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

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dc.contributor.authorNunes, Afonso W. [UNESP]
dc.contributor.authorSilva, Samuel da [UNESP]
dc.contributor.authorRuiz, Adrian
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.contributor.institutionUniv Cadiz
dc.date.accessioned2023-07-29T11:56:15Z
dc.date.available2023-07-29T11:56:15Z
dc.date.issued2022-08-17
dc.description.abstractA 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.en
dc.description.affiliationSao Paulo State Univ, UNESP, Sch Engn Ilha Solteira, Mech Engn Dept, BR-15385 Ilha Solteira, Brazil
dc.description.affiliationUniv Cadiz, Dept Math, Puerto Real 11510, Spain
dc.description.affiliationUnespSao Paulo State Univ, UNESP, Sch Engn Ilha Solteira, Mech Engn Dept, BR-15385 Ilha Solteira, Brazil
dc.description.sponsorshipConselho Nacional de Desenvolvimento Cient�fico e Tecnol�gico (CNPq)
dc.description.sponsorshipFunda��o de Amparo � Pesquisa do Estado de S�o Paulo (FAPESP)
dc.description.sponsorshipFEDER -Ministerio de Ciencia, Innovacion y Universidades - Agencia Estatal de Investigacion
dc.description.sponsorshipJunta de Andalucia
dc.description.sponsorshipIdCNPq: 131846/2020-5
dc.description.sponsorshipIdCNPq: 306526/2019-0
dc.description.sponsorshipIdCNPq: 404463/2016-9
dc.description.sponsorshipIdFAPESP: 21/12894-2
dc.description.sponsorshipIdFAPESP: 16/22473-6
dc.description.sponsorshipIdFEDER -Ministerio de Ciencia, Innovacion y Universidades - Agencia Estatal de Investigacion: PGC2018-101514-B-I00
dc.description.sponsorshipIdJunta de Andalucia: FQM-377
dc.format.extent10
dc.identifierhttp://dx.doi.org/10.1016/j.jsv.2022.117216
dc.identifier.citationJournal of Sound and Vibration. London: Academic Press Ltd- Elsevier Science Ltd, v. 538, 10 p., 2022.
dc.identifier.doi10.1016/j.jsv.2022.117216
dc.identifier.issn0022-460X
dc.identifier.urihttp://hdl.handle.net/11449/245480
dc.identifier.wosWOS:000873990000005
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofJournal Of Sound And Vibration
dc.sourceWeb of Science
dc.subjectGeneral solutions
dc.subjectNon-uniform rods
dc.subjectMode shapes
dc.subjectElementary rod theory
dc.subjectLie symmetries
dc.titleExact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetriesen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.orcid0000-0001-6430-3746[2]
unesp.departmentEngenharia Mecânica - FEISpt

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Ilha Solteira - FEIS - Faculdade de Engenharia