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

Yeo Brahima, Dakouri Narcisse, Adou Jérôme and Birendra Nath Mandal

International Journal of Mathematics and Mathematical Sciences, 2022, vol. 2022, 1-8

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.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:7647568

DOI: 10.1155/2022/7647568

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