混合模型试验中截断系泊缆动力特性差异研究
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摘要
随着深海油气开发,越来越多的深海平台将用于实际生产。而模型试验仍然是深海平台设计中重要的步骤之一。然而采用常规缩尺比,现有水池无法进行全水深模型试验。混合模型试验是解决这一矛盾主要方法。混合模型试验的关键是设计一套等效的截断系泊系统。如何设计一套可以和全水深系泊系统静动力特性一致的水深截断系泊系统是截断设计的最终目标。
目前主要采用基于静力相似进行截断系泊系统设计。根据经验得知:基于静力相似所设计的截断系泊缆在动力特性上和全水深系泊缆存在明显差异,进而导致系泊缆张力预报的误差。基于动力特性上的差异研究,本文选取某座即将工作于中国南海的半潜平台进行基于静力相似截断系泊系统设计,对截断系泊缆,截断系泊系统进行了一系列动态差异研究。此座半潜平台锚泊最大工作水深1500m,采用动力定位工作最大水深可达3000m。
本文主要工作包括以下几个方面:
1:对模型水动力试验的发展进行了介绍,同时对深海平台模型试验技术和混合模型试验技术进行了阐述。
2:对系泊缆静力计算中悬链线方程进行了推导,简要阐述了系泊缆动力计算模型和计算方法。
3:基于静力相似准则对半潜平台1500m水深系泊系统进行截断优化设计,截断水深分别为1200m,900m,600m,分别给出了各截断系泊系统的静力特性曲线。
4:对各截断水深和全水深耦合数值模型进行时域耦合计算。其中各水深耦合模型采用一致的水动力参数,实际上此过程相当于混合模型试验中的数值外推过程。研究相同水动力参数下,截断系泊系统和全水深系泊系统之间运动预报以及系泊缆张力预报之间的差异,试图证明基于静力相似所设计的截断系泊系统具有一定的预报能力,但是在系泊缆动力特性上仍然无法完全满足全水深动力特性。环境条件选择南海十年一遇的海洋条件,分别选择迎风,迎浪(No Current)和迎风,迎浪,迎流(With Current)两种环境条件。
5:选取600m截断系泊系统,对其进行全面的动力特性计算,并和全水深系泊系统进行比较,包括单根截断系泊缆动力特性差异研究和截断系泊系统动力特性差异研究。其中系泊缆动力特性研究中,分别使系泊缆顶端进行多个振幅,多个振荡周期的规则运动以及不规则运动,运动包括水平和垂向两个方向。截断系泊系统同样进行相同的顶端运动,只不过顶端为浮体-半潜平台。动态差异研究比较项目包括锚泊阻尼,单位振幅动态张力,张力谱以及张力传递函数RAO等。比较过程中对各项对比项目的含义进行了解释说明,其中重点阐述了锚泊阻尼的含义和计算方法,并得出了锚泊阻尼和顶端振荡周期,振荡振幅,拖曳力系数选取,轴向刚度,海流速度等参数间的变化关系。
本论文对截断系泊缆和截断系泊系统进行了全面的动力特性计算,得到了全水深系泊系统和截断系泊系统之间的动力特性差异,对混合模型试验中的系泊缆截断设计有重要意义。
With the development of deep water oil and gas exploration, more and more deepwater platforms will be used for production. Model test is still one of the most important steps for deepwater platform design. However, full water depth model test still can not be performed under conventional scale in current wave basin. Hybrid model test is the most advanced method to solve the problem. And the key problem in hybrid model test is designing an equivalent truncated mooring system. How to design the truncated mooring system which can simulate the full mooring system including static and dynamic characteristics is the ultimate purpose of the truncation design Currently, designing of truncation system is mainly based on static equivalence.
There are obvious dynamic differences between the truncated mooring system and full depth mooring system if the truncation is only based on static equivalence. The dynamic difference will lead to error of prediction of the mooring line tension. In this paper, the author choose a semi submersible, which will be set up in South China Sea, for truncation design based on static equivalence. Then the truncated single mooring line and truncated mooring system are used for dynamic difference studies. The semi submersible can work for 1500m water depth with mooring system and up to 3000m with dynamic positioning.
The following aspects are included in this research:
1: Introduction to the development of the model test, technique of the deepwater platform model test and hybrid model test.
2: Brief introduction of mooring line calculation, including catenary equation for static analysis and numerical model and calculation methods for dynamic analysis.
3: Based on the static equivalence, the truncated mooring systems of semi submersible for 1500m full water depth are designed respectively for 1200m, 900m, and 600m water depth. The static characteristic curves are provided for all truncated mooring systems.
4: Time domain coupled analyses are performed for all water depth numerical models, including truncated and full water depth model. In the analysis, same hydrodynamic parameters are adopted for all numerical models, including truncated model and full depth model. In fact, this process is equivalent to the numerical extrapolation in the hybrid model test. Research on the motion and tension prediction difference between truncated mooring system and full water depth mooring system, under same hydrodynamic parameters; we try to prove that truncated mooring system based on static equivalence has some prediction capability, but dynamic characteristics difference of mooring line still can not fully meet the requirement. 10-years-wave in South China Sea is selected for the analysis. Two types of sea states will be included: 1: 180°waves and wind, without current; 2: 180°waves, wind and current.
5: 600m truncated mooring system is selected for dynamic characteristics difference research, including single truncated mooring line and truncated mooring system. In the single mooring line dynamic studies, the top end of the mooring line will be given regular oscillation with different amplitudes and oscillation periods, and irregular oscillation, including horizontal oscillation and vertical oscillation. The same top end oscillations are performed for the truncated mooring system; with the difference that top end is changed to floating body--semi submersible instead of top end of mooring line. Comparative items for dynamic difference research includes mooring line damping, dynamic tension force per unit amplitude, tension spectrum and tension RAO. Definitions of the items are explained in the comparative process. Especially, mooring line damping is explained in details, including the definition and calculation methods. Through changing the pretension, amplitude, frequency, stiffness, normal drag coefficient, and current speed, the author obtains the results of individual parameter effect on the mooring induced horizontal damping and vertical damping respectively.
In this paper, comprehensive dynamic characteristics are calculated for truncated mooring line and mooring system. The dynamic differences between truncated system and full system are given for further research. The understanding and research of the dynamic difference between truncated mooring system and full mooring system have great benefit for future truncation design.
目前主要采用基于静力相似进行截断系泊系统设计。根据经验得知:基于静力相似所设计的截断系泊缆在动力特性上和全水深系泊缆存在明显差异,进而导致系泊缆张力预报的误差。基于动力特性上的差异研究,本文选取某座即将工作于中国南海的半潜平台进行基于静力相似截断系泊系统设计,对截断系泊缆,截断系泊系统进行了一系列动态差异研究。此座半潜平台锚泊最大工作水深1500m,采用动力定位工作最大水深可达3000m。
本文主要工作包括以下几个方面:
1:对模型水动力试验的发展进行了介绍,同时对深海平台模型试验技术和混合模型试验技术进行了阐述。
2:对系泊缆静力计算中悬链线方程进行了推导,简要阐述了系泊缆动力计算模型和计算方法。
3:基于静力相似准则对半潜平台1500m水深系泊系统进行截断优化设计,截断水深分别为1200m,900m,600m,分别给出了各截断系泊系统的静力特性曲线。
4:对各截断水深和全水深耦合数值模型进行时域耦合计算。其中各水深耦合模型采用一致的水动力参数,实际上此过程相当于混合模型试验中的数值外推过程。研究相同水动力参数下,截断系泊系统和全水深系泊系统之间运动预报以及系泊缆张力预报之间的差异,试图证明基于静力相似所设计的截断系泊系统具有一定的预报能力,但是在系泊缆动力特性上仍然无法完全满足全水深动力特性。环境条件选择南海十年一遇的海洋条件,分别选择迎风,迎浪(No Current)和迎风,迎浪,迎流(With Current)两种环境条件。
5:选取600m截断系泊系统,对其进行全面的动力特性计算,并和全水深系泊系统进行比较,包括单根截断系泊缆动力特性差异研究和截断系泊系统动力特性差异研究。其中系泊缆动力特性研究中,分别使系泊缆顶端进行多个振幅,多个振荡周期的规则运动以及不规则运动,运动包括水平和垂向两个方向。截断系泊系统同样进行相同的顶端运动,只不过顶端为浮体-半潜平台。动态差异研究比较项目包括锚泊阻尼,单位振幅动态张力,张力谱以及张力传递函数RAO等。比较过程中对各项对比项目的含义进行了解释说明,其中重点阐述了锚泊阻尼的含义和计算方法,并得出了锚泊阻尼和顶端振荡周期,振荡振幅,拖曳力系数选取,轴向刚度,海流速度等参数间的变化关系。
本论文对截断系泊缆和截断系泊系统进行了全面的动力特性计算,得到了全水深系泊系统和截断系泊系统之间的动力特性差异,对混合模型试验中的系泊缆截断设计有重要意义。
With the development of deep water oil and gas exploration, more and more deepwater platforms will be used for production. Model test is still one of the most important steps for deepwater platform design. However, full water depth model test still can not be performed under conventional scale in current wave basin. Hybrid model test is the most advanced method to solve the problem. And the key problem in hybrid model test is designing an equivalent truncated mooring system. How to design the truncated mooring system which can simulate the full mooring system including static and dynamic characteristics is the ultimate purpose of the truncation design Currently, designing of truncation system is mainly based on static equivalence.
There are obvious dynamic differences between the truncated mooring system and full depth mooring system if the truncation is only based on static equivalence. The dynamic difference will lead to error of prediction of the mooring line tension. In this paper, the author choose a semi submersible, which will be set up in South China Sea, for truncation design based on static equivalence. Then the truncated single mooring line and truncated mooring system are used for dynamic difference studies. The semi submersible can work for 1500m water depth with mooring system and up to 3000m with dynamic positioning.
The following aspects are included in this research:
1: Introduction to the development of the model test, technique of the deepwater platform model test and hybrid model test.
2: Brief introduction of mooring line calculation, including catenary equation for static analysis and numerical model and calculation methods for dynamic analysis.
3: Based on the static equivalence, the truncated mooring systems of semi submersible for 1500m full water depth are designed respectively for 1200m, 900m, and 600m water depth. The static characteristic curves are provided for all truncated mooring systems.
4: Time domain coupled analyses are performed for all water depth numerical models, including truncated and full water depth model. In the analysis, same hydrodynamic parameters are adopted for all numerical models, including truncated model and full depth model. In fact, this process is equivalent to the numerical extrapolation in the hybrid model test. Research on the motion and tension prediction difference between truncated mooring system and full water depth mooring system, under same hydrodynamic parameters; we try to prove that truncated mooring system based on static equivalence has some prediction capability, but dynamic characteristics difference of mooring line still can not fully meet the requirement. 10-years-wave in South China Sea is selected for the analysis. Two types of sea states will be included: 1: 180°waves and wind, without current; 2: 180°waves, wind and current.
5: 600m truncated mooring system is selected for dynamic characteristics difference research, including single truncated mooring line and truncated mooring system. In the single mooring line dynamic studies, the top end of the mooring line will be given regular oscillation with different amplitudes and oscillation periods, and irregular oscillation, including horizontal oscillation and vertical oscillation. The same top end oscillations are performed for the truncated mooring system; with the difference that top end is changed to floating body--semi submersible instead of top end of mooring line. Comparative items for dynamic difference research includes mooring line damping, dynamic tension force per unit amplitude, tension spectrum and tension RAO. Definitions of the items are explained in the comparative process. Especially, mooring line damping is explained in details, including the definition and calculation methods. Through changing the pretension, amplitude, frequency, stiffness, normal drag coefficient, and current speed, the author obtains the results of individual parameter effect on the mooring induced horizontal damping and vertical damping respectively.
In this paper, comprehensive dynamic characteristics are calculated for truncated mooring line and mooring system. The dynamic differences between truncated system and full system are given for further research. The understanding and research of the dynamic difference between truncated mooring system and full mooring system have great benefit for future truncation design.
引文
[1]杨建民,肖龙飞,盛振邦.海洋工程水动力学试验研究.上海:上海交通大学出版社,2008,18-19.
[2] Moxnes,S, and Larsen,K, 1998, Ultra Small Scale Model Testing of a FPSO Ship. Proc.of 17th OMAE Conf., Lisbon, Portugal, Paper No. OMAE98-0381.
[3] Proceedings of 22nd ITTC, Sep1999.
[4] Proceedings of 23nd ITTC, Sep2002.
[5] Stansberg C. T., Oritsland O, Kleiven G. VERIDEEP:Reliable methods for laboratory verification of mooring and stationkeeping in deep water [C]. Offshore Technology Conference. Houston, USA:OTC,2002:12087.
[6] Watts, S., Hybrid Hydrodynamic modeling, Journal of Offshore Technology,1999, Vol.7,no1, 13-17.
[7] Watts,S, Simulation of Metocean Dynamics: Extension of the Hybrid Modelling Technique to Include Additional Environmental Factor, Presented at the SUT Workshop: Deepwater and Open Oceans, The design Basis for Floaters, Houston, TX, 2000.
[8] Buchner, B., Wichers, J.E.W., and de wilde,J.J., Features of the state of the art Deepwater Offshore Basin, OTC,1999, Houston, TX, Paper No.10841.
[9] Stansberg C. T., Ormberg, H., and Oritsland, o., Challenges in Deep Water Experiments:Hybrid Approach. Journal of Offshore Mechanics and Arctic Engineering. 2002, 124(2), 90-96.
[10]张火明.基于等效水深截断的深海平台混合模型试验方法研究.上海交通大学,2005.
[11] Maritime Research Institute Netherland(MARIN), Master User’s Guide For Dynfloat.
[12] Huse,E., Influence of Mooring Line Damping upon Rig Motions, OTC5204, 1986, 433-438.
[13] Huse, E., and Matsumoto, K. Practical Estimation of Mooring Line Damping. OTC5676, 1988, 543-552.
[14] Huse, E., and Matsumoto, K. Mooring Line Damping Due to First and Second Order Vessel Motion, OTC6137, 1989, 135-148.
[15] Van Sluijs, M.F. and Blok,J.J, The Dynamic Behavior of Mooring Lines, Pro. OTC, 1977, OTC2881,Vol.III,31-38.
[16] Van den Boom, H.J.J, Dynamic Behavior of Mooring Lines, Proc. Boss conf, 1985, 359-368.
[17] Kwan, C.T. Design Practice for Mooring of Floating Production Systems, Marine Technology, 1991, Vol 28, No1,30-38.
[18] Triantafyllou, M. S., Belik, A and Shin, H. Dynamic Analysis as a Tool for Open-Sea Mooring System Design, SNAME Transactions, 1985, Vol.93,303-324.
[19] Chen, X.H., Zhang, J. and Peter Jonson, etc, Studies on the Dynamics of Truncated Mooring Line, Pro. 10th ISOPE Conf, 2000, 94-101.
[20] Faltinsen, O.M. Sea Loads on Ships and Offshore Structures. Cambridge University Press, 1993.
[21] Wavesurfer.锚链线静力分析理论推导,精准石油论坛.
[22]唐友刚,张素侠等,深海系泊系统动力特性研究进展,海洋工程,2008,26(1),120-126.
[23] Korterayama,W., Motions of moored floating body and dynamic tension of mooring lines in regular waves. Rep. Res, Inst. Appl. Mech. 1978, X X IV: 99-126.
[24]刘应中,缪国平等,系泊系统动力分析的时域方法,上海交通大学学报,1997,31(11),7-12.
[25] Garrett DL. Dynamic analysis of slender rods. In Proceedings of the 1st International OMAE Conference. Dallas, 1982. 127 -132.
[26] Paulling J R, Webster W C. A consistent, large amplitude analysis of the coupled response of a TLP and tendon system,. In Proceedings of the 5th OMAE Conference. Tokyo, 1986. 3: 126 - 133.
[27] Srinivas N, Deb K. Mutiobjective function optimization using nondominated sorting genetic algorithms. Evolutionary Computation, 1995, 2(3):221-248.
[28] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6 (2):182-197.
[29] DNV-OS-E301_2008-12-09-20-43-16-562
[30] API_2SM, Recommended Practice for Design,Manufacture, Installation, and Maintenance of Synthetic Fiber Ropes for Offshore Mooring.2007
[31]刘应中,缪国平,船舶和海洋结构物在波浪中的运动理论[M].上海:上海交通大学出版社,1987.
[32] Zhao, R. Faltisen, O.M. A comparative study of theoretical models for slow drift sway motions of a marine structure. OMAE, 1988, 2: 153-158
[33] Pinkster,J. A. van Oortmerssen,G. Computation of the first and second order wave forces onoscillation bodies in regular waves. Proc. Second Int. Conf. Numerical Ship Hydrodynamics,136-156.
[34] Cummins W E. The Impulse Response Function and Ship Motions[J]. Schiffstechnik, 1962, 9: 101-109.
[35] C .W William. Webster,.Mooring induced damping[J]. Ocean Engineering, 1995, 22 (6): 571-591.
[36]范菊,锚系阻尼对浮式结构物慢漂运动的影响[D].博士论文.船舶与海洋工程学院,上海交通大学.
[37] Lars Johanning, G.H.Smith, J.Wolfram. Measurements of static and dynamic mooring line damping and their importance for floating WEC devices[J]. Ocean Engineering, 2007, 34,1918-1934
[38] Christian Bauduin, M.Naciri, A contribution on quasi-static mooring line damping [A]. 18th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING, 2000, 125-133.
[39] D.T.Brown, S.Mavrakos. Comparative study on mooring line dynamic loading [J], Journal of Marine Structures 1999, 12(3), 131-151.
[40] Hwang,Y.L Numerical model test for mooring damping [A]. 17th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING, 1998, 98444.
[41] Hamiliton,J., Kitney,N., An alternative mooring line damping methodology for deep water[A]. The 14th International Society of Offshore and Polar Engineers [A], 2004, 23-28
[42] Huse,E. New development in prediction of mooring line damping [A], 23rd offshore Technology Conference, 1991.
[43] Liu,Y and Bergdahl,L Improvement on Huse’s model for estimating mooring cable induced damping[A]. 17th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING , 1998.
[44]张帆,深海立柱式平台概念设计及水动力性能研究[D].博士论文.船舶海洋与建筑工程学院,上海交通大学.
[45]苏一华,杨建民等,基于静力相似的水深截断系泊系统多目标优化设计[J],中国海洋平台,2008,23(1):14-19.
[46] OrcaFlex Manual, Version 9.0a. www.orcina.com.
[2] Moxnes,S, and Larsen,K, 1998, Ultra Small Scale Model Testing of a FPSO Ship. Proc.of 17th OMAE Conf., Lisbon, Portugal, Paper No. OMAE98-0381.
[3] Proceedings of 22nd ITTC, Sep1999.
[4] Proceedings of 23nd ITTC, Sep2002.
[5] Stansberg C. T., Oritsland O, Kleiven G. VERIDEEP:Reliable methods for laboratory verification of mooring and stationkeeping in deep water [C]. Offshore Technology Conference. Houston, USA:OTC,2002:12087.
[6] Watts, S., Hybrid Hydrodynamic modeling, Journal of Offshore Technology,1999, Vol.7,no1, 13-17.
[7] Watts,S, Simulation of Metocean Dynamics: Extension of the Hybrid Modelling Technique to Include Additional Environmental Factor, Presented at the SUT Workshop: Deepwater and Open Oceans, The design Basis for Floaters, Houston, TX, 2000.
[8] Buchner, B., Wichers, J.E.W., and de wilde,J.J., Features of the state of the art Deepwater Offshore Basin, OTC,1999, Houston, TX, Paper No.10841.
[9] Stansberg C. T., Ormberg, H., and Oritsland, o., Challenges in Deep Water Experiments:Hybrid Approach. Journal of Offshore Mechanics and Arctic Engineering. 2002, 124(2), 90-96.
[10]张火明.基于等效水深截断的深海平台混合模型试验方法研究.上海交通大学,2005.
[11] Maritime Research Institute Netherland(MARIN), Master User’s Guide For Dynfloat.
[12] Huse,E., Influence of Mooring Line Damping upon Rig Motions, OTC5204, 1986, 433-438.
[13] Huse, E., and Matsumoto, K. Practical Estimation of Mooring Line Damping. OTC5676, 1988, 543-552.
[14] Huse, E., and Matsumoto, K. Mooring Line Damping Due to First and Second Order Vessel Motion, OTC6137, 1989, 135-148.
[15] Van Sluijs, M.F. and Blok,J.J, The Dynamic Behavior of Mooring Lines, Pro. OTC, 1977, OTC2881,Vol.III,31-38.
[16] Van den Boom, H.J.J, Dynamic Behavior of Mooring Lines, Proc. Boss conf, 1985, 359-368.
[17] Kwan, C.T. Design Practice for Mooring of Floating Production Systems, Marine Technology, 1991, Vol 28, No1,30-38.
[18] Triantafyllou, M. S., Belik, A and Shin, H. Dynamic Analysis as a Tool for Open-Sea Mooring System Design, SNAME Transactions, 1985, Vol.93,303-324.
[19] Chen, X.H., Zhang, J. and Peter Jonson, etc, Studies on the Dynamics of Truncated Mooring Line, Pro. 10th ISOPE Conf, 2000, 94-101.
[20] Faltinsen, O.M. Sea Loads on Ships and Offshore Structures. Cambridge University Press, 1993.
[21] Wavesurfer.锚链线静力分析理论推导,精准石油论坛.
[22]唐友刚,张素侠等,深海系泊系统动力特性研究进展,海洋工程,2008,26(1),120-126.
[23] Korterayama,W., Motions of moored floating body and dynamic tension of mooring lines in regular waves. Rep. Res, Inst. Appl. Mech. 1978, X X IV: 99-126.
[24]刘应中,缪国平等,系泊系统动力分析的时域方法,上海交通大学学报,1997,31(11),7-12.
[25] Garrett DL. Dynamic analysis of slender rods. In Proceedings of the 1st International OMAE Conference. Dallas, 1982. 127 -132.
[26] Paulling J R, Webster W C. A consistent, large amplitude analysis of the coupled response of a TLP and tendon system,. In Proceedings of the 5th OMAE Conference. Tokyo, 1986. 3: 126 - 133.
[27] Srinivas N, Deb K. Mutiobjective function optimization using nondominated sorting genetic algorithms. Evolutionary Computation, 1995, 2(3):221-248.
[28] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6 (2):182-197.
[29] DNV-OS-E301_2008-12-09-20-43-16-562
[30] API_2SM, Recommended Practice for Design,Manufacture, Installation, and Maintenance of Synthetic Fiber Ropes for Offshore Mooring.2007
[31]刘应中,缪国平,船舶和海洋结构物在波浪中的运动理论[M].上海:上海交通大学出版社,1987.
[32] Zhao, R. Faltisen, O.M. A comparative study of theoretical models for slow drift sway motions of a marine structure. OMAE, 1988, 2: 153-158
[33] Pinkster,J. A. van Oortmerssen,G. Computation of the first and second order wave forces onoscillation bodies in regular waves. Proc. Second Int. Conf. Numerical Ship Hydrodynamics,136-156.
[34] Cummins W E. The Impulse Response Function and Ship Motions[J]. Schiffstechnik, 1962, 9: 101-109.
[35] C .W William. Webster,.Mooring induced damping[J]. Ocean Engineering, 1995, 22 (6): 571-591.
[36]范菊,锚系阻尼对浮式结构物慢漂运动的影响[D].博士论文.船舶与海洋工程学院,上海交通大学.
[37] Lars Johanning, G.H.Smith, J.Wolfram. Measurements of static and dynamic mooring line damping and their importance for floating WEC devices[J]. Ocean Engineering, 2007, 34,1918-1934
[38] Christian Bauduin, M.Naciri, A contribution on quasi-static mooring line damping [A]. 18th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING, 2000, 125-133.
[39] D.T.Brown, S.Mavrakos. Comparative study on mooring line dynamic loading [J], Journal of Marine Structures 1999, 12(3), 131-151.
[40] Hwang,Y.L Numerical model test for mooring damping [A]. 17th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING, 1998, 98444.
[41] Hamiliton,J., Kitney,N., An alternative mooring line damping methodology for deep water[A]. The 14th International Society of Offshore and Polar Engineers [A], 2004, 23-28
[42] Huse,E. New development in prediction of mooring line damping [A], 23rd offshore Technology Conference, 1991.
[43] Liu,Y and Bergdahl,L Improvement on Huse’s model for estimating mooring cable induced damping[A]. 17th International Conference on OFFSHORE MECHANICS & ARCTIC ENGINEERING , 1998.
[44]张帆,深海立柱式平台概念设计及水动力性能研究[D].博士论文.船舶海洋与建筑工程学院,上海交通大学.
[45]苏一华,杨建民等,基于静力相似的水深截断系泊系统多目标优化设计[J],中国海洋平台,2008,23(1):14-19.
[46] OrcaFlex Manual, Version 9.0a. www.orcina.com.