| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 5, 2019
Nonlocal and delay equations
|
|
|---|---|---|
| Article Number | 501 | |
| Number of page(s) | 29 | |
| DOI | https://doi.org/10.1051/mmnp/2018057 | |
| Published online | 04 April 2019 | |
Stabilization of a viscoelastic Timoshenko beam fixed into a moving base
1
Faculty of Mathematics & Informatics, University Mohamed El Bachir El Ibrahimi,
El-Anasser 34030,
Bordj Bou Arréridj, Algeria.
2
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals,
Dhahran
31261, Saudi Arabia.
* Corresponding author: aberkanid@gmail.com
Received:
7
April
2018
Accepted:
26
September
2018
In this paper, we are concerned with a cantilevered Timoshenko beam. The beam is viscoelastic and subject to a translational displacement. Consequently, the Timoshenko system is complemented by an ordinary differential equation describing the dynamic of the base to which the beam is attached to. We establish a control force capable of driving the system to the equilibrium state with a certain speed depending on the decay rate of the relaxation function.
Mathematics Subject Classification: 35L20 / 35B37 / 93D15 / 93D20
Key words: Translational Timoshenko beam / viscoelastic damping / vibrations control / stabilization
© EDP Sciences, 2019
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