@misc{10498/34750,
year = {2022},
month = {11},
url = {http://hdl.handle.net/10498/34750},
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.},
keywords = {General solutions},
keywords = {Non-uniform rods},
keywords = {Mode shapes},
keywords = {Elementary rod theory},
keywords = {Lie symmetries},
title = {Exact general solutions for the mode shapes of longitudinally vibrating non-uniform rods via Lie symmetries},
doi = {10.1016/J.JSV.2022.117216},
author = {Nunes, Afonso and Da Silva, Samuel and Ruiz Serván, Adrián},
}