On the critical forcing amplitude of forced nonlinear oscillators

Autores
Febbo, Mariano; Ji, Jinchen C.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.
Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ji, Jinchen C.. University of Technology; Australia
Materia
CRITICAL FORCING AMPLITUDE
FORCED NONLINEAR SYSTEMS
FREQUENCY-RESPONSE CURVE
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/26377
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/26377
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On the critical forcing amplitude of forced nonlinear oscillatorsFebbo, MarianoJi, Jinchen C.CRITICAL FORCING AMPLITUDEFORCED NONLINEAR SYSTEMSFREQUENCY-RESPONSE CURVEhttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; ArgentinaFil: Ji, Jinchen C.. University of Technology; AustraliaDe Gruyter2013-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/26377Febbo, Mariano; Ji, Jinchen C.; On the critical forcing amplitude of forced nonlinear oscillators; De Gruyter; Central European Journal of Engineering; 3; 4; 12-2013; 764-7701896-15412081-9927enginfo:eu-repo/semantics/altIdentifier/doi/10.2478/s13531-013-0117-6info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/eng.2013.3.issue-4/s13531-013-0117-6/s13531-013-0117-6.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:43:55Zoai:ri.conicet.gov.ar:11336/26377instacron: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 10:43:55.674CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the critical forcing amplitude of forced nonlinear oscillators
title On the critical forcing amplitude of forced nonlinear oscillators
spellingShingle On the critical forcing amplitude of forced nonlinear oscillators
Febbo, Mariano
CRITICAL FORCING AMPLITUDE
FORCED NONLINEAR SYSTEMS
FREQUENCY-RESPONSE CURVE
title_short On the critical forcing amplitude of forced nonlinear oscillators
title_full On the critical forcing amplitude of forced nonlinear oscillators
title_fullStr On the critical forcing amplitude of forced nonlinear oscillators
title_full_unstemmed On the critical forcing amplitude of forced nonlinear oscillators
title_sort On the critical forcing amplitude of forced nonlinear oscillators
dc.creator.none.fl_str_mv Febbo, Mariano
Ji, Jinchen C.
author Febbo, Mariano
author_facet Febbo, Mariano
Ji, Jinchen C.
author_role author
author2 Ji, Jinchen C.
author2_role author
dc.subject.none.fl_str_mv CRITICAL FORCING AMPLITUDE
FORCED NONLINEAR SYSTEMS
FREQUENCY-RESPONSE CURVE
topic CRITICAL FORCING AMPLITUDE
FORCED NONLINEAR SYSTEMS
FREQUENCY-RESPONSE CURVE
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.3
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.
Fil: Febbo, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Física del Sur. Universidad Nacional del Sur. Departamento de Física. Instituto de Física del Sur; Argentina
Fil: Ji, Jinchen C.. University of Technology; Australia
description The steady-state response of forced single degree-of-freedom weakly nonlinear oscillators under primary resonance conditions can exhibit saddle-node bifurcations, jump and hysteresis phenomena, if the amplitude of the excitation exceeds a certain value. This critical value of excitation amplitude or critical forcing amplitude plays an important role in determining the occurrence of saddle-node bifurcations in the frequency-response curve. This work develops an alternative method to determine the critical forcing amplitude for single degree-of-freedom nonlinear oscillators. Based on Lagrange multipliers approach, the proposed method considers the calculation of the critical forcing amplitude as an optimization problem with constraints that are imposed by the existence of locations of vertical tangency. In comparison with the Gröbner basis method, the proposed approach is more straightforward and thus easy to apply for finding the critical forcing amplitude both analytically and numerically. Three examples are given to confirm the validity of the theoretical predictions. The first two present the analytical form for the critical forcing amplitude and the third one is an example of a numerically computed solution.
publishDate 2013
dc.date.none.fl_str_mv 2013-12
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/11336/26377
Febbo, Mariano; Ji, Jinchen C.; On the critical forcing amplitude of forced nonlinear oscillators; De Gruyter; Central European Journal of Engineering; 3; 4; 12-2013; 764-770
1896-1541
2081-9927
url http://hdl.handle.net/11336/26377
identifier_str_mv Febbo, Mariano; Ji, Jinchen C.; On the critical forcing amplitude of forced nonlinear oscillators; De Gruyter; Central European Journal of Engineering; 3; 4; 12-2013; 764-770
1896-1541
2081-9927
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.2478/s13531-013-0117-6
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/eng.2013.3.issue-4/s13531-013-0117-6/s13531-013-0117-6.xml
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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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