Control of a viscoelastic translational Euler–Bernoulli beam |
| |
| Authors: | Amirouche Berkani Nasser‐eddine Tatar Ammar Khemmoudj |
| |
| Affiliation: | 1. Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, Algiers, Algeria;2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia |
| |
| Abstract: | In this paper, we study a cantilevered Euler–Bernoulli beam fixed to a base in a translational motion at one end and to a tip mass at its free end. The beam is subject to undesirable vibrations, and it is made of a viscoelastic material that permits a certain weak damping. By applying a control force at the base, we shall attenuate these vibrations in a fast manner. In fact, we establish the exponential stability of the system. Our method is based on the multiplier technique. Copyright © 2016 John Wiley & Sons, Ltd. |
| |
| Keywords: | vibration control exponential decay translational Euler– Bernoulli beam memory term relaxation function viscoelasticity subclass 35L20 93D15 93D20 |
|
|
