海洋输流立管涡激振动试验研究及数值模拟
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摘要
海洋输流立管是海面与海底井口间的主要连接件,是海洋基础结构的关键组成部分,作为海面与海底的一种联系通道,既可用于浮式海洋平台,又可用于固定式平台及钻探船舶。海洋立管内部一般有高压的油或气流过,外部承受波浪、海流作用,当波浪、海流流经立管时,在一定的流速下会产生涡旋脱落,使立管发生涡激振动,当海洋立管自振频率与旋涡脱落频率接近时,振动会迫使旋涡脱落频率固定在结构自振频率附近,发生频率锁定(lock-in)现象,引起管道振动加强。所以,在海洋立管(包括注水立管,生产立管及输出立管)的设计中,涡激振动是一个非常重要问题。
当管内介质流经挠曲的管道时,由于管道曲率的变化和管道的横向振动,流体发生加速,这些加速的力会反过来作用在管道上,引起管道的附加振动。海洋输流立管在涡激振动和管内流体流动的共同作用下可能引起大幅度的振动,使得应力加大,易引起管道的疲劳破坏。目前,同时考虑管道内外流共同作用的涡激振动理论研究较少,试验研究尚未见有报道。因此,考虑管内流体流动及管外海洋环境共同作用的海洋立管试验、理论研究,不仅有重要的科学意义,在工程上亦有较大的应用价值。
本文以海洋输流立管为研究对象,考虑管内流体流动及管外海洋环境的共同作用,对浅水刚性立管进行了有比尺涡激振动试验研究,对深水柔性立管进行了无比尺涡激振动试验研究;采用能量守恒原理建立了立管振动方程,并用Matteoluca尾流振子模型来模拟流体对立管的涡激振动作用力,求解立管涡激振动响应,编制Matlab计算程序,并将数值模拟结果与试验结果进行了对比。结果表明:对于浅水刚性海洋立管,由于立管较短,刚度较大,且管内流速不大,管内流体流动对立管动力特性及动力响应影响不明显;而对于深水柔性立管,随着内流流速的增加,立管自振频率,包括一阶自振频率并二阶自振频率都降低,涡激振动振幅增加,频率降低,立管不同位置处的振动相关性减弱,其振动轨迹愈加规整。
Marine risers are the main connecter between a platform and the mouth of a well in the seabed and can be applied to floating platform, fixed platform and drilling shipping systems. The risers generally contain flowing oil or high pressure gas and bear the action of wave and current outside. When current or wave flows across the risers at certain speed, there will appear vortex shedding, and if the frequency of the risers is close to that of the vortex shedding, oscillation will make the vortex shedding frequency fixed nearby to the structural natural frequency and cause large amplitude vibration which is called‘lock-in’state. So the vortex-induced vibration is an important factor in the design of all riser system, including drilling, production and export riser.
When internal fluid travels along the curved path inside the deflected risers, it experiences centrifugal and coriolis accelerations because of the curvature of the risers and the relative motion of fluid to the time dependent risers motion, respectively. Those accelerations exert against the risers and, in turn, affect the dynamic behavior of the risers and cause additional vibrations. Risers subjected to the vortex-induced vibration and the internal fluid may experience large response which gives rise to oscillatory stresses and cause fatigue damage. Only few numerical studies were focused on the VIV considering internal flowing. For the experimental study, has not been carried out yet. So the experimental study and numerical simulation on VIV considering internal flow flowing has both scientific and practical value.
In this paper, considering internal flowing fluid and external marine environment, the scale experiment on the rigid riser in the shallow water and no-scale experiment on the flexible riser in the deep water were both conducted. For the numerical simulation, the equation of motion was derived based on work-energy principles and vortex strength was expressed using wake oscillate model. The program in Matlab was complied to get the dynamic response. Comparisons were made between the experimental and numerical results. The results indicate that: for the rigid riser in shallow water, the effect of internal flow on its dynamic characteristic and dynamic response is not obvious because of its high stiffness and low internal flow speed. For the flexible riser in the deep water, with the increasing of the internal fluid speed, the natural frequency from the lower one to the higher one all will decrease, the response amplitude increases while the vibration frequency decreases. And the internal fluid flowing lessens the correlation of the vibration between different sections. In addition to that, by plotting both in-line strain and cross-flow strain simultaneously, the figure-of-eight of bending strain is also observed, and the trajectories in different cycle are more accordant with the increase of internal flow speed.
当管内介质流经挠曲的管道时,由于管道曲率的变化和管道的横向振动,流体发生加速,这些加速的力会反过来作用在管道上,引起管道的附加振动。海洋输流立管在涡激振动和管内流体流动的共同作用下可能引起大幅度的振动,使得应力加大,易引起管道的疲劳破坏。目前,同时考虑管道内外流共同作用的涡激振动理论研究较少,试验研究尚未见有报道。因此,考虑管内流体流动及管外海洋环境共同作用的海洋立管试验、理论研究,不仅有重要的科学意义,在工程上亦有较大的应用价值。
本文以海洋输流立管为研究对象,考虑管内流体流动及管外海洋环境的共同作用,对浅水刚性立管进行了有比尺涡激振动试验研究,对深水柔性立管进行了无比尺涡激振动试验研究;采用能量守恒原理建立了立管振动方程,并用Matteoluca尾流振子模型来模拟流体对立管的涡激振动作用力,求解立管涡激振动响应,编制Matlab计算程序,并将数值模拟结果与试验结果进行了对比。结果表明:对于浅水刚性海洋立管,由于立管较短,刚度较大,且管内流速不大,管内流体流动对立管动力特性及动力响应影响不明显;而对于深水柔性立管,随着内流流速的增加,立管自振频率,包括一阶自振频率并二阶自振频率都降低,涡激振动振幅增加,频率降低,立管不同位置处的振动相关性减弱,其振动轨迹愈加规整。
Marine risers are the main connecter between a platform and the mouth of a well in the seabed and can be applied to floating platform, fixed platform and drilling shipping systems. The risers generally contain flowing oil or high pressure gas and bear the action of wave and current outside. When current or wave flows across the risers at certain speed, there will appear vortex shedding, and if the frequency of the risers is close to that of the vortex shedding, oscillation will make the vortex shedding frequency fixed nearby to the structural natural frequency and cause large amplitude vibration which is called‘lock-in’state. So the vortex-induced vibration is an important factor in the design of all riser system, including drilling, production and export riser.
When internal fluid travels along the curved path inside the deflected risers, it experiences centrifugal and coriolis accelerations because of the curvature of the risers and the relative motion of fluid to the time dependent risers motion, respectively. Those accelerations exert against the risers and, in turn, affect the dynamic behavior of the risers and cause additional vibrations. Risers subjected to the vortex-induced vibration and the internal fluid may experience large response which gives rise to oscillatory stresses and cause fatigue damage. Only few numerical studies were focused on the VIV considering internal flowing. For the experimental study, has not been carried out yet. So the experimental study and numerical simulation on VIV considering internal flow flowing has both scientific and practical value.
In this paper, considering internal flowing fluid and external marine environment, the scale experiment on the rigid riser in the shallow water and no-scale experiment on the flexible riser in the deep water were both conducted. For the numerical simulation, the equation of motion was derived based on work-energy principles and vortex strength was expressed using wake oscillate model. The program in Matlab was complied to get the dynamic response. Comparisons were made between the experimental and numerical results. The results indicate that: for the rigid riser in shallow water, the effect of internal flow on its dynamic characteristic and dynamic response is not obvious because of its high stiffness and low internal flow speed. For the flexible riser in the deep water, with the increasing of the internal fluid speed, the natural frequency from the lower one to the higher one all will decrease, the response amplitude increases while the vibration frequency decreases. And the internal fluid flowing lessens the correlation of the vibration between different sections. In addition to that, by plotting both in-line strain and cross-flow strain simultaneously, the figure-of-eight of bending strain is also observed, and the trajectories in different cycle are more accordant with the increase of internal flow speed.
引文
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[3] Feodos’ev, V.P.. Vibrations and stability of a pipe when liquid flows through it [J]. Inzhenernyi Sbornik, 10: 169-170.
[4] Housner, G.W.. Bending vibration of pipeline containing flowing fluid [J]. Journal of Applied Mechanics, 1952, Vol.19: 205-208.
[5] Paidoussis, M. P.. Issid, N.T., Dynamic Stability of pipes conveying fluid [J]. Journal of Sound and Vibration, 1974, Vol.33 (3): 267-294.
[6] Shilling, R.III.. Lou, Y.K., An experimental study on the dynamic response of a vertical cantilever pipe conveying fluid [J]. Journal of Energy Resources Technology, 1980, 102: 129-135.
[7] Wu, M.C., Lou, J.Y.K.. Effect of rigidity and internal flow on marine riser dynamics [J].Applied Ocean Research, 1991, Vol.13 (5): 235-244.
[8] Chen, S.S.. Dynamics stability of tube conveying fluid [J]. Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, 1971, 1469-1485.
[9] Moe.G. and Chucheepsakul.S, 1998. The effect of internal flow on Marine risers. 7th Internatinal Conference on Offshore Mechanics and Arctic Engineering, 375-382.
[10] Namseeg Hong, Taiknyung Huh. Effect of internal flow on vortex-induced viration of riser. Proceediings of the Ninth (1999) International Offshore and Polar Engineering Conference, Brest, France, 688-693.
[11] Carl M. Larsen & Karl H. Halse. Comparison of models for vortex induced vibration of slender structures, Marine Structures, 1997,10,413-441.
[12] Stansby, P. K. & Dixon, A.G.. Simulation of flows around cylinders by a Langrangian vortex scheme. Applied Ocean Research, 1983, 5, 167-178.
[13] Skomedal, N.G. and Vada, T.. Numerical simulation of vortex shedding induced oscillations of circular cylinder. A.S. Veritas Research Report No.87-2005, Oslo, Norway, 1987.
[14] Hansen, H.T., Skomedal, N.G. and Vada, T.. A method for computation of intergrated vortex induced fluid loading and response interaction of marine risers in waves and current. In Proc. Fifth Int. Conf. on Behaviour of Offshore Structures, Trondheim, Norway, 1988, 841-857.
[15] Hansen, H.T., Skomedal, N.G. and Vada, T.. Compution of vortex induced fluid loading and response interaction of marine risers. Proc. Eighth Int. Conf. on Offshore Mechanics and Arctic Engineering, The Hague, The Netherlands, 1989, 327-334.
[16] Skomedal, N.G., Teigen, P. and Vada, T.. Computation of vortex induced vibration and the effect of correlation on ciucular cylinders in oscillatory flow. In Proc. Eighth Int. Conf. on Offshore Mechanics and Arctic Engineering , The Hague, The Netherlands, 1989, 311-318.
[17] Ottesen Hansen, N.E.. Vibrations of pipe arrays in waves. In Proc.Third Int. Conf. on Behaviour of Offshore Structures, Boston, MA, 1982, 641-650.
[18] Nedergaard, H., Ottesen Hansen, N.E. and Fines, S.. Response of free hanging tethers. In Proc. Seventh Int. Conf. on Behaviour of Offshore Stuctures, Boston, MA, 1994, 315-326.
[19] Lie, H.. A time domain model for simulation of vortex induced vibrations on a cable. In Proc. Sixth Int. Conf. on Flow Induced Vibrations, London, UK, 1995, 455-466.
[20] Sarpkaya, T.. Fluid forces on oscillating cylinders. Journal of Waterway, Port, Coastal and Ocean Division, 1978, 104, 275-290.
[21] Triantafyllou, M.S., Engebretsen, K., Burgess, J.J., Yoerger, D.R. and Grosenbaugh, M.A.. A full-scale experiment and theoretical study of the dynamics of underwater vehicles employing very long tethers. In Proc. Fifth Int. Conf. on Behaviour of Offshore Structures, Trondheim, Norway, 1988, 549-563.
[22] Vandiver, J.K., Li, L. and Venogupal, M. SHEAR Program Theoretical Manual. Dept. of Ocean Engineering, MIT, Cambridge, MA, 1993.
[23] Vandiver, J.K., and Li, L.. SHEAR 7 Progarm Theoretical Manual. Dept. of Ocean Engineering, MIT, Cambridge, MA, 1994.
[24] Vandiver, J.K. and Chung, T.Y.. Predicted and measured response of flexible cylinders in sheared flow. Presented at ASME Winter Annual Meeting Symposium on Vortex-Induced Vibration, Chicago, IL, 1988.
[25] Vandiver, J.K.& Jong, J.Y.. The relationship between in-line and cross-flow vortex-induced vibration of cylinders. Journal of Fluids and Structures, 1987, 381-399.
[26] Vandiver, J.K.. Drag coefficients of long flexible cylinders. In Proc. 1983 Offshore Technology Conf., Paper No. 4490, Houston, TX, 1983, 405-414.
[27] Moe. G. and Overvik, T..Current-induced motions of multiple risers. In Proc. Third Int. Conf. on Bahaviour of Offshore Structures, Boston, MA, 1982, 618-639.
[28] Larsen, C.M. and Bech, A.. Stress analysis of marine risers under lockin condition. In Proc. Fifth Int. Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, 1986, 450-457.
[29] Lyons, G. J. & Patel, M.H.. A prediction technique for vortex induced transverse response of marine risers and tethers. Journal of Sound and Vibration, 1986, 111, 467-487.
[30] Lyons, G. J. & Patel, M.H.. Application of a general technique for prediction of riser vortex-induced response in wave and current. Journal of Offshore Mechanics and Arctic Engineering, 1989, 111, 82-91.
[31] Allen, D.W. , Vortex-induced vibration analysis of the auger TLP production and steel catenary export risers. OTC 7821, 1995
[32] Denison, E.B., Mars TLP drilling and production riser systems. OTC 8514, 1997.
[33] Huse, E., Kleiven, G. and Nielsen, F.G., Large scale model testing of deep sea risers. OTC,1998.
[34] Jaap J.de Wilde & Rene H. M. Huijsmans. Laboratory inverstigation of long riser VIV response. 14th International Offshore and Polar Engineering Conference. 2004,511-516.
[35] Hidetaka Senga, Wataru Koterayama. An experiment and numerical study on vortex induced vibrations of a long flexible riser undergoing irregular motion at its top end. The Proceedings of the International Offshore and Polar Engineering Conference, 2005,vol.15: 265-271.
[36] G.S.Baarholm, C.M.Larsen, H.Lie. On fatigue damage accumulation from in-line and cross-flow vortex-induced vibrations on risers. Journal of Fluids and Structures, 2006, 109-127.
[37] Jim Maher,Lyle Finn. A combined time-frequency domain procedure to estimate riser fatigue caused by vortex-induced vibration. 32nd Annual Offshore Technology Conference, 2000, 541-546.
[38] Francisco E.Roveri与J.Kim Vandiver. Slender EX: using shear7 for assessment of fatigue damage caused by current induced vibrations. 20th International Conference on Offshore Mechanics and Arctic Engineering, 2001, 427-434.
[39] Bernt J.Leira, Trond Stokka Meling, Carl M. Larsen et.al. Assessment of fatigue safety factors for deep-water risers in relation to VIV. Journal of Offshore Mechanics and Arctic Engineering, 2005, 353-358.
[40] Paolo Simantiras, Neil Willis. Investigation on vortex induced oscillations and helical strakes effectiveness at very high incidence angles, ISOPE, 1999.
[41] J.C.Owen and P.W.Bearman.Passive Control of VIV With Drag Reduction.Journal of Fluid and Structures (2001) 15,597—605.
[42] Naoaki Mikta, Akiyoshi Bando, Koji Otsuka. Experimental study of a flexible riser covered with helical strakes. The Thirteenth Internatinal Offshore and Polar Engineering Conference, 2003.
[43] Sea Technology Group. Retrofit to reduce drag and vortex-induced vibration. Sea Technology, 2004.
[44] A.D.Trim, H.Braaten, H.Lie, M.A.Tognarelli, 2005. Experimental investigation of vortex-induced vibration of long marine risers, Journal of Fluids and Structures, 21:335-361.
[45] Gro Sagli Baarholm, Carl Martin Larsen, Halvor Lie, 2005. Reduction of VIV using suppression devices- An empirical approach, Marine Structures, 18:489-510.
[46] Carl M. Larsen, Gro Sagli Baarholm, Halvor Lie. Influence from helical strakes on vortex induced vibrations and static deflection of drilling risers. International Conference on Offshore Mechanics and Arctic Engineering, 2005,477-483.
[47] Aiten, J.. An account of some experiments on rigidity produced by centrifugal force [J]. Philosophical Magazine, 1878, Vol.5: 81-105.
[48]娄敏,郭海燕,杨新华,傅强.海底输液管道内流、轴向力和压强对允许悬空长度的影响.中国海洋大学学报, 2006, Vol.36 No.2: 341-344.
[49]杨新华,郭海燕,娄敏.考虑阻尼海底悬跨段管道的动力特性及允许悬空长度.海洋工程,2005,Vol. 23 No.1:1-5.
[50] Recommended fractice DNV-RP-C203, 2005.
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[52] Jen-Yi Jong and J.Kim Vandiver. Response analysis of the flow-induced vibration of flexible cylinders tested at castine, maine in July and August of 1981. Massachusetts Institute of Technology, 1983.
[53] N.Jauvtis, C.H.K.Williamson. The effect of two degrees of freedom on vortex-induced vibration at low mass and damping. J.Fluid Mech, 2004, 509, 23-62.
[54] Matteoluca F., Emmanuel D. L.. Coupling of structure and wake oscillators in vortex-induced vibrations [J]. Journal of Fluids and Structures, 2004, 1: 116-133.
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[2] Blevins, R D. Flow-induced vibrations[M].2nd edn. New York: Van Nostrand & Co., 1990.
[3] Feodos’ev, V.P.. Vibrations and stability of a pipe when liquid flows through it [J]. Inzhenernyi Sbornik, 10: 169-170.
[4] Housner, G.W.. Bending vibration of pipeline containing flowing fluid [J]. Journal of Applied Mechanics, 1952, Vol.19: 205-208.
[5] Paidoussis, M. P.. Issid, N.T., Dynamic Stability of pipes conveying fluid [J]. Journal of Sound and Vibration, 1974, Vol.33 (3): 267-294.
[6] Shilling, R.III.. Lou, Y.K., An experimental study on the dynamic response of a vertical cantilever pipe conveying fluid [J]. Journal of Energy Resources Technology, 1980, 102: 129-135.
[7] Wu, M.C., Lou, J.Y.K.. Effect of rigidity and internal flow on marine riser dynamics [J].Applied Ocean Research, 1991, Vol.13 (5): 235-244.
[8] Chen, S.S.. Dynamics stability of tube conveying fluid [J]. Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, 1971, 1469-1485.
[9] Moe.G. and Chucheepsakul.S, 1998. The effect of internal flow on Marine risers. 7th Internatinal Conference on Offshore Mechanics and Arctic Engineering, 375-382.
[10] Namseeg Hong, Taiknyung Huh. Effect of internal flow on vortex-induced viration of riser. Proceediings of the Ninth (1999) International Offshore and Polar Engineering Conference, Brest, France, 688-693.
[11] Carl M. Larsen & Karl H. Halse. Comparison of models for vortex induced vibration of slender structures, Marine Structures, 1997,10,413-441.
[12] Stansby, P. K. & Dixon, A.G.. Simulation of flows around cylinders by a Langrangian vortex scheme. Applied Ocean Research, 1983, 5, 167-178.
[13] Skomedal, N.G. and Vada, T.. Numerical simulation of vortex shedding induced oscillations of circular cylinder. A.S. Veritas Research Report No.87-2005, Oslo, Norway, 1987.
[14] Hansen, H.T., Skomedal, N.G. and Vada, T.. A method for computation of intergrated vortex induced fluid loading and response interaction of marine risers in waves and current. In Proc. Fifth Int. Conf. on Behaviour of Offshore Structures, Trondheim, Norway, 1988, 841-857.
[15] Hansen, H.T., Skomedal, N.G. and Vada, T.. Compution of vortex induced fluid loading and response interaction of marine risers. Proc. Eighth Int. Conf. on Offshore Mechanics and Arctic Engineering, The Hague, The Netherlands, 1989, 327-334.
[16] Skomedal, N.G., Teigen, P. and Vada, T.. Computation of vortex induced vibration and the effect of correlation on ciucular cylinders in oscillatory flow. In Proc. Eighth Int. Conf. on Offshore Mechanics and Arctic Engineering , The Hague, The Netherlands, 1989, 311-318.
[17] Ottesen Hansen, N.E.. Vibrations of pipe arrays in waves. In Proc.Third Int. Conf. on Behaviour of Offshore Structures, Boston, MA, 1982, 641-650.
[18] Nedergaard, H., Ottesen Hansen, N.E. and Fines, S.. Response of free hanging tethers. In Proc. Seventh Int. Conf. on Behaviour of Offshore Stuctures, Boston, MA, 1994, 315-326.
[19] Lie, H.. A time domain model for simulation of vortex induced vibrations on a cable. In Proc. Sixth Int. Conf. on Flow Induced Vibrations, London, UK, 1995, 455-466.
[20] Sarpkaya, T.. Fluid forces on oscillating cylinders. Journal of Waterway, Port, Coastal and Ocean Division, 1978, 104, 275-290.
[21] Triantafyllou, M.S., Engebretsen, K., Burgess, J.J., Yoerger, D.R. and Grosenbaugh, M.A.. A full-scale experiment and theoretical study of the dynamics of underwater vehicles employing very long tethers. In Proc. Fifth Int. Conf. on Behaviour of Offshore Structures, Trondheim, Norway, 1988, 549-563.
[22] Vandiver, J.K., Li, L. and Venogupal, M. SHEAR Program Theoretical Manual. Dept. of Ocean Engineering, MIT, Cambridge, MA, 1993.
[23] Vandiver, J.K., and Li, L.. SHEAR 7 Progarm Theoretical Manual. Dept. of Ocean Engineering, MIT, Cambridge, MA, 1994.
[24] Vandiver, J.K. and Chung, T.Y.. Predicted and measured response of flexible cylinders in sheared flow. Presented at ASME Winter Annual Meeting Symposium on Vortex-Induced Vibration, Chicago, IL, 1988.
[25] Vandiver, J.K.& Jong, J.Y.. The relationship between in-line and cross-flow vortex-induced vibration of cylinders. Journal of Fluids and Structures, 1987, 381-399.
[26] Vandiver, J.K.. Drag coefficients of long flexible cylinders. In Proc. 1983 Offshore Technology Conf., Paper No. 4490, Houston, TX, 1983, 405-414.
[27] Moe. G. and Overvik, T..Current-induced motions of multiple risers. In Proc. Third Int. Conf. on Bahaviour of Offshore Structures, Boston, MA, 1982, 618-639.
[28] Larsen, C.M. and Bech, A.. Stress analysis of marine risers under lockin condition. In Proc. Fifth Int. Offshore Mechanics and Arctic Engineering Symposium, Tokyo, Japan, 1986, 450-457.
[29] Lyons, G. J. & Patel, M.H.. A prediction technique for vortex induced transverse response of marine risers and tethers. Journal of Sound and Vibration, 1986, 111, 467-487.
[30] Lyons, G. J. & Patel, M.H.. Application of a general technique for prediction of riser vortex-induced response in wave and current. Journal of Offshore Mechanics and Arctic Engineering, 1989, 111, 82-91.
[31] Allen, D.W. , Vortex-induced vibration analysis of the auger TLP production and steel catenary export risers. OTC 7821, 1995
[32] Denison, E.B., Mars TLP drilling and production riser systems. OTC 8514, 1997.
[33] Huse, E., Kleiven, G. and Nielsen, F.G., Large scale model testing of deep sea risers. OTC,1998.
[34] Jaap J.de Wilde & Rene H. M. Huijsmans. Laboratory inverstigation of long riser VIV response. 14th International Offshore and Polar Engineering Conference. 2004,511-516.
[35] Hidetaka Senga, Wataru Koterayama. An experiment and numerical study on vortex induced vibrations of a long flexible riser undergoing irregular motion at its top end. The Proceedings of the International Offshore and Polar Engineering Conference, 2005,vol.15: 265-271.
[36] G.S.Baarholm, C.M.Larsen, H.Lie. On fatigue damage accumulation from in-line and cross-flow vortex-induced vibrations on risers. Journal of Fluids and Structures, 2006, 109-127.
[37] Jim Maher,Lyle Finn. A combined time-frequency domain procedure to estimate riser fatigue caused by vortex-induced vibration. 32nd Annual Offshore Technology Conference, 2000, 541-546.
[38] Francisco E.Roveri与J.Kim Vandiver. Slender EX: using shear7 for assessment of fatigue damage caused by current induced vibrations. 20th International Conference on Offshore Mechanics and Arctic Engineering, 2001, 427-434.
[39] Bernt J.Leira, Trond Stokka Meling, Carl M. Larsen et.al. Assessment of fatigue safety factors for deep-water risers in relation to VIV. Journal of Offshore Mechanics and Arctic Engineering, 2005, 353-358.
[40] Paolo Simantiras, Neil Willis. Investigation on vortex induced oscillations and helical strakes effectiveness at very high incidence angles, ISOPE, 1999.
[41] J.C.Owen and P.W.Bearman.Passive Control of VIV With Drag Reduction.Journal of Fluid and Structures (2001) 15,597—605.
[42] Naoaki Mikta, Akiyoshi Bando, Koji Otsuka. Experimental study of a flexible riser covered with helical strakes. The Thirteenth Internatinal Offshore and Polar Engineering Conference, 2003.
[43] Sea Technology Group. Retrofit to reduce drag and vortex-induced vibration. Sea Technology, 2004.
[44] A.D.Trim, H.Braaten, H.Lie, M.A.Tognarelli, 2005. Experimental investigation of vortex-induced vibration of long marine risers, Journal of Fluids and Structures, 21:335-361.
[45] Gro Sagli Baarholm, Carl Martin Larsen, Halvor Lie, 2005. Reduction of VIV using suppression devices- An empirical approach, Marine Structures, 18:489-510.
[46] Carl M. Larsen, Gro Sagli Baarholm, Halvor Lie. Influence from helical strakes on vortex induced vibrations and static deflection of drilling risers. International Conference on Offshore Mechanics and Arctic Engineering, 2005,477-483.
[47] Aiten, J.. An account of some experiments on rigidity produced by centrifugal force [J]. Philosophical Magazine, 1878, Vol.5: 81-105.
[48]娄敏,郭海燕,杨新华,傅强.海底输液管道内流、轴向力和压强对允许悬空长度的影响.中国海洋大学学报, 2006, Vol.36 No.2: 341-344.
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