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.
Highlights
When a cylinder is submerged in a moving fluid we assist to the formation of complex vertices which destabilize the cylinder from its initial position
We refer the reader to [4, 6, 8, 13, 17, 23] where the authors studied the boundary control of flexible marine riser
R > 0, The main objective of this work, is to establish different types of decay rates of the system (1.1)–(1.2) under a suitable control acting on top of the riser. This will be shown for a large class of kernels
Summary
When a cylinder is submerged in a moving fluid we assist to the formation of complex vertices which destabilize the cylinder from its initial position. We refer the reader to [4, 6, 8, 13, 17, 23] where the authors studied the boundary control of flexible marine riser It is worth mentioning the work of Seghour et al [29] where the authors considered the problem t ρwtt(x, t)+EIwxxxx(x, t)−EI h (t−s) wxxxx (x, s) ds−T wxx(x, t)=0, (1.1). R > 0, The main objective of this work, is to establish different types of decay rates of the system (1.1)–(1.2) under a suitable control acting on top of the riser This will be shown for a large class of kernels.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
