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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/67610
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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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score |
13.070432 |