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Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity

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  • Yeo Brahima
  • Dakouri Narcisse
  • Adou Jérôme
  • Birendra Nath Mandal

Abstract

Our model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that we implement. This numerical scheme results from the Crank–Nicolson algorithm for the discretization in time and from the finite element method based on the approximation by Hermith cubic functions for the discretization in space. The study shows that, compared to the velocity control, the displacement control has an almost negligible effect on the stabilization of the beam. This result is confirmed later by a sensitivity study on the control parameters involved in our model.

Suggested Citation

  • Yeo Brahima & Dakouri Narcisse & Adou Jérôme & Birendra Nath Mandal, 2022. "Numerical Study of an Euler-Bernoulli Beam Stabilization Controlled in Displacement and Velocity," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2022, pages 1-8, October.
    • Handle: RePEc:hin:jijmms:7647568
    DOI: 10.1155/2022/7647568
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