Stabilization of a viscoelastic Timoshenko beam

Abstract

A viscoelastic Timoshenko beam is investigated. We prove an exponential decay of solutions for a large class of kernels with weaker conditions than the existing ones in the literature. This will allow the use of other types of viscoelastic material for Timoshenko type beams than the usually used ones.

Keywords:

• exponential decay
• memory term
• relaxation function
• Timoshenko beam
• viscoelastic material

AMS Subject Classifications:

• 35L20
• 35B40
• 45K05

Acknowledgements

The author would like to thank the anonymous referees for their valuable comments and suggestions. The author is also grateful for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals.