A finite extensibility nonlinear oscillator

Autores
Febbo, Mariano
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The dynamics of a finite extensibility nonlinear oscillator (FENO) is studied analytically by means of two different approaches: a generalized decomposition method (GDM) and a linearized harmonic balance procedure (LHB). From both approaches, analytical approximations to the frequency of oscillation and periodic solutions are obtained, which are valid for a large range of amplitudes of oscillation. Within the generalized decomposition method, two different versions are presented, which provide different kinds of approximate analytical solutions. In the first version, it is shown that the truncation of the perturbation solution up to the third order provides a remarkable degree of accuracy for almost the whole range of amplitudes. The second version, which expands the nonlinear term in Taylor's series around the equilibrium point, exhibits a little lower degree of accuracy, but it supplies an infinite series as the approximate solution. On the other hand, a linearized harmonic balance method is also employed, and the comparison between the approximate period and the exact one (numerically calculated) is slightly better than that obtained by both versions of the GDM. In general, the agreement between the results obtained by the three methods and the exact solution (numerically integrated) for amplitudes (A) between 0 < A ≤ 0.9 is very good both for the period and the amplitude of oscillation. For the rest of the amplitude range (0.9 < A < 1), an exponentially large L2 error demonstrates that all three approximations do not represent a good description for the FENO, and higher order perturbation solutions are needed instead. As a complement, very accurate asymptotic representations of the period are provided for the whole range of amplitudes of oscillation. © 2011 Elsevier Inc. All rights reserved.
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. Universidad Nacional del Sur. Departamento de Física; Argentina
Materia
Finite Extensibility
Nonlinear Oscillator
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:11336/67610

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spelling A finite extensibility nonlinear oscillatorFebbo, MarianoFinite ExtensibilityNonlinear Oscillatorhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The dynamics of a finite extensibility nonlinear oscillator (FENO) is studied analytically by means of two different approaches: a generalized decomposition method (GDM) and a linearized harmonic balance procedure (LHB). From both approaches, analytical approximations to the frequency of oscillation and periodic solutions are obtained, which are valid for a large range of amplitudes of oscillation. Within the generalized decomposition method, two different versions are presented, which provide different kinds of approximate analytical solutions. In the first version, it is shown that the truncation of the perturbation solution up to the third order provides a remarkable degree of accuracy for almost the whole range of amplitudes. The second version, which expands the nonlinear term in Taylor's series around the equilibrium point, exhibits a little lower degree of accuracy, but it supplies an infinite series as the approximate solution. On the other hand, a linearized harmonic balance method is also employed, and the comparison between the approximate period and the exact one (numerically calculated) is slightly better than that obtained by both versions of the GDM. In general, the agreement between the results obtained by the three methods and the exact solution (numerically integrated) for amplitudes (A) between 0 < A ≤ 0.9 is very good both for the period and the amplitude of oscillation. For the rest of the amplitude range (0.9 < A < 1), an exponentially large L2 error demonstrates that all three approximations do not represent a good description for the FENO, and higher order perturbation solutions are needed instead. As a complement, very accurate asymptotic representations of the period are provided for the whole range of amplitudes of oscillation. © 2011 Elsevier Inc. All rights reserved.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. Universidad Nacional del Sur. Departamento de Física; ArgentinaElsevier Science Inc2011-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/67610Febbo, Mariano; A finite extensibility nonlinear oscillator; Elsevier Science Inc; Applied Mathematics and Computation; 217; 14; 3-2011; 6464-64750096-3003CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2011.01.011info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0096300311000257info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:24:47Zoai:ri.conicet.gov.ar:11336/67610instacron: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 10:24:47.341CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A finite extensibility nonlinear oscillator
title A finite extensibility nonlinear oscillator
spellingShingle A finite extensibility nonlinear oscillator
Febbo, Mariano
Finite Extensibility
Nonlinear Oscillator
title_short A finite extensibility nonlinear oscillator
title_full A finite extensibility nonlinear oscillator
title_fullStr A finite extensibility nonlinear oscillator
title_full_unstemmed A finite extensibility nonlinear oscillator
title_sort A finite extensibility nonlinear oscillator
dc.creator.none.fl_str_mv Febbo, Mariano
author Febbo, Mariano
author_facet Febbo, Mariano
author_role author
dc.subject.none.fl_str_mv Finite Extensibility
Nonlinear Oscillator
topic Finite Extensibility
Nonlinear Oscillator
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The dynamics of a finite extensibility nonlinear oscillator (FENO) is studied analytically by means of two different approaches: a generalized decomposition method (GDM) and a linearized harmonic balance procedure (LHB). From both approaches, analytical approximations to the frequency of oscillation and periodic solutions are obtained, which are valid for a large range of amplitudes of oscillation. Within the generalized decomposition method, two different versions are presented, which provide different kinds of approximate analytical solutions. In the first version, it is shown that the truncation of the perturbation solution up to the third order provides a remarkable degree of accuracy for almost the whole range of amplitudes. The second version, which expands the nonlinear term in Taylor's series around the equilibrium point, exhibits a little lower degree of accuracy, but it supplies an infinite series as the approximate solution. On the other hand, a linearized harmonic balance method is also employed, and the comparison between the approximate period and the exact one (numerically calculated) is slightly better than that obtained by both versions of the GDM. In general, the agreement between the results obtained by the three methods and the exact solution (numerically integrated) for amplitudes (A) between 0 < A ≤ 0.9 is very good both for the period and the amplitude of oscillation. For the rest of the amplitude range (0.9 < A < 1), an exponentially large L2 error demonstrates that all three approximations do not represent a good description for the FENO, and higher order perturbation solutions are needed instead. As a complement, very accurate asymptotic representations of the period are provided for the whole range of amplitudes of oscillation. © 2011 Elsevier Inc. All rights reserved.
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. Universidad Nacional del Sur. Departamento de Física; Argentina
description The dynamics of a finite extensibility nonlinear oscillator (FENO) is studied analytically by means of two different approaches: a generalized decomposition method (GDM) and a linearized harmonic balance procedure (LHB). From both approaches, analytical approximations to the frequency of oscillation and periodic solutions are obtained, which are valid for a large range of amplitudes of oscillation. Within the generalized decomposition method, two different versions are presented, which provide different kinds of approximate analytical solutions. In the first version, it is shown that the truncation of the perturbation solution up to the third order provides a remarkable degree of accuracy for almost the whole range of amplitudes. The second version, which expands the nonlinear term in Taylor's series around the equilibrium point, exhibits a little lower degree of accuracy, but it supplies an infinite series as the approximate solution. On the other hand, a linearized harmonic balance method is also employed, and the comparison between the approximate period and the exact one (numerically calculated) is slightly better than that obtained by both versions of the GDM. In general, the agreement between the results obtained by the three methods and the exact solution (numerically integrated) for amplitudes (A) between 0 < A ≤ 0.9 is very good both for the period and the amplitude of oscillation. For the rest of the amplitude range (0.9 < A < 1), an exponentially large L2 error demonstrates that all three approximations do not represent a good description for the FENO, and higher order perturbation solutions are needed instead. As a complement, very accurate asymptotic representations of the period are provided for the whole range of amplitudes of oscillation. © 2011 Elsevier Inc. All rights reserved.
publishDate 2011
dc.date.none.fl_str_mv 2011-03
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/11336/67610
Febbo, Mariano; A finite extensibility nonlinear oscillator; Elsevier Science Inc; Applied Mathematics and Computation; 217; 14; 3-2011; 6464-6475
0096-3003
CONICET Digital
CONICET
url http://hdl.handle.net/11336/67610
identifier_str_mv Febbo, Mariano; A finite extensibility nonlinear oscillator; Elsevier Science Inc; Applied Mathematics and Computation; 217; 14; 3-2011; 6464-6475
0096-3003
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.amc.2011.01.011
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0096300311000257
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
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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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