Symmetry theory-based approaches for the computation of mode shapes of vibrating s...
Transport of magnetic field lines and particles in tokamaks and plasma modeling fo...
| Full text | |
| Author(s): |
Nunes, Afonso W.
;
da Silva, Samuel
;
Ruiz, Adrian
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Sound and Vibration; v. 538, p. 10-pg., 2022-08-17. |
| 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. (AU) | |
| FAPESP's process: | 16/22473-6 - Applications of Lie symmetries in beams theory |
| Grantee: | Afonso Willian Nunes |
| Support Opportunities: | Scholarships in Brazil - Scientific Initiation |
| FAPESP's process: | 21/12894-2 - Symmetry theory-based approaches for the computation of mode shapes of vibrating structures |
| Grantee: | Afonso Willian Nunes |
| Support Opportunities: | Scholarships in Brazil - Doctorate (Direct) |