Shaw
Michael Friswell
format Journal article
container_title Nonlinear Dynamics
container_volume 105
container_issue 1
container_start_page 25
publishDate 2021
institution Swansea University
issn 0924-090X
1573-269X
doi_str_mv 10.1007/s11071-021-06589-8
publisher Springer Science and Business Media LLC
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 Nonlinearities in rotating systems have been seen to cause a wide variety of rich phenomena; however, the understanding of these phenomena has been limited because numerical approaches typically rely on “brute force” time simulation, which is slow due to issues of step size and settling time, cannot locate unstable solution families, and may miss key responses if the correct initial conditions are not used. This work uses numerical continuation to explore the responses of such systems in a more systematic way. A simple isotropic rotor system with a smooth nonlinearity is studied, and the rotating frame is used to obtain periodic solutions. Asynchronous responses with oscillating amplitude are seen to initiate at certain drive speeds due to internal resonance, in a manner similar to that observed for nonsmooth rotor–stator contact systems in the previous literature. These responses are isolated, in the sense that they will only meet the more trivial synchronous responses in the limit of zero damping and out of balance forcing. In addition to increasing our understanding of the responses of these systems, the work establishes the potential of numerical continuation as a tool to systematically explore the responses of nonlinear rotor systems.
published_date 2021-07-01T04:12:52Z
_version_ 1763753876021837824
score 11.037603

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