Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T17:40:39.493Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method

Published online by Cambridge University Press:  28 May 2015

Arash Reza  and
Hamid M. Sedighi
Arash Reza*
Affiliation:
Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran
Hamid M. Sedighi
Affiliation:
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Iran
*
*Corresponding author. Email: arashreza@gmail.com (A. Reza), hmsedighi@gmail.com (H. M. Sedighi)
Get access

Abstract

One of the useful methods for offshore oil exploration in the deep regions is the use of tension leg platforms (TLP). The effective mass fluctuating of the structure which due to its vibration can be noted as one of the important issues about these platforms. With this description, dynamic analysis of these structures will play a significant role in their design. Differential equations of motion of such systems are nonlinear and providing a useful method for its analysis is very important. Also, the amount of added mass coefficient has a direct effect on the level of nonlinearity of partial differential equation of these systems. In this study, Homotopy analysis method has been used for closed form solution of the governing differential equation. Linear springs have been used for modeling the stiffness of this system and the effects of torsion, bending and damping of water have been ignored. In the study of obtained results, the effect of added mass coefficient has been investigated. The results show that increasing of this coefficient decreases the bottom amplitude of fluctuations and the system frequency. The obtained results from this method are in good agreement with the published results on the valid articles.

Keywords

70G9970K2582C80TLPHomotopy analysis methodnonlinear vibrational equationadded massvertical vibration
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015 , pp. 357 - 368
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ahmad, S. , Stochastic TLP response under long crested random sea, Comput. Struct., 61 (1996), pp.975–993.CrossRefGoogle Scholar
[2]Chandrasekaran, S. and Jain, A.K., Triangular configuration tension leg platform behaviour under random sea wave loads, Ocean Eng., 29 (2002), pp. 1895–1928.Google Scholar
[3]Siddiqui, N.A. and Ahmad, S., Fatigue and fracture reliability of TLP tethers under random loading, Marine Struct., 14 (2001), pp. 331–352.Google Scholar
[4]Tabeshpour, M.R., Golafshani, A.A. and Seif, M.S., Second-order perturbation added mass fluctuation on vertical vibration of tension leg platforms, Marine Struct., 19 (2006), pp. 271–283.CrossRefGoogle Scholar
[5]Tabeshpour, M.R., Conceptual discussion on free vibration analysis of tension leg platforms, Development and Applications of Oceanic Engineering, 2 (2013), pp. 45–52.Google Scholar
[6]Adrezin, R. and Benaroya, H., Response of a tension leg platform to stochastic wave forces, Probabilistic Engineering Mechanics, 14 (1999), pp. 3–17.Google Scholar
[7]Adrezin, R. and Benaroya, H., Non-linear stochastic dynamics of tension leg platforms, J. Sound Vibration, 220 (1999), pp. 27–65.Google Scholar
[8]Chandrasekaran, S. and Jain, A.K., Dynamic behaviour of square and triangular offshore tension leg platforms under regular wave loads, ocean Eng., 29 (2002), pp. 279–313.CrossRefGoogle Scholar
[9]Senjanovic, I., Tomic, M. and Hadzic, N., Formulation of consistent nonlinear restoring stiffness for dynamic analysis of tension leg platform and its influence on response, Marine Structures, 30 (2013), pp. 1–32.CrossRefGoogle Scholar
[10]Liao, S., Beyond Perturbation: Introduction to Homotopy Analysis Method, Boca Raton: Chapman & Hall/CRC Press, 2003.CrossRefGoogle Scholar
[11]Liao, S., On the homotopy analysis method for nonlinear problems, Appl. Math. Comput., 147 (2004), pp. 499–513.Google Scholar
[12]Sedighi, H.M., Shirazi, K.H. and Zare, J., An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method, Int. J. Non-Linear Mech., 47 (2012), pp. 777–784.Google Scholar
[13]Liao, S., Homotopy analysis method: A new analytical technique for nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997), pp. 95–100.Google Scholar
[14]Liao, S., Notes on the homotopy analysis method: some definitions and theorems, Communications in Nonlinear Science and Numerical Simulation, 14 (2009), pp. 983–997.Google Scholar
[15]Liao, S., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 15 (2010), pp. 2003–2016.Google Scholar
[16]Liao, S.J., An analytic approximate approach for free oscillations of self-excited systems, Int. J. Non-Linear Mech., 39 (2004), pp. 271–280.Google Scholar
[17]Fardi, M., Kazemi, E., Ezzati, R. and Ghasemi, M., Periodic solution for strongly nonlinear vibration systems by using the homotopy analysis method, Math. Sci., 6 (2012), pp. 1–5.CrossRefGoogle Scholar