The shear deformation effect on the nonlinear dynamic of a simple rotor blade

Autores
Machado, Sebastián Pablo; Saravia, César Martín
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The nonlinear planar response of a cantilever rotating slender beam to a principal parametric resonance of its first bending mode is analyzed considering the effect of shear deformation. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of small strains. The beam is subjected to a harmonic transverse load in the presence of internal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady state responses and their stability. Nonlinear normal modes are obtained for the two models, considering and neglecting the effect of shear deformation. The results of the analysis show that the equilibrium solutions are influenced by the transverse shear effect. When this effect is ignored the amplitude of vibration is reduced significantly, thus altering the dynamic response of the beam. This alteration can lead to an incorrect stability prediction of the periodic solutions.
Fil: Machado, Sebastián Pablo. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Saravia, César Martín. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Composite material
thin-walled rotating beam
non-linear dynamic
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:11336/215842
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling The shear deformation effect on the nonlinear dynamic of a simple rotor bladeMachado, Sebastián PabloSaravia, César MartínComposite materialthin-walled rotating beamnon-linear dynamichttps://purl.org/becyt/ford/2.3https://purl.org/becyt/ford/2The nonlinear planar response of a cantilever rotating slender beam to a principal parametric resonance of its first bending mode is analyzed considering the effect of shear deformation. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of small strains. The beam is subjected to a harmonic transverse load in the presence of internal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady state responses and their stability. Nonlinear normal modes are obtained for the two models, considering and neglecting the effect of shear deformation. The results of the analysis show that the equilibrium solutions are influenced by the transverse shear effect. When this effect is ignored the amplitude of vibration is reduced significantly, thus altering the dynamic response of the beam. This alteration can lead to an incorrect stability prediction of the periodic solutions.Fil: Machado, Sebastián Pablo. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Saravia, César Martín. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAsociación Argentina de Mecánica Computacional2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/215842Machado, Sebastián Pablo; Saravia, César Martín; The shear deformation effect on the nonlinear dynamic of a simple rotor blade; Asociación Argentina de Mecánica Computacional; Mecánica Computacional; 31; 11-2012; 2469-2484CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.amcaonline.org.ar/ojs/index.php/mc/article/view/4201/4127info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:49:05Zoai:ri.conicet.gov.ar:11336/215842instacron: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 09:49:05.499CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The shear deformation effect on the nonlinear dynamic of a simple rotor blade
title The shear deformation effect on the nonlinear dynamic of a simple rotor blade
spellingShingle The shear deformation effect on the nonlinear dynamic of a simple rotor blade
Machado, Sebastián Pablo
Composite material
thin-walled rotating beam
non-linear dynamic
title_short The shear deformation effect on the nonlinear dynamic of a simple rotor blade
title_full The shear deformation effect on the nonlinear dynamic of a simple rotor blade
title_fullStr The shear deformation effect on the nonlinear dynamic of a simple rotor blade
title_full_unstemmed The shear deformation effect on the nonlinear dynamic of a simple rotor blade
title_sort The shear deformation effect on the nonlinear dynamic of a simple rotor blade
dc.creator.none.fl_str_mv Machado, Sebastián Pablo
Saravia, César Martín
author Machado, Sebastián Pablo
author_facet Machado, Sebastián Pablo
Saravia, César Martín
author_role author
author2 Saravia, César Martín
author2_role author
dc.subject.none.fl_str_mv Composite material
thin-walled rotating beam
non-linear dynamic
topic Composite material
thin-walled rotating beam
non-linear dynamic
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 nonlinear planar response of a cantilever rotating slender beam to a principal parametric resonance of its first bending mode is analyzed considering the effect of shear deformation. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of small strains. The beam is subjected to a harmonic transverse load in the presence of internal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady state responses and their stability. Nonlinear normal modes are obtained for the two models, considering and neglecting the effect of shear deformation. The results of the analysis show that the equilibrium solutions are influenced by the transverse shear effect. When this effect is ignored the amplitude of vibration is reduced significantly, thus altering the dynamic response of the beam. This alteration can lead to an incorrect stability prediction of the periodic solutions.
Fil: Machado, Sebastián Pablo. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Saravia, César Martín. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca. Grupo de Análisis de Sistemas Mecánicos; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description The nonlinear planar response of a cantilever rotating slender beam to a principal parametric resonance of its first bending mode is analyzed considering the effect of shear deformation. The equation of motion is obtained in the form of an integro-partial differential equation, taking into account mid-plane stretching, a rotation speed and modal damping. A composite linear elastic material is considered and the cross-section properties are assumed to be constant given the assumption of small strains. The beam is subjected to a harmonic transverse load in the presence of internal resonance. The internal resonance can be activated for a range of the beam rotating speed, where the second natural frequency is approximately three times the first natural frequency. The method of multiple scales method is used to derive four-first ordinary differential equations that govern the evolution of the amplitude and phase of the response. These equations are used to determine the steady state responses and their stability. Nonlinear normal modes are obtained for the two models, considering and neglecting the effect of shear deformation. The results of the analysis show that the equilibrium solutions are influenced by the transverse shear effect. When this effect is ignored the amplitude of vibration is reduced significantly, thus altering the dynamic response of the beam. This alteration can lead to an incorrect stability prediction of the periodic solutions.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/215842
Machado, Sebastián Pablo; Saravia, César Martín; The shear deformation effect on the nonlinear dynamic of a simple rotor blade; Asociación Argentina de Mecánica Computacional; Mecánica Computacional; 31; 11-2012; 2469-2484
CONICET Digital
CONICET
url http://hdl.handle.net/11336/215842
identifier_str_mv Machado, Sebastián Pablo; Saravia, César Martín; The shear deformation effect on the nonlinear dynamic of a simple rotor blade; Asociación Argentina de Mecánica Computacional; Mecánica Computacional; 31; 11-2012; 2469-2484
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.amcaonline.org.ar/ojs/index.php/mc/article/view/4201/4127
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 Asociación Argentina de Mecánica Computacional
publisher.none.fl_str_mv Asociación Argentina de Mecánica Computacional
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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