Control of a viscoelastic translational Euler–Bernoulli beam

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.