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: da Silva, Samuel [UNESP], Ruiz, Adrián
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/11449/241505
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 symmetriesElementary rod theoryGeneral solutionsLie symmetriesMode shapesNon-uniform rodsA 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 Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Junta de AndalucíaAgencia Estatal de InvestigaciónMechanical Engineering Department School of Engineering of Ilha Solteira UNESP – São Paulo State UniversityDepartment of Mathematics University of CádizMechanical Engineering Department School of Engineering of Ilha Solteira UNESP – São Paulo State UniversityCNPq: 131846/2020-5FAPESP: 16/22473-6FAPESP: 21/12894-2CNPq: 306526/2019-0CNPq: 404463/2016-9Junta de Andalucía: FQM–377Agencia Estatal de Investigación: PGC2018-101514-B-I00Universidade Estadual Paulista (UNESP)University of CádizNunes, Afonso W. [UNESP]da Silva, Samuel [UNESP]Ruiz, Adrián2023-03-01T21:06:59Z2023-03-01T21:06:59Z2022-11-10info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1016/j.jsv.2022.117216Journal of Sound and Vibration, v. 538.1095-85680022-460Xhttp://hdl.handle.net/11449/24150510.1016/j.jsv.2022.1172162-s2.0-85135878562Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengJournal of Sound and Vibrationinfo:eu-repo/semantics/openAccess2023-03-01T21:06:59Zoai:repositorio.unesp.br:11449/241505Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-03-01T21:06:59Repositório 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]
Elementary rod theory
General solutions
Lie symmetries
Mode shapes
Non-uniform rods
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]
da Silva, Samuel [UNESP]
Ruiz, Adrián
author_role author
author2 da Silva, Samuel [UNESP]
Ruiz, Adrián
author2_role author
author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (UNESP)
University of Cádiz
dc.contributor.author.fl_str_mv Nunes, Afonso W. [UNESP]
da Silva, Samuel [UNESP]
Ruiz, Adrián
dc.subject.por.fl_str_mv Elementary rod theory
General solutions
Lie symmetries
Mode shapes
Non-uniform rods
topic Elementary rod theory
General solutions
Lie symmetries
Mode shapes
Non-uniform rods
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 2022-11-10
2023-03-01T21:06:59Z
2023-03-01T21:06:59Z
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, v. 538.
1095-8568
0022-460X
http://hdl.handle.net/11449/241505
10.1016/j.jsv.2022.117216
2-s2.0-85135878562
url http://dx.doi.org/10.1016/j.jsv.2022.117216
http://hdl.handle.net/11449/241505
identifier_str_mv Journal of Sound and Vibration, v. 538.
1095-8568
0022-460X
10.1016/j.jsv.2022.117216
2-s2.0-85135878562
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.source.none.fl_str_mv Scopus
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
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