Abstract
In this study, we consider first- and second-order random wave loads and the effects of time-varying displacement volume and transient wave elevation to establish motion equations of the Spar platform’s coupled heave-pitch. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project (JONSWAP) wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of second-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. Second-order mean wave loads mainly affect the average heave value. The platform’s pitch increases after the second-order low frequency wave loads are taken into account. The platform’s heave is underestimated if the transient wave elevation term in the motion equations is neglected.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dong Yanqiu, 2005. Wave loads and response of the oil-extraction platform in deep ocean. Tianjin University Press, Tianjin, China, 94–102. (in Chinese)
Gavassoni E, Gonçalves PB, Roehl DM, 2014. Nonlinear vibration modes and instability of a conceptual model of a spar platform. Nonlinear Dynamics, 76(1), 809–826. DOI: 10.1007/s11071-013-1171-6
Hong YP, Lee DY, Choi YH, Hong SK, Kim SE, 2005. An experimental study on the extreme motion responses of a spar platform in the heave resonant waves. The Fifteenth International Offshore and Polar Engineering Conference, Seoul, Korea, 225–232.
Islam AS, Jameel M, Ahmad S, Jumaat MZ, 2012. Nonlinear response of coupled integrated spar platform under severe sea states. The 31st International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil, 559–567. DOI: 10.1115/OMAE2012-83862
Jameel M, Ahmad S, Islam AS, Jumaat MZ, 2014. Wind induced nonlinear response of coupled spar platform. The 33rd International Conference on Ocean, Offshore and Arctic Engineering. San Francisco, USA, V08AT06A061. DOI: 10.1115/OMAE2014-23779
Kurian VJ, Montasir OA, Narayanan SP, 2009. Numerical and model test results for truss spar platform. The Nineteenth International Offshore and Polar Engineering Conference, Osaka, Japan, 99–104.
Kurian VJ, Ng CY, Liew MS, 2013. Effect of short-crested waves on the dynamic responses of truss Spar platforms. The Twenty-third International Offshore and Polar Engineering Conference, Anchorage, USA, 899–906.
Langley RS, 1986. On the time domain simulation of second order wave forces and induced responses. Applied Ocean Research, 8(3), 134–143. DOI: 10.1016/S0141-1187(86)80012-8
Li Binbin, Ou Jinping, 2009. Heave response analysis of truss Spar in frequency domain. The Ocean Engineering, 27(1): 8–15. (in Chinese) DOI:10.3969/j.issn.1005-9865.2009.01.002
Liu Liqin, Incecik A, Zhang Yongheng, Tang Yougang, 2014. Analysis of heave motions of a Truss Spar platform with semi-closed moon pool. Ocean Engineering, 92, 162–174. DOI:10.1016/j.oceaneng.2014.09.048
Liu Liqin, Tang Yougang, Wang Wenjie, 2009. Unstability of coupled heave-pitch motions for spar platform. Journal of Ship Mechanics, 13(4), 551–556. (in Chinese) DOI: 10.3969/j.issn.1007-7294.2009.04.006
Liu Liqin, Zhou Han, Tang Yougang, 2015. Coupling response of heave and moonpool water motion of a truss Spar platform in random waves. China Ocean Engineering, 29(2), 169–182. DOI: 10.1007/s13344-015-0013-3
Montasir OA, Kurian VJ, 2011. Effect of slowly varying drift forces on the motion characteristics of truss spar platforms. Ocean Engineering, 38, 1417–1429. DOI: 10.1016/j.oceaneng.2011.07.007
Montasir OA, Yenduri A, Kurian VJ, 2015. Effect of mooring line configurations on the dynamic responses of truss spar platforms. Ocean Engineering, 96, 161–172. DOI: 10.1016/j.oceaneng.2014.11.027
Neves MA, Sphaier SH, Mattoso BM, Rodríguez CA, Santos AL, Vileti VL, Torres FG, 2008. On the occurrence of Mathieu instabilities of vertical cylinders. The 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal, 619–627. DOI: 10.1115/OMAE2008-57567
Newman JN, 1974. Second-order, slowly-varying forces on vessels in irregular waves. International Symposium on the Dynamics of Marine Vehicles and Structures in Waves, London, 182–186.
Rho JB, Choi HS, 2004. Vertical motion characteristics of truss Spars in waves. The Fourteenth International Offshore and Polar Engineering Conference, Toulon, France, 662–665.
Rho JB, Choi HS, Lee WC, Shin HS, Park IK, 2002. Heave and pitch motions of a spar platform with damping plate. The Twelfth International Offshore and Polar Engineering Conference, Kitakyushu, Japan, 198–201.
Rho JB, Choi HS, Shin HS, Park IK, 2003. An experimental study for mooring effects on the stability of spar platform. The Thirteenth International Offshore and Polar Engineering Conference, Honolulu, USA, 285–288.
Rodriguez CA, Neves MA, 2012. Nonlinear instabilities of spar platforms in waves. The 31st International Conference on Ocean, Offshore and Arctic Engineering, Rio de Janeiro, Brazil, 605–614. DOI: 10.1115/OMAE2012-83577
Sang Song, Li Changdong, Xu Xuejun, Shi Xiao, 2014. Study on stability of Spar platform in deep sea under combination resonance excitation. Journal of Ship Mechanics, 18(10), 1195–1203. (in Chinese) DOI: 10.3969/j.issn.1007-7294.2014.10.005
Shen Wenjun, Tang Yougang, 2011. Stochastic analysis of nonlinear coupled heave-pitch motion for the Truss Spar platform. Journal of Marine Science and Application, 10(4), 471–477. DOI: 10.1007/s11804-011-1093-y
Shen Wenjun, Tang Yougang, Li Hongxia, 2012. Time domain analysis of heave motion for Truss Spar in random seas. The Ocean Engineering, 30(1), 60–65. (in Chinese) DOI: 10.3969/j.issn.1005-9865.2012.01.009
Tang Yougang, Shen Guoguang, Liu Liqin, 2008. Structural dynamics of ocean engineering. Tianjin University Press, Tianjin, China, 284–288. (in Chinese)
Tao LB, Lim KY, Thiagarajan K, 2004. Heave response of classic Spar with variable geometry. Journal of Offshore Mechanics and Arctic Engineering, 126(1), 90–95. DOI: 10.1115/1.1643085
Wang Bin, Liu Liqin, Tang Yougang, 2014. CFD simulation of the vertical motion characteristics of the moonpool fluid for the Truss Spar. Journal of Marine Science and Application, 13(1), 92–98. DOI: 10.1007/s11804-014-1232-3
Yang Hezhen, Xu Peiji, 2015. Effect of hull geometry on parametric resonances of spar in irregular waves. Ocean Engineering, 99, 14–22. DOI: 10.1016/j.oceaneng.2015.03.006
Yu Yuxiu, Liu Shuxue, 2011. Random wave and its application for engineering. Dalian University of Technology Press, Dalian, China, 221–230. (in Chinese)
Zhang Haiyan, 2008. Study on nonlinear motion behavior of coupled heave-pitch for the spar platform. PhD thesis, Tianjin University, Tianjin, 19–28. (in Chinese)
Zhao Jingrui, Tang Lizhi, Tang Yougang, Wang Wenjie, 2009. Internal resonant responses of heave-pitch coupled motions of classic Spar platform. Journal of Tianjin University, 42(3), 201–207. (in Chinese) DOI: 10.3969/j.issn.0493-2137.2009.03.003
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Supported by the National Natural Science Foundation of China under Grant No. 51279130 and No. 51239008
Rights and permissions
About this article
Cite this article
Liu, S., Tang, Y. & Li, W. Nonlinear random motion analysis of coupled heave-pitch motions of a spar platform considering 1st-order and 2nd-order wave loads. J. Marine. Sci. Appl. 15, 166–174 (2016). https://doi.org/10.1007/s11804-016-1349-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11804-016-1349-7