| Texto completo | |
| Autor(es): |
Nunes, Afonso W.
;
da Silva, Samuel
;
Ruiz, Adrian
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Sound and Vibration; v. 538, p. 10-pg., 2022-08-17. |
| 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. (AU) | |
| Processo FAPESP: | 16/22473-6 - Simetrias de Lie na Propagação de Ondas em Estruturas |
| Beneficiário: | Afonso Willian Nunes |
| Modalidade de apoio: | Bolsas no Brasil - Iniciação Científica |
| Processo FAPESP: | 21/12894-2 - Modos de vibrar de estruturas via métodos de simetria |
| Beneficiário: | Afonso Willian Nunes |
| Modalidade de apoio: | Bolsas no Brasil - Doutorado Direto |