Publication Cover
Applicable Analysis
An International Journal
Volume 95, 2016 - Issue 9
128
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Control of a riser through the dynamic of the vessel

, &
Pages 1957-1973 | Received 04 Mar 2015, Accepted 31 Jul 2015, Published online: 26 Aug 2015

References

  • He W, Ge SS, How BVE, Choo YS, Hong KS. Robust adaptive boundary control of a flexible marine riser with vessel dynamics. Automatica. 2011;47:722–732.
  • Canbolat H, Dawson D, Rahn C, Vedagarbha P. Boundary control of a cantilevered flexible beam with point-mass dynamics at the free end. Center for Advanced Manufacturing, Clemson, USA, Clemson University.
  • Conrad F, Morgül Ö. On the stabilization of a flexible beam with a tip mass. SIAM J. Control Optim. 1998;36:1962–1986.
  • Chentouf B, Wang JM. Optimal energy decay for a nonhomogeneous flexible beam with a tip mass. J. Dyn. Control Syst. 2007;13:37–53.
  • Nguyen TL, Do KD, Pan J. Boundary control of coupled nonlinear three dimensional marine risers. J. Marine Sci. Appl. 2013;12:72–88.
  • Ge SS, He W, How BVE, Choo YS. Boundary control of a coupled nonlinear flexible marine riser. Trans. Control Syst. Technol. 2010;18:1080–1091.
  • He W, Ge SS, Zhang S. Adaptive boundary control of a flexible marine installation system. Automatica. 2011;47:2728–2734.
  • He W, Zhang S, Ge SS. Boundary control of a flexible riser with the application to marine installation. Trans. Ind. Electron. 2013;60: 5802–5810.
  • Borges F, Roitman N, Magluta C, Castello D, Franciss R. Vibration reduction through the use of viscoelastic materials. Int. J. Model. Simul. Pet. Ind. 2012;6: 1–7.
  • Liu W, Sun Y. General decay of solutions for a weak viscoelastic equation with acoustic boundary conditions. Z. Angew. Math. Phys. 2014;65:125–134.
  • Lazzari B, Nibbi R. On the exponential decay of the Euler-Bernoulli beam with boundary energy dissipation. J. Math. Anal. Appl. 2012;389:1078–1085.
  • Aassila M, Cavalcanti MM, Cavalcanti VN. Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term. Calc. Var. 2002;15:155–180.
  • Aassila M, Cavalcanti MM, Soriano JA. Asymptotic stability and energy decay rates for solutions of the wave equation with memory in a star-shaped domain. SIAM J. Control Optim. 2000;38:1581–1602.
  • Bae JJ, Yoon SB. On uniform decay of wave equation of carrier model subject to memory condition at the boundary. J. Korean Math. Soc. 2007;44:1013–1024.
  • Cavalcanti MM, Domingos Cavalcanti VN, Martinez P. General decay rate estimates for viscoelastic dissipative systems. Nonlinear Anal. Theory Methods Appl. 2008;68:177–193.
  • Cornilleau P, Nicaise S. Energy decay for solutions of the wave equation with general memory boundary conditions. Differ. Integral Equ. 2009;22:1173–1192.
  • Kang YH, Park JY, Kim JA. A memory type boundary stabilization for an Euler-Bernoulli beam under boundary output feedback control. J. Korean Math. Soc. 2012;49:947–964.
  • Kirane M, Tatar N-E. Non-existence results for a semilinear hyperbolic problem with boundary condition of memory type. Zeit. Anal. Anwend. 2000;19:453–468.
  • Messaoudi S, Mustafa MI. On the control of solutions of viscoelastic equations with boundary feedback. Nonlinear Anal.: Real World Appl. 2009;10:3132–3140.
  • Nicaise S, Pignotti C. Stabilization of the wave equation with variable coefficients and boundary condition of memory type. Asymp. Anal. 2006;50:31–67.
  • Propst G, Prüss J. On wave equations with boundary dissipation of memory type. J. Integral Equ. Appl. 1994;8:99–123.
  • Santos ML, Junior F. A boundary condition with memory for Kirchhoff plates equations. Appl. Math. Comput. 2004;148:475–496.
  • Tatar N. On a perturbed kernel in viscoelasticity. Appl. Math. Lett. 2011;24:766–770.
  • Messaoudi S. General decay of solutions of a viscoelastic equation. J. Math. Anal. Appl. 2008;341:1457–1467.
  • Cavalcanti MM, Domingos Cavalcanti VN, Ferreira J. Existence and uniform decay for a non-linear viscoelastic equation with strong damping. Math. Meth. Appl. Sci. 24:1043–1053.
  • Park JY, Ha TG. Well-posedness and uniform decay rates for the Klein-Gordon equation with damping term and acoustic boundary conditions. J. Math. Phys. 2009;50:013506. doi:10.1063/1.3040185.
  • Hoang NS, Ramm AG. A nonlinear inequality and applications. Nonlinear Anal. Theory Methods Appl. 2009;71:2744–2752.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.