No Cover Image

Journal article 739 views

Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis

Karin Mora, Alan R. Champneys, Alexander Shaw Orcid Logo, Michael Friswell

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume: 476, Issue: 2237, Start page: 20190549

Swansea University Authors: Alexander Shaw Orcid Logo, Michael Friswell

Full text not available from this repository: check for access using links below.

Check full text

DOI (Published version): 10.1098/rspa.2019.0549

Abstract

The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce...

Full description

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
ISSN: 1364-5021 1471-2946
Published: The Royal Society 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa54468
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2020-06-15T13:09:33Z
last_indexed 2020-11-07T04:13:00Z
id cronfa54468
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2020-11-06T14:34:15.0092074</datestamp><bib-version>v2</bib-version><id>54468</id><entry>2020-06-15</entry><title>Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis</title><swanseaauthors><author><sid>10cb5f545bc146fba9a542a1d85f2dea</sid><ORCID>0000-0002-7521-827X</ORCID><firstname>Alexander</firstname><surname>Shaw</surname><name>Alexander Shaw</name><active>true</active><ethesisStudent>false</ethesisStudent></author><author><sid>5894777b8f9c6e64bde3568d68078d40</sid><firstname>Michael</firstname><surname>Friswell</surname><name>Michael Friswell</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2020-06-15</date><deptcode>AERO</deptcode><abstract>The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed &#x3A9; of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed &#x3A9;p:q. The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and &#x3A9;&#x2009;=&#x2009;&#x3A9;p:q. An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping &#x3B6;, stable bouncing motion bifurcates in the direction of increasing &#x3A9; speed in a smooth fold bifurcation point that is at rotor speed O(&#x3B6;) beyond &#x3A9;p:q. The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.</abstract><type>Journal Article</type><journal>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</journal><volume>476</volume><journalNumber>2237</journalNumber><paginationStart>20190549</paginationStart><paginationEnd/><publisher>The Royal Society</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>1364-5021</issnPrint><issnElectronic>1471-2946</issnElectronic><keywords>rotordynamics, resonance, bouncing, grazing, bifurcation</keywords><publishedDay>27</publishedDay><publishedMonth>5</publishedMonth><publishedYear>2020</publishedYear><publishedDate>2020-05-27</publishedDate><doi>10.1098/rspa.2019.0549</doi><url/><notes/><college>COLLEGE NANME</college><department>Aerospace Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>AERO</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2020-11-06T14:34:15.0092074</lastEdited><Created>2020-06-15T09:50:45.8249971</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Uncategorised</level></path><authors><author><firstname>Karin</firstname><surname>Mora</surname><order>1</order></author><author><firstname>Alan R.</firstname><surname>Champneys</surname><order>2</order></author><author><firstname>Alexander</firstname><surname>Shaw</surname><orcid>0000-0002-7521-827X</orcid><order>3</order></author><author><firstname>Michael</firstname><surname>Friswell</surname><order>4</order></author></authors><documents/><OutputDurs/></rfc1807>
spelling 2020-11-06T14:34:15.0092074 v2 54468 2020-06-15 Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis 10cb5f545bc146fba9a542a1d85f2dea 0000-0002-7521-827X Alexander Shaw Alexander Shaw true false 5894777b8f9c6e64bde3568d68078d40 Michael Friswell Michael Friswell true false 2020-06-15 AERO The dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ωp:q. The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ωp:q. An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ, stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O(ζ) beyond Ωp:q. The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings. Journal Article Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476 2237 20190549 The Royal Society 1364-5021 1471-2946 rotordynamics, resonance, bouncing, grazing, bifurcation 27 5 2020 2020-05-27 10.1098/rspa.2019.0549 COLLEGE NANME Aerospace Engineering COLLEGE CODE AERO Swansea University 2020-11-06T14:34:15.0092074 2020-06-15T09:50:45.8249971 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Karin Mora 1 Alan R. Champneys 2 Alexander Shaw 0000-0002-7521-827X 3 Michael Friswell 4
title Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
spellingShingle Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
Alexander Shaw
Michael Friswell
title_short Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_full Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_fullStr Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_full_unstemmed Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
title_sort Explanation of the onset of bouncing cycles in isotropic rotor dynamics; a grazing bifurcation analysis
author_id_str_mv 10cb5f545bc146fba9a542a1d85f2dea
5894777b8f9c6e64bde3568d68078d40
author_id_fullname_str_mv 10cb5f545bc146fba9a542a1d85f2dea_***_Alexander Shaw
5894777b8f9c6e64bde3568d68078d40_***_Michael Friswell
author Alexander Shaw
Michael Friswell
author2 Karin Mora
Alan R. Champneys
Alexander Shaw
Michael Friswell
format Journal article
container_title Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
container_volume 476
container_issue 2237
container_start_page 20190549
publishDate 2020
institution Swansea University
issn 1364-5021
1471-2946
doi_str_mv 10.1098/rspa.2019.0549
publisher The Royal Society
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 dynamics associated with bouncing-type partial contact cycles are considered for a 2 degree-of-freedom unbalanced rotor in the rigid-stator limit. Specifically, analytical explanation is provided for a previously proposed criterion for the onset upon increasing the rotor speed Ω of single-bounce-per-period periodic motion, namely internal resonance between forward and backward whirling modes. Focusing on the cases of 2 : 1 and 3 : 2 resonances, detailed numerical results for small rotor damping reveal that stable bouncing periodic orbits, which coexist with non-contacting motion, arise just beyond the resonance speed Ωp:q. The theory of discontinuity maps is used to analyse the problem as a codimension-two degenerate grazing bifurcation in the limit of zero rotor damping and Ω = Ωp:q. An analytic unfolding of the map explains all the features of the bouncing orbits locally. In particular, for non-zero damping ζ, stable bouncing motion bifurcates in the direction of increasing Ω speed in a smooth fold bifurcation point that is at rotor speed O(ζ) beyond Ωp:q. The results provide the first analytic explanation of partial-contact bouncing orbits and has implications for prediction and avoidance of unwanted machine vibrations in a number of different industrial settings.
published_date 2020-05-27T04:08:01Z
_version_ 1763753571289923584
score 11.016235

Similar Items