Exponential stabilization of an Euler-Bernoulli beam under boundary control

Main Article Content

Billal Lekdim
https://orcid.org/0000-0002-9710-9883

Abstract

We study the free vibration of an Euler-Bernoulli beam without internal damping. By applying suitable control at the free boundary, we can exponentially dampen these vibrations. The exponential stability was proven using the Lyapunov method, and the results were confirmed through numerical simulation.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Article Details

How to Cite
[1]
Lekdim, B. 2023. Exponential stabilization of an Euler-Bernoulli beam under boundary control. Journal of Innovative Applied Mathematics and Computational Sciences. 3, 1 (May 2023), 28–34.
Section
Research Articles

References

M. DADFARNIA, N. JALILI, B. XIAN AND D. M. DAWSON, Lyapunov-based vibration control of translational Euler-Bernoulli beams using the stabilizing effect of beam damping mechanisms, Journal of Vibration and Control, 10(7) (2004), 933–961.

B. Z. GUO AND K. Y. CHAN, Riesz basis generation, eigenvalues distribution, and exponential stability for a Euler–Bernoulli beam with joint feedback control, Revista Matem´atica Complutense, 14(1) (2001), 205–229.

W. HE, S. S. GE, B. V. E. HOW, Y. S. CHOO AND K. S. HONG, Robust adaptive boundary

control of a flexible marine riser with vessel dynamics, Automatica. A Journal of IFAC, 47(4)

(2011), 722–732.

B. LEKDIM, A. KHEMMOUDJ, General decay of energy to a nonlinear viscoelastic two dimensional beam, Applied Mathematics and Mechanics. English Edition, 39(11) (2018), 1661–1678.

B. LEKDIM, A. KHEMMOUDJ, Uniform decay of a viscoelastic nonlinear beam in two dimensional space, Asian Journal of Mathematics and Computer Research, 25(1) (2018), 50–73.

B. LEKDIM, A. KHEMMOUDJ, Existence and energy decay of solution to a nonlinear viscoelastic two-dimensional beam with a delay, Multidimensional Systems and Signal Processing, 32(3) (2021), 915–931.

B. LEKDIM, A. KHEMMOUDJ, Existence and general decay of solution for nonlinear viscoelastic two-dimensional beam with a nonlinear delay, Ricerche di Matematica, (2021), 1–22.

B. LEKDIM, A. KHEMMOUDJ, General Stability of Two-dimensional Viscoelastic Nonlinear Beam with Bending Couplings, 2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), Tebessa, Algeria, 2021, pp. 1-4.

M. MILETI, D. STÜRZER AND A. ARNOLD, An Euler-Bernoulli beam with nonlinear damping and a nonlinear spring at the tip, Discrete and Continuous Dynamical Systems. Series B, 20(9) (2015), 3029–3055.

L. SEGHOUR, A. KHEMMOUDJ AND N. E. TATAR, Control of a riser through the dynamic of the vessel, Applicable Analysis, 95(9) (2016), 1957–1973.

Y. F. SHANG, G. Q. XU AND Y. L. CHEN, Stability analysis of Euler–Bernoulli beam with input delay in the boundary control, Asian Journal of Control, 14(1) (2012), 186–196.

P. WANG AND J. HAO, Asymptotic Stability of Memory-Type Euler-Bernoulli Plate with Variable Coefficients and Time Delay, Journal of Systems Science & Complexity, 32(5) (2019), 1375-1392