Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Effect of the Delay Between the Detection of Vibration and the Action of Tendons on the Dynamics Response of Tension Leg Platform (TLP) Under Sea Waves Excitation

Journal of Applied Nonlinear Dynamics 10(4) (2021) 627--643 | DOI:10.5890/JAND.2021.12.004

A.M. Ngounou$^1$, B.R. Nana Nbendjo$^{1,2}$ , U. Dorka$^2$

$^1$ Laboratory of Modelling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

$^2$ Steel and Composite Structures, University of Kassel,Kurt-Wolters-Strasse 3, Kassel 34125, Germany

Download Full Text PDF



In this study, the dynamic response of the tension leg platform (TLP) under sea waves excitation is investigated. One establishes the analytical framework consisting of mathematical modeling of TLP taking into account the tendons and the delay. We analyse the stability and determine the physical characteristics of tendon system that allow the system to be always stable. Conditions on the space parameters of the system for which harmonic, subharmonic, superharmonic, combination resonants states are obtained using the multiple time scales method. The results show that the stability area of the system decreases when the delay increases and increases when the damping coefficient increases. Furthermore, increasing the time- delay only increases the value of the maximum amplitude response of the system. However, reasonable selection of the system parameters can effectively reduce the level of vibration of the system.


A.M. Ngounou is grateful to University of Kassel in Germany for invitation for a research visit within the renew stay Humboldt Fellowship. Prof Nana Nbendjo is grateful to the Alexander von Humboldt Foundation for financial support.


  1. [1]  Adrezin, R., Bar-Avi, P., and Benaroya, H. (1996), Dynamic response of compliant offshore structures: review, Journal of Aerospace Engineering, 9(4), 114-31.
  2. [2]  Adrezin, R. and Benaroya, H. (1999), Non-linear stochastic dynamics of tension leg platforms, Journal of Sound and Vibration, 220, 27-65.
  3. [3]  Adrezin, R. and Benaroya, H. (1999), Response of a tension leg platform to stochastic wave forces, Probababilistic Engineering and Mechanics, 14, 3-17.
  4. [4]  Han, S.M. and Benaroya, H. (2002), Comparison of linear and nonlinear responses of a compliant tower to random wave forces, Chaos Solitons and Fractals, 14, 269-291.
  5. [5]  Yigit, A.S. and Christoforou, A.P. ( 1996), Coupled axial and transverse vibrations of oilwell drillstrings, Journal of sound and Vibration, 195, 617-27.
  6. [6]  Patel, M.H. and Park, H.I. (1991), Dynamics of tension leg platform tethers at low tension. Part I-Mathieu stability at large parameters, Marine structures, 4, 257-273.
  7. [7]  Gadagi, M.M. and Benaroya, H. (2006), Dynamic response of an axially loaded tendon of a tension leg platform, Journal of Sound and Vibration, 293, 38-58.
  8. [8]  Yang, C.K. and Kim, M.H. (2010), Transient effects of tendon disconnection of a TLP by hull-tendon-riser coupled dynamic analysis, Ocean Engineering, 37, 667-677.
  9. [9]  Taflanidis, A.A., Vetter, C., and Loukogeorgaki, E. (2013), Impact of modeling and excitation uncertainties on operational and structural reliability of tension leg platforms, Applied Ocean Research, 43, 131-147.
  10. [10]  Rudman, M. and Cleary, P.W. (2013), Rogue wave impact on a tension leg platform: the effect of wave incidence angle and mooring line tension, Ocean Engineering, 61, 123-138.
  11. [11]  Srinivasan, C., Gaurav, G., Serino, G., and Miranda, S. (2011), Ringing and springing response of triangular TLPs, International Shipbuild Programm, 58, 141-163.
  12. [12]  Abdussamie, N., Drobyshevski, Y., Ojeda, R., Thomas, G., and Amin, W. (2017), Experimental investigation of wave-in-deck impact events on a TLP model, Ocean Engineering, 142, 541-562.
  13. [13]  Matsui, T., Sakoh, Y., and Nozu, T. (1993), Second-order sum-frequency oscillations of tension-leg platforms: Prediction and measurement, Applied Ocean Research, 15, 107-118.
  14. [14]  Feng, W.H., Hua, F.Y., and Yang, L. (2014), Dynamic analysis of a tension leg platform for offshore wind turbines, Journal of Power Technologie, 94, 42-49.
  15. [15]  Nayfeh, A.H. and Mook, D.H. (1995), Nonlinear Oscillations, Wiley Classics Library, New York.
  16. [16]  Jahangiri, V., Mirab, H., Fathi, R., and Ettefaghand, M.M. (2016), TLP Structural Health Monitoring Based on Vibration Signal of Energy Harvesting System, Latin American Journal of Solids Structures, 13, 897-915.
  17. [17]  Anii, K.A., Kosaka, S.H., and Yamanaka, H. (1994), Stability of active-trndon structural control with time delay, Journal of Engineering Mechanics, 120, 2240-2243.
  18. [18]  Morison, J.R., OBrien, M.P., Johnson, J.W., and Schaaf, S.A. (1950), The force exerted by surface waves on piles, Pet Trans, AIME 189, 149-57.
  19. [19]  Zhang, L., Yang, C.Y., Chajes, M.J., and Cheng, A.H.D. (1993), Stability of active-tendon structural control with time delay, Jounal of Engineering Mechanics, 119, 1017-1024.
  20. [20]  Korak, S. and Ranjan, G. (2013), Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition, Meccanica , 48, 1661-1676.
  21. [21]  Bernstein, A. and Rand, R. (2016), Delay-Coupled Mathieu Equations in Synchrotron Dynamics, Journal of Applied Nonlinear Dynamics, 5(3), 337-348.
  22. [22]  Bernstein, A. and Rand, R., (2018), Delay-Coupled Mathieu Equations in Synchrotron Dynamics Revisited: Delay Terms in the Slow Flow, Journal of Applied Nonlinear Dynamics, 7(4), 349-360.
  23. [23]  Yang, T., Fang, B., Chen, Y., and Zhen, Y. (2009), Approximate solutions of axially moving viscoelastic beams subject to multi-frequency excitations, International Journal and Non-Linear Mechanics, 44, 230-238.