A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics

Autores
Rosales, Marta Beatriz; Filipich, Carlos Pedro
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
An analytical-numerical methodology for solving nonlinear problems governed by partial differential equations (PDE) is presented. The authors have previously used a method named WEM that consists essentially of the statement of extended trigonometric series of uniform convergence (UC). Theorems, demonstrated previously, ensure the UC of the essential functions and the exactness of the eigenvalues. WEM has been applied to nonlinear dynamic problems in two different ways: As a direct variational method and as a solution in the classical sense. The present tool is applied in the second fashion and starts from the statement of the extended trigonometric series for all the unknown functions and derivatives involved in the PDE. The nonlinearities are treated in the same way. The application of consistence conditions leads to recurrence relationships among the coefficients of the extended series. For the sake of comparison an initial conditions problem (the well-known Duffing oscillator) is numerically solved. Then a beam example is solved in detail: A linear (both material and geometrical) supported beam, with end springs of nonlinear analytical response, under the action of a dynamic distributed load and/or prescribed initial conditions, is studied. Two numerical examples are included.
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
Fil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; Argentina
Materia
NONLINEAR BOUNDARY CONDITIONS
NONLINEAR VIBRATIONS
PARTIAL DIFFERENTIAL EQUATIONS
TRIGONOMETRIC RECURRENCE
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:11336/94814
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/94814
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural DynamicsRosales, Marta BeatrizFilipich, Carlos PedroNONLINEAR BOUNDARY CONDITIONSNONLINEAR VIBRATIONSPARTIAL DIFFERENTIAL EQUATIONSTRIGONOMETRIC RECURRENCEhttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2An analytical-numerical methodology for solving nonlinear problems governed by partial differential equations (PDE) is presented. The authors have previously used a method named WEM that consists essentially of the statement of extended trigonometric series of uniform convergence (UC). Theorems, demonstrated previously, ensure the UC of the essential functions and the exactness of the eigenvalues. WEM has been applied to nonlinear dynamic problems in two different ways: As a direct variational method and as a solution in the classical sense. The present tool is applied in the second fashion and starts from the statement of the extended trigonometric series for all the unknown functions and derivatives involved in the PDE. The nonlinearities are treated in the same way. The application of consistence conditions leads to recurrence relationships among the coefficients of the extended series. For the sake of comparison an initial conditions problem (the well-known Duffing oscillator) is numerically solved. Then a beam example is solved in detail: A linear (both material and geometrical) supported beam, with end springs of nonlinear analytical response, under the action of a dynamic distributed load and/or prescribed initial conditions, is studied. Two numerical examples are included.Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; ArgentinaSage Publications Ltd2006-06-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/94814Rosales, Marta Beatriz; Filipich, Carlos Pedro; A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics; Sage Publications Ltd; Journal Of Vibration And Control; 12; 6; 9-6-2006; 557-5751077-54631741-2986CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.sagepub.com/doi/pdf/10.1177/1077546306063505info:eu-repo/semantics/altIdentifier/doi/10.1177/1077546306063505info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:12:41Zoai:ri.conicet.gov.ar:11336/94814instacron: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:34982025-09-10 13:12:41.853CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
title A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
spellingShingle A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
Rosales, Marta Beatriz
NONLINEAR BOUNDARY CONDITIONS
NONLINEAR VIBRATIONS
PARTIAL DIFFERENTIAL EQUATIONS
TRIGONOMETRIC RECURRENCE
title_short A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
title_full A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
title_fullStr A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
title_full_unstemmed A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
title_sort A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics
dc.creator.none.fl_str_mv Rosales, Marta Beatriz
Filipich, Carlos Pedro
author Rosales, Marta Beatriz
author_facet Rosales, Marta Beatriz
Filipich, Carlos Pedro
author_role author
author2 Filipich, Carlos Pedro
author2_role author
dc.subject.none.fl_str_mv NONLINEAR BOUNDARY CONDITIONS
NONLINEAR VIBRATIONS
PARTIAL DIFFERENTIAL EQUATIONS
TRIGONOMETRIC RECURRENCE
topic NONLINEAR BOUNDARY CONDITIONS
NONLINEAR VIBRATIONS
PARTIAL DIFFERENTIAL EQUATIONS
TRIGONOMETRIC RECURRENCE
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv An analytical-numerical methodology for solving nonlinear problems governed by partial differential equations (PDE) is presented. The authors have previously used a method named WEM that consists essentially of the statement of extended trigonometric series of uniform convergence (UC). Theorems, demonstrated previously, ensure the UC of the essential functions and the exactness of the eigenvalues. WEM has been applied to nonlinear dynamic problems in two different ways: As a direct variational method and as a solution in the classical sense. The present tool is applied in the second fashion and starts from the statement of the extended trigonometric series for all the unknown functions and derivatives involved in the PDE. The nonlinearities are treated in the same way. The application of consistence conditions leads to recurrence relationships among the coefficients of the extended series. For the sake of comparison an initial conditions problem (the well-known Duffing oscillator) is numerically solved. Then a beam example is solved in detail: A linear (both material and geometrical) supported beam, with end springs of nonlinear analytical response, under the action of a dynamic distributed load and/or prescribed initial conditions, is studied. Two numerical examples are included.
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
Fil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; Argentina
description An analytical-numerical methodology for solving nonlinear problems governed by partial differential equations (PDE) is presented. The authors have previously used a method named WEM that consists essentially of the statement of extended trigonometric series of uniform convergence (UC). Theorems, demonstrated previously, ensure the UC of the essential functions and the exactness of the eigenvalues. WEM has been applied to nonlinear dynamic problems in two different ways: As a direct variational method and as a solution in the classical sense. The present tool is applied in the second fashion and starts from the statement of the extended trigonometric series for all the unknown functions and derivatives involved in the PDE. The nonlinearities are treated in the same way. The application of consistence conditions leads to recurrence relationships among the coefficients of the extended series. For the sake of comparison an initial conditions problem (the well-known Duffing oscillator) is numerically solved. Then a beam example is solved in detail: A linear (both material and geometrical) supported beam, with end springs of nonlinear analytical response, under the action of a dynamic distributed load and/or prescribed initial conditions, is studied. Two numerical examples are included.
publishDate 2006
dc.date.none.fl_str_mv 2006-06-09
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/11336/94814
Rosales, Marta Beatriz; Filipich, Carlos Pedro; A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics; Sage Publications Ltd; Journal Of Vibration And Control; 12; 6; 9-6-2006; 557-575
1077-5463
1741-2986
CONICET Digital
CONICET
url http://hdl.handle.net/11336/94814
identifier_str_mv Rosales, Marta Beatriz; Filipich, Carlos Pedro; A Trigonometric Recurrence Algorithm for Solving Nonlinear Problems in Structural Dynamics; Sage Publications Ltd; Journal Of Vibration And Control; 12; 6; 9-6-2006; 557-575
1077-5463
1741-2986
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://journals.sagepub.com/doi/pdf/10.1177/1077546306063505
info:eu-repo/semantics/altIdentifier/doi/10.1177/1077546306063505
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 Sage Publications Ltd
publisher.none.fl_str_mv Sage Publications Ltd
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
_version_ 1842980663909679104
score 12.993085

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