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Forced Harmonic Vibration of an Asymmetric Duffing Oscillator

Bibliographic Details
Main Author: Kovacic, Ivana
Publication Date: 2011
Other Authors: Brennan, Michael J. [UNESP]
Format: Book part
Language: eng
Source: Repositório Institucional da UNESP
Download full: http://dx.doi.org/10.1002/9780470977859.ch8
http://hdl.handle.net/11449/219947
Summary: Two nonlinear asymmetric systems are described in this chapter. The first is a pure cubic nonlinear oscillator with a constant and a harmonic force acting on it, associated with a vibration isolator. The second is a hanging cable which the asymmetry is caused by gravity. Both of these systems have a single-well potential. The equations of motion can be written in such a way that they include a quadratic and cubic nonlinearity, and only a harmonic forcing term. Different analytical and numerical approaches are used to study and illustrate the rich dynamics of the systems. © 2011 John Wiley & Sons, Ltd. All rights reserved.
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spelling Forced Harmonic Vibration of an Asymmetric Duffing OscillatorAsymmetryChaosHysteresisPeriod-doubling bifurcationSaddle-node bifurcationSingle-well potentialTwo nonlinear asymmetric systems are described in this chapter. The first is a pure cubic nonlinear oscillator with a constant and a harmonic force acting on it, associated with a vibration isolator. The second is a hanging cable which the asymmetry is caused by gravity. Both of these systems have a single-well potential. The equations of motion can be written in such a way that they include a quadratic and cubic nonlinearity, and only a harmonic forcing term. Different analytical and numerical approaches are used to study and illustrate the rich dynamics of the systems. © 2011 John Wiley & Sons, Ltd. All rights reserved.University of Novi Sad Faculty of Technical SciencesUniversity of Southampton Institute of Sound and Vibration ResearchUNESP, Ilha SolteiraUNESP, Ilha SolteiraFaculty of Technical SciencesInstitute of Sound and Vibration ResearchUniversidade Estadual Paulista (UNESP)Kovacic, IvanaBrennan, Michael J. [UNESP]2022-04-28T18:58:35Z2022-04-28T18:58:35Z2011-03-03info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookPart277-322http://dx.doi.org/10.1002/9780470977859.ch8The Duffing Equation: Nonlinear Oscillators and their Behaviour, p. 277-322.http://hdl.handle.net/11449/21994710.1002/9780470977859.ch82-s2.0-84886061506Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengThe Duffing Equation: Nonlinear Oscillators and their Behaviourinfo:eu-repo/semantics/openAccess2025-04-03T15:34:39Zoai:repositorio.unesp.br:11449/219947Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestrepositoriounesp@unesp.bropendoar:29462025-04-03T15:34:39Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
title Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
spellingShingle Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
Kovacic, Ivana
Asymmetry
Chaos
Hysteresis
Period-doubling bifurcation
Saddle-node bifurcation
Single-well potential
title_short Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
title_full Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
title_fullStr Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
title_full_unstemmed Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
title_sort Forced Harmonic Vibration of an Asymmetric Duffing Oscillator
author Kovacic, Ivana
author_facet Kovacic, Ivana
Brennan, Michael J. [UNESP]
author_role author
author2 Brennan, Michael J. [UNESP]
author2_role author
dc.contributor.none.fl_str_mv Faculty of Technical Sciences
Institute of Sound and Vibration Research
Universidade Estadual Paulista (UNESP)
dc.contributor.author.fl_str_mv Kovacic, Ivana
Brennan, Michael J. [UNESP]
dc.subject.por.fl_str_mv Asymmetry
Chaos
Hysteresis
Period-doubling bifurcation
Saddle-node bifurcation
Single-well potential
topic Asymmetry
Chaos
Hysteresis
Period-doubling bifurcation
Saddle-node bifurcation
Single-well potential
description Two nonlinear asymmetric systems are described in this chapter. The first is a pure cubic nonlinear oscillator with a constant and a harmonic force acting on it, associated with a vibration isolator. The second is a hanging cable which the asymmetry is caused by gravity. Both of these systems have a single-well potential. The equations of motion can be written in such a way that they include a quadratic and cubic nonlinearity, and only a harmonic forcing term. Different analytical and numerical approaches are used to study and illustrate the rich dynamics of the systems. © 2011 John Wiley & Sons, Ltd. All rights reserved.
publishDate 2011
dc.date.none.fl_str_mv 2011-03-03
2022-04-28T18:58:35Z
2022-04-28T18:58:35Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/bookPart
format bookPart
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1002/9780470977859.ch8
The Duffing Equation: Nonlinear Oscillators and their Behaviour, p. 277-322.
http://hdl.handle.net/11449/219947
10.1002/9780470977859.ch8
2-s2.0-84886061506
url http://dx.doi.org/10.1002/9780470977859.ch8
http://hdl.handle.net/11449/219947
identifier_str_mv The Duffing Equation: Nonlinear Oscillators and their Behaviour, p. 277-322.
10.1002/9780470977859.ch8
2-s2.0-84886061506
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv The Duffing Equation: Nonlinear Oscillators and their Behaviour
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 277-322
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 repositoriounesp@unesp.br
_version_ 1834482673285857280

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