Stabilisation of a viscoelastic flexible marine riser under unknown spatiotemporally varying disturbance

ABSTRACT

In this work, we study a viscoelastic flexible marine riser problem with vessel dynamics subject to a distributed disturbance. The dynamic of the problem is modelled as a viscoelastic Euler–Bernoulli beam structure. Based on the multiplier method and some ideas introduced by N.-E. Tatar (J. Contemp. Math. Anal., 48(6):285–296, 2013), we shall suppress the riser's vibration in a certain manner that we will determine. In fact, we prove uniform stability of the system for a large class of relaxation functions. Moreover, the relationship between the behaviour of the relaxation function and the decay rate of the energy is established. This improves earlier work where a control on the top of the structure has been imposed and the ocean disturbance was ignored.

KEYWORDS:

• Marine riser
• stability
• vibration control
• Euler–Bernoulli beam structure
• viscoelasticity
• relaxation function

AMS Classifications:

• 35L20
• 93D15
• 93D20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The second author is very grateful to King Fahd University of Petroleum and Minerals for its continuous financial support through project number IN 171002.