Vibration control of a viscoelastic flexible marine riser with vessel dynamics

In this work, we investigate the asymptotic behavior of solutions of a viscoelastic exible 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 multi- plier technique. Numerical simulations justifying the effectiveness of the proposed boundary control to suppress the vibrations of the exible marine riser are provided.