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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.authorda Silva, Samuel [UNESP]
dc.contributor.authorRuiz, Adrián
dc.contributor.institutionUniversidade Estadual Paulista (UNESP)
dc.contributor.institutionUniversity of Cádiz
dc.date.accessioned2023-03-01T21:06:59Z
dc.date.available2023-03-01T21:06:59Z
dc.date.issued2022-11-10
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.affiliationMechanical Engineering Department School of Engineering of Ilha Solteira UNESP – São Paulo State University
dc.description.affiliationDepartment of Mathematics University of Cádiz
dc.description.affiliationUnespMechanical Engineering Department School of Engineering of Ilha Solteira UNESP – São Paulo State University
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipJunta de Andalucía
dc.description.sponsorshipAgencia Estatal de Investigación
dc.description.sponsorshipIdCNPq: 131846/2020-5
dc.description.sponsorshipIdFAPESP: 16/22473-6
dc.description.sponsorshipIdFAPESP: 21/12894-2
dc.description.sponsorshipIdCNPq: 306526/2019-0
dc.description.sponsorshipIdCNPq: 404463/2016-9
dc.description.sponsorshipIdJunta de Andalucía: FQM–377
dc.description.sponsorshipIdAgencia Estatal de Investigación: PGC2018-101514-B-I00
dc.identifierhttp://dx.doi.org/10.1016/j.jsv.2022.117216
dc.identifier.citationJournal of Sound and Vibration, v. 538.
dc.identifier.doi10.1016/j.jsv.2022.117216
dc.identifier.issn1095-8568
dc.identifier.issn0022-460X
dc.identifier.scopus2-s2.0-85135878562
dc.identifier.urihttp://hdl.handle.net/11449/241505
dc.language.isoeng
dc.relation.ispartofJournal of Sound and Vibration
dc.sourceScopus
dc.subjectElementary rod theory
dc.subjectGeneral solutions
dc.subjectLie symmetries
dc.subjectMode shapes
dc.subjectNon-uniform rods
dc.titleExact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetriesen
dc.typeArtigo
dspace.entity.typePublication
unesp.author.orcid0000-0002-5220-983X[1]
unesp.author.orcid0000-0002-5417-4773[3]
unesp.departmentEngenharia Mecânica - FEISpt

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Ilha Solteira - FEIS - Faculdade de Engenharia