Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators

Autores
Arroyo, Sebastián Ismael; Zanette, Damian Horacio
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled-contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators-and, in particular, micromechanical oscillators-provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phaseshift control oscillations are stable over the whole resonance curve, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higherharmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices.
Fil: Arroyo, Sebastián Ismael. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; Argentina
Fil: Zanette, Damian Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
Materia
NONLINEAR OSCILLATORS
INTERNAL RESONANCE
DYNAMICAL SYSTEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/106664
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/106664
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillatorsArroyo, Sebastián IsmaelZanette, Damian HoracioNONLINEAR OSCILLATORSINTERNAL RESONANCEDYNAMICAL SYSTEMShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled-contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators-and, in particular, micromechanical oscillators-provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phaseshift control oscillations are stable over the whole resonance curve, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higherharmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices.Fil: Arroyo, Sebastián Ismael. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Zanette, Damian Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; ArgentinaSpringer2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106664Arroyo, Sebastián Ismael; Zanette, Damian Horacio; Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators; Springer; European Physical Journal B - Condensed Matter; 89; 12; 1-2016; 1-81434-6028CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1140/epjb/e2015-60517-3info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1140/epjb/e2015-60517-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:30Zoai:ri.conicet.gov.ar:11336/106664instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:54:30.423CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
title Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
spellingShingle Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
Arroyo, Sebastián Ismael
NONLINEAR OSCILLATORS
INTERNAL RESONANCE
DYNAMICAL SYSTEMS
title_short Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
title_full Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
title_fullStr Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
title_full_unstemmed Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
title_sort Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators
dc.creator.none.fl_str_mv Arroyo, Sebastián Ismael
Zanette, Damian Horacio
author Arroyo, Sebastián Ismael
author_facet Arroyo, Sebastián Ismael
Zanette, Damian Horacio
author_role author
author2 Zanette, Damian Horacio
author2_role author
dc.subject.none.fl_str_mv NONLINEAR OSCILLATORS
INTERNAL RESONANCE
DYNAMICAL SYSTEMS
topic NONLINEAR OSCILLATORS
INTERNAL RESONANCE
DYNAMICAL SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled-contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators-and, in particular, micromechanical oscillators-provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phaseshift control oscillations are stable over the whole resonance curve, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higherharmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices.
Fil: Arroyo, Sebastián Ismael. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; Argentina
Fil: Zanette, Damian Horacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina
description We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First, we study the stability of periodic motion when the phase shift between the external force and the oscillation is controlled-contrary to the standard case, where the control parameter is the frequency of the force. Phase-shift control is the operational configuration under which self-sustained oscillators-and, in particular, micromechanical oscillators-provide a frequency reference useful for time keeping. We show that, contrary to the standard forced Duffing oscillator, under phaseshift control oscillations are stable over the whole resonance curve, and provide analytical approximate expressions for the time dependence of the oscillation amplitude and frequency during transients. Second, we analyze a model for the internal resonance between the main Duffing oscillation mode and a higherharmonic mode of a vibrating solid bar clamped at its two ends. We focus on the stabilization of the oscillation frequency when the resonance takes place, and present preliminary experimental results that illustrate the phenomenon. This synchronization process has been proposed to counteract the undesirable frequency-amplitude interdependence in nonlinear time-keeping micromechanical devices.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/106664
Arroyo, Sebastián Ismael; Zanette, Damian Horacio; Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators; Springer; European Physical Journal B - Condensed Matter; 89; 12; 1-2016; 1-8
1434-6028
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106664
identifier_str_mv Arroyo, Sebastián Ismael; Zanette, Damian Horacio; Duffing revisited: Phase-shift control and internal resonance in self-sustained oscillators; Springer; European Physical Journal B - Condensed Matter; 89; 12; 1-2016; 1-8
1434-6028
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1140/epjb/e2015-60517-3
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1140/epjb/e2015-60517-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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