Stabilisation of a viscoelastic beam conveying fluid

Abstract

In this paper, vibration reduction of a viscoelastic flexible beam conveying fluid with variable velocity is studied. A control is designed at the top boundary of the beam based on original infinite dimensionality PDEs model and Lyapunov's direct method to reduce the beam's vibrations. The uniform stability under external disturbance and exponential stability without external disturbance are proved based on the proposed boundary control.

Keywords:

• Beam
• boundary control
• Lyapunov's direct method
• uniform stability
• exponential stability
• internal fluid

Acknowledgments

The author would like to express his gratitude to the anonymous referees for giving constructive and fruitful suggestions which allow to improve considerably the initial version of the present manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.