Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
A Lie Symmetry Approach for the Computation of the Vibration Modes of Beams
Submission Author:
AFONSO NUNES , SP
Co-Authors:
AFONSO NUNES, Samuel da Silva, Jean-Mathieu Mencik
Presenter: AFONSO NUNES
doi://10.26678/ABCM.COBEM2019.COB2019-0227
Abstract
Lie symmetries constitute an interesting tool to solve differential equations, consisting in reducing and simplifying these equations by only retaining some invariant solutions. In this paper, Lie symmetries are applied to solve the differential equation of Euler-Bernoulli beams with a view to computing their vibration modes. It is shown that the differential equation can be mapped on a subspace where smooth solutions can be obtained. This suggests nice features (i.e., good conditioning) for computing the high order modes of the beams.
Keywords
Lie symmetries, Euler-Bernoulli beam, vibration modes
