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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.