Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries

Detalhes bibliográficos
Autor(a) principal: Nunes, Afonso W. [UNESP]
Data de Publicação: 2022
Outros Autores: Silva, Samuel da [UNESP], Ruiz, Adrian
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.jsv.2022.117216
http://hdl.handle.net/11449/245480
Resumo: A Lie symmetry method-based approach is proposed for systematically computing general solutions in closed-form for the mode shape equation of non-uniform and unconventional vibrating rods. The mode shape equation is modeled by the elementary rod theory, addressing polynomial, exponential, trigonometric, and hyperbolic cross-section variations. The method provides algorithmic order-reduction steps for solving the investigated mode shape equation, producing a first-order Riccati equation whose integration reveals the aimed solutions for the problem. Illustrative examples are presented, including original solutions in closed-form as well as solutions previously obtained in the literature by other approaches. Mode shapes from general solutions with appropriate rod boundary conditions are also considered for different examples.
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spelling Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetriesGeneral solutionsNon-uniform rodsMode shapesElementary rod theoryLie symmetriesA Lie symmetry method-based approach is proposed for systematically computing general solutions in closed-form for the mode shape equation of non-uniform and unconventional vibrating rods. The mode shape equation is modeled by the elementary rod theory, addressing polynomial, exponential, trigonometric, and hyperbolic cross-section variations. The method provides algorithmic order-reduction steps for solving the investigated mode shape equation, producing a first-order Riccati equation whose integration reveals the aimed solutions for the problem. Illustrative examples are presented, including original solutions in closed-form as well as solutions previously obtained in the literature by other approaches. Mode shapes from general solutions with appropriate rod boundary conditions are also considered for different examples.Conselho Nacional de Desenvolvimento Cient�fico e Tecnol�gico (CNPq)Funda��o de Amparo � Pesquisa do Estado de S�o Paulo (FAPESP)FEDER -Ministerio de Ciencia, Innovacion y Universidades - Agencia Estatal de InvestigacionJunta de AndaluciaSao Paulo State Univ, UNESP, Sch Engn Ilha Solteira, Mech Engn Dept, BR-15385 Ilha Solteira, BrazilUniv Cadiz, Dept Math, Puerto Real 11510, SpainSao Paulo State Univ, UNESP, Sch Engn Ilha Solteira, Mech Engn Dept, BR-15385 Ilha Solteira, BrazilCNPq: 131846/2020-5CNPq: 306526/2019-0CNPq: 404463/2016-9FAPESP: 21/12894-2FAPESP: 16/22473-6FEDER -Ministerio de Ciencia, Innovacion y Universidades - Agencia Estatal de Investigacion: PGC2018-101514-B-I00Junta de Andalucia: FQM-377Elsevier B.V.Universidade Estadual Paulista (UNESP)Univ CadizNunes, Afonso W. [UNESP]Silva, Samuel da [UNESP]Ruiz, Adrian2023-07-29T11:56:15Z2023-07-29T11:56:15Z2022-08-17info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article10http://dx.doi.org/10.1016/j.jsv.2022.117216Journal of Sound and Vibration. London: Academic Press Ltd- Elsevier Science Ltd, v. 538, 10 p., 2022.0022-460Xhttp://hdl.handle.net/11449/24548010.1016/j.jsv.2022.117216WOS:000873990000005Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal Of Sound And Vibrationinfo:eu-repo/semantics/openAccess2023-07-29T11:56:15Zoai:repositorio.unesp.br:11449/245480Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T11:56:15Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
title Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
spellingShingle Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
Nunes, Afonso W. [UNESP]
General solutions
Non-uniform rods
Mode shapes
Elementary rod theory
Lie symmetries
title_short Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
title_full Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
title_fullStr Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
title_full_unstemmed Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
title_sort Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
author Nunes, Afonso W. [UNESP]
author_facet Nunes, Afonso W. [UNESP]
Silva, Samuel da [UNESP]
Ruiz, Adrian
author_role author
author2 Silva, Samuel da [UNESP]
Ruiz, Adrian
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
Univ Cadiz
dc.contributor.author.fl_str_mv Nunes, Afonso W. [UNESP]
Silva, Samuel da [UNESP]
Ruiz, Adrian
dc.subject.por.fl_str_mv General solutions
Non-uniform rods
Mode shapes
Elementary rod theory
Lie symmetries
topic General solutions
Non-uniform rods
Mode shapes
Elementary rod theory
Lie symmetries
description A Lie symmetry method-based approach is proposed for systematically computing general solutions in closed-form for the mode shape equation of non-uniform and unconventional vibrating rods. The mode shape equation is modeled by the elementary rod theory, addressing polynomial, exponential, trigonometric, and hyperbolic cross-section variations. The method provides algorithmic order-reduction steps for solving the investigated mode shape equation, producing a first-order Riccati equation whose integration reveals the aimed solutions for the problem. Illustrative examples are presented, including original solutions in closed-form as well as solutions previously obtained in the literature by other approaches. Mode shapes from general solutions with appropriate rod boundary conditions are also considered for different examples.
publishDate 2022
dc.date.none.fl_str_mv 2022-08-17
2023-07-29T11:56:15Z
2023-07-29T11:56:15Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.jsv.2022.117216
Journal of Sound and Vibration. London: Academic Press Ltd- Elsevier Science Ltd, v. 538, 10 p., 2022.
0022-460X
http://hdl.handle.net/11449/245480
10.1016/j.jsv.2022.117216
WOS:000873990000005
url http://dx.doi.org/10.1016/j.jsv.2022.117216
http://hdl.handle.net/11449/245480
identifier_str_mv Journal of Sound and Vibration. London: Academic Press Ltd- Elsevier Science Ltd, v. 538, 10 p., 2022.
0022-460X
10.1016/j.jsv.2022.117216
WOS:000873990000005
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Journal Of Sound And Vibration
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 10
dc.publisher.none.fl_str_mv Elsevier B.V.
publisher.none.fl_str_mv Elsevier B.V.
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
_version_ 1799965073406427136

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