Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity
Autor(a) principal: | |
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Data de Publicação: | 2023 |
Outros Autores: | , , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/978-3-031-04086-3_36 http://hdl.handle.net/11449/245888 |
Resumo: | In this work, we determine the quality of the harmonic balance method (HBM) using a single degree-of-freedom forced Duffing oscillator with free play. HBM results are compared to results obtained using direct time integration with an event location procedure to properly capture contact behavior and identify nonperiodic motions. The comparison facilitates an evaluation of the accuracy of nonlinear, periodic responses computed with HBM, specifically by comparing super- and subharmonic resonances, regions of periodic and nonperiodic (i.e., quasiperiodic or chaotic) responses, and discontinuity-induced bifurcations, such as grazing bifurcations. Convergence analysis of HBM determines the appropriate number of harmonics required to capture nonlinear contact behavior, while satisfying the governing equations. Hill’s method and Floquet theory are used to compute the stability of periodic solutions and identify the types of bifurcations in the system. Extensions to multi- degree-of-freedom oscillators will be discussed as well. |
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Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play NonlinearityBifurcationsConvergence analysisFloquet stabilityHarmonic balancePiecewise-smoothIn this work, we determine the quality of the harmonic balance method (HBM) using a single degree-of-freedom forced Duffing oscillator with free play. HBM results are compared to results obtained using direct time integration with an event location procedure to properly capture contact behavior and identify nonperiodic motions. The comparison facilitates an evaluation of the accuracy of nonlinear, periodic responses computed with HBM, specifically by comparing super- and subharmonic resonances, regions of periodic and nonperiodic (i.e., quasiperiodic or chaotic) responses, and discontinuity-induced bifurcations, such as grazing bifurcations. Convergence analysis of HBM determines the appropriate number of harmonics required to capture nonlinear contact behavior, while satisfying the governing equations. Hill’s method and Floquet theory are used to compute the stability of periodic solutions and identify the types of bifurcations in the system. Extensions to multi- degree-of-freedom oscillators will be discussed as well.Sandia National LaboratoriesMechanical & Aerospace Engineering Department New Mexico State UniversityCampus of São João da Boa Vista São Paulo State UniversitySandia National LaboratoriesCampus of São João da Boa Vista São Paulo State UniversityNew Mexico State UniversityUniversidade Estadual Paulista (UNESP)Sandia National LaboratoriesSaunders, Brian EvanVasconcellos, Rui M. G. [UNESP]Kuether, Robert J.Abdelkefi, Abdessattar2023-07-29T12:25:54Z2023-07-29T12:25:54Z2023-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject249-251http://dx.doi.org/10.1007/978-3-031-04086-3_36Conference Proceedings of the Society for Experimental Mechanics Series, p. 249-251.2191-56522191-5644http://hdl.handle.net/11449/24588810.1007/978-3-031-04086-3_362-s2.0-85135789799Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengConference Proceedings of the Society for Experimental Mechanics Seriesinfo:eu-repo/semantics/openAccess2023-07-29T12:25:54Zoai:repositorio.unesp.br:11449/245888Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T12:25:54Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
title |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
spellingShingle |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity Saunders, Brian Evan Bifurcations Convergence analysis Floquet stability Harmonic balance Piecewise-smooth |
title_short |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
title_full |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
title_fullStr |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
title_full_unstemmed |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
title_sort |
Stability and Convergence Analysis of the Harmonic Balance Method for a Duffing Oscillator with Free Play Nonlinearity |
author |
Saunders, Brian Evan |
author_facet |
Saunders, Brian Evan Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
author_role |
author |
author2 |
Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
New Mexico State University Universidade Estadual Paulista (UNESP) Sandia National Laboratories |
dc.contributor.author.fl_str_mv |
Saunders, Brian Evan Vasconcellos, Rui M. G. [UNESP] Kuether, Robert J. Abdelkefi, Abdessattar |
dc.subject.por.fl_str_mv |
Bifurcations Convergence analysis Floquet stability Harmonic balance Piecewise-smooth |
topic |
Bifurcations Convergence analysis Floquet stability Harmonic balance Piecewise-smooth |
description |
In this work, we determine the quality of the harmonic balance method (HBM) using a single degree-of-freedom forced Duffing oscillator with free play. HBM results are compared to results obtained using direct time integration with an event location procedure to properly capture contact behavior and identify nonperiodic motions. The comparison facilitates an evaluation of the accuracy of nonlinear, periodic responses computed with HBM, specifically by comparing super- and subharmonic resonances, regions of periodic and nonperiodic (i.e., quasiperiodic or chaotic) responses, and discontinuity-induced bifurcations, such as grazing bifurcations. Convergence analysis of HBM determines the appropriate number of harmonics required to capture nonlinear contact behavior, while satisfying the governing equations. Hill’s method and Floquet theory are used to compute the stability of periodic solutions and identify the types of bifurcations in the system. Extensions to multi- degree-of-freedom oscillators will be discussed as well. |
publishDate |
2023 |
dc.date.none.fl_str_mv |
2023-07-29T12:25:54Z 2023-07-29T12:25:54Z 2023-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/978-3-031-04086-3_36 Conference Proceedings of the Society for Experimental Mechanics Series, p. 249-251. 2191-5652 2191-5644 http://hdl.handle.net/11449/245888 10.1007/978-3-031-04086-3_36 2-s2.0-85135789799 |
url |
http://dx.doi.org/10.1007/978-3-031-04086-3_36 http://hdl.handle.net/11449/245888 |
identifier_str_mv |
Conference Proceedings of the Society for Experimental Mechanics Series, p. 249-251. 2191-5652 2191-5644 10.1007/978-3-031-04086-3_36 2-s2.0-85135789799 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Conference Proceedings of the Society for Experimental Mechanics Series |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
249-251 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799964719648342016 |