Vibration control of a viscoelastic flexible marine riser with vessel dynamics

Abstract

In this work, we investigate the asymptotic behavior of solutions of a viscoelastic flexible marine riser with vessel dynamics. Under a suitable control applied at the top end of the riser, we establish explicit decay rates for a large class of relaxation functions. In particular, exponentially and polynomially (or power type) decaying functions are included in this class. Our method is based on the multiplier technique. Numerical simulations justifying the effectiveness of the proposed boundary control to suppress the vibrations of the flexible marine riser are provided.

Keywords

• stability
• vibration control
• flexible marine riser
• boundary control
• Euler-Bernoulli beam structure
• viscoelasticity