Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam
DOI:
https://doi.org/10.33993/jnaat531-1384Keywords:
beam equation, finite element method, asymptotic stabilityAbstract
In this work, we numerically study the influence of control parameters on the stabilization of a flexible Euler-Bernoulli beam fixed at one end and subjected at the other end to a force control and a punctual moment control proportional respectively to velocity and rotation velocity. First, we analyze the displacement stabilization and the asymptotic behavior of the beam energy using a stable numerical scheme, resulting from the Crank-Nicholson algorithm for time discretization and the finite element method based on the approximation by Hermite's cubic polynomial functions, for discretization in space. Then, by means of the finite element method, we represent the spectrum of the operator associated with this beam problem and we carry out a qualitative study of the
locus of the eigenvalues according to the positive control parameters. From these studies we conclude that rotation velocity control has more effect on the stabilization of the beam compared to velocity control. Finally, this result is confirmed by a sensitivity study on the control parameters involved in the stabilization of the beam.
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Copyright (c) 2024 Goh André-Pascal Abro, Kidjégbo Augustin Touré , Gossrin Jean-Marc Bomisso
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
