Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
dc.contributor.author | Nunes, Afonso Willian [UNESP] | |
dc.contributor.author | Silva, Samuel da [UNESP] | |
dc.contributor.author | Ruiz, Adrián | |
dc.contributor.institution | Universidade Estadual Paulista (Unesp) | |
dc.date.accessioned | 2023-02-02T13:01:29Z | |
dc.date.available | 2023-02-02T13:01:29Z | |
dc.date.issued | 2022-11-10 | |
dc.description.abstract | 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. | en |
dc.description.affiliation | Universidade Estadual Paulista (UNESP) | |
dc.description.affiliation | Universidad de Cádiz | |
dc.description.sponsorship | Outra | |
dc.description.sponsorshipId | 131846/2020-5 | |
dc.description.sponsorshipId | 306526/2019-0 | |
dc.description.sponsorshipId | 404463/2016-9 | |
dc.description.sponsorshipId | 21/12894-2 | |
dc.description.sponsorshipId | 16/22473-6 | |
dc.description.sponsorshipId | PGC2018-101514-B-I00 | |
dc.description.version | Preprint | pt |
dc.identifier.doi | 10.1016/j.jsv.2022.117216 | |
dc.identifier.issn | 0022-460X | |
dc.identifier.lattes | 4294762593811986 | |
dc.identifier.lattes | 6807553800607803 | |
dc.identifier.orcid | 0000-0002-5220-983X | |
dc.identifier.orcid | 0000-0001-6430-3746 | |
dc.identifier.uri | http://hdl.handle.net/11449/239255 | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.relation.ispartof | Journal of Sound and Vibration | en |
dc.rights.accessRights | Acesso restrito | |
dc.subject | General solutions | en |
dc.subject | Non-uniform rods | en |
dc.subject | Mode shapes | en |
dc.subject | Elementary rod theory | en |
dc.subject | Lie symmetries | en |
dc.title | Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries | en |
dc.type | Artigo | |
unesp.campus | Universidade Estadual Paulista (Unesp), Faculdade de Engenharia, Ilha Solteira | pt |
unesp.department | Engenharia Mecânica - FEIS | pt |
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