RT journal article
T1 Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries
A1 Nunes, Afonso
A1 Da Silva, Samuel
A1 Ruiz Serván, Adrián
A2 Matemáticas
K1 General solutions
K1 Non-uniform rods
K1 Mode shapes
K1 Elementary rod theory
K1 Lie symmetries
AB 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.
SN 1095-8568
YR 2022
FD 2022-11-10
LK http://hdl.handle.net/10498/34750
UL http://hdl.handle.net/10498/34750
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026