Exponential stability of a rotating Timoshenko beam under thermo-viscoelastic damping

Abstract

In this article, we study a rotating cantilevered Timoshenko beam with a tip mass at its free end coupled with a heat equation of hyperbolic type. The beam is subject to some undesirables vibrations. Under the thermal effect we shall attenuate these vibrations. In fact, we establish the exponential stability of the system under the control torque applied on the hub. The proofs is obtained by using the multiplier technique.

Keywords:

• Vibration control
• rotational motion
• Timoshenko beam
• memory term
• relaxation function
• heat conduction

2010 Mathematics Subject Classifications:

• 35L20
• 93D15
• 93D20

Acknowledgments

The author gratefully acknowledge Faculty of Mathematics and Informatics, University Mohamed El Bachir El Ibrahimi of Algeria, and this presented work is in memory of his beloved grandmother (1933–2020) Ms Dahbia Berkani.

Disclosure statement

No potential conflict of interest was reported by the author(s).