Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam

Authors

  • Goh André-Pascal Abro Université Alassane Ouattara, Bouaké, Côte d'Ivoire https://orcid.org/0000-0001-9096-963X
  • Kidjégbo Augustin Touré Institut National Polytechnique Houphouët Boigny, Yamoussoukro, Côte d'Ivoire
  • Gossrin Jean-Marc Bomisso Université Nangui Abrogoua D’Abobo-Adjamé, Abidjan, Côte d'Ivoire https://orcid.org/0000-0002-3069-2752

DOI:

https://doi.org/10.33993/jnaat531-1384

Keywords:

beam equation, finite element method, asymptotic stability
Abstract views: 107

Abstract

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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References

Abro Goh A. P., Bomisso G. J. M., Toure K. A. and Coulibaly Adama, A numerical study for a flexible Euler-Bernoulli beam with a force control in velocity and a moment control in rotating velocity, Journal of the Indian Math. Soc., 90 (2023), pp. 125–148. https://doi.org/10.18311/jims/2023/3304 DOI: https://doi.org/10.18311/jims/2023/33044

Advanpix,Multiprecision Computing Toolbox for MATLAB

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H. Laousy, On some problems of stabilization of systems with distributed parameters, Doctoral thesis, Paul Verlaine University - Metz, (1997). https://doi.org/10.1051/COCV:200206

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Mensah E. Patrice, On the numerical approximation of the spectrum of a flexible Euler-Bernoulli beam with a force control in velocity and a moment control in rotating velocity, Far East Journal of Mathematical Sciences (FJMS), 126 (2020), pp. 13–31. http://dx.doi.org/10.17654/MS126010013 DOI: https://doi.org/10.17654/MS126010013

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Published

2024-07-11

How to Cite

Abro, G. A.-P., Touré , K. A., & Bomisso , G. J.-M. (2024). Influence of control parameters on the stabilization of an Euler-Bernoulli flexible beam. J. Numer. Anal. Approx. Theory, 53(1), 5–19. https://doi.org/10.33993/jnaat531-1384

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