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

dc.contributor.authorNunes, Afonso Willian [UNESP]
dc.contributor.authorSilva, Samuel da [UNESP]
dc.contributor.authorRuiz, Adrián
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2023-02-02T13:01:29Z
dc.date.available2023-02-02T13:01:29Z
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.affiliationUniversidade Estadual Paulista (UNESP)
dc.description.affiliationUniversidad de Cádiz
dc.description.sponsorshipOutra
dc.description.sponsorshipId131846/2020-5
dc.description.sponsorshipId306526/2019-0
dc.description.sponsorshipId404463/2016-9
dc.description.sponsorshipId21/12894-2
dc.description.sponsorshipId16/22473-6
dc.description.sponsorshipIdPGC2018-101514-B-I00
dc.description.versionPreprintpt
dc.identifier.doi10.1016/j.jsv.2022.117216
dc.identifier.issn0022-460X
dc.identifier.lattes4294762593811986
dc.identifier.lattes6807553800607803
dc.identifier.orcid0000-0002-5220-983X
dc.identifier.orcid0000-0001-6430-3746
dc.identifier.urihttp://hdl.handle.net/11449/239255
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Sound and Vibrationen
dc.rights.accessRightsAcesso restrito
dc.subjectGeneral solutionsen
dc.subjectNon-uniform rodsen
dc.subjectMode shapesen
dc.subjectElementary rod theoryen
dc.subjectLie symmetriesen
dc.titleExact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetriesen
dc.typeArtigo
unesp.campusUniversidade Estadual Paulista (Unesp), Faculdade de Engenharia, Ilha Solteirapt

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