海洋柔性结构涡激振动的流固耦合机理和响应

陈伟民; 付一钦; 郭双喜; 姜春晖

doi:10.6052/1000-0992-16-005

海洋柔性结构涡激振动的流固耦合机理和响应

doi: 10.6052/1000-0992-16-005

陈伟民^{1, 2, ,},
付一钦^{1, 2},
郭双喜^{1, 2},
姜春晖^{1, 2}

1.
中国科学院力学研究所流固耦合系统力学重点实验室, 北京 100190
2.
中国科学院大学工程科学学院, 北京 100049

详细信息

通讯作者:
陈伟民,女,博士,中国科学院力学研究所研究员.2000年北京航空航天大学获工学博士学位,2002年北京大学力学系博士后出站进入中科院力学所,2012年曾于美国德州大学奥斯汀分校做高级访问学者.主要从事海洋和航空工程中的结构流固耦合动响应研究,研究领域涉及水弹性/气动弹性力学、结构振动和动响应、深水柔性立管涡激振动、缺陷材料中弹性波传播和反问题等.先后在Ocean Engineering和Materials Science and Engineering A等海洋工程和结构材料期刊上发表论文50余篇. E-mail: wmchen@imech.ac.cn

中图分类号: O353.4
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出版历程
- 收稿日期: 2016-01-27
- 网络出版日期: 2016-09-18
- 刊出日期: 2017-02-24

Review on fluid-solid coupling and dynamic response of vortex-induced vibration of slender ocean cylinders

CHEN W M^{1, 2
, ,},
FU Yiqin^{1, 2},
GUO Shuangxi^{1, 2},
JIANG Chunhui^{1, 2}

1.
Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
2.
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

More Information

Corresponding author: CHEN W M

摘要

摘要: 对近几十年来国内外在涡激振动的基础研究包括机理认识和动响应分析等方面的进展进行了论述，尤其针对海洋油气平台中的立管、隔水管等细长柔性结构的涡激振动.描述了涡激振动这种典型的非线性流固耦合现象所具有的特征，包括自激、自限制、展向相关、尾迹水动力与结构动力的流固耦合等及其主要影响参数.介绍了目前常用的结构响应预测方法和相关实验.通过讨论当前理论研究和实际工程中的热点问题，诸如多模态宽带振动、浮体运动与水下立管的耦合、响应抑制措施、双向振动、高雷诺数下的大尺度物理实验等，对今后该领域的研究方向进行了力所能及的展望.
- 涡激振动 /
- 流固耦合 /
- 深水立管 /
- 振动与波
Abstract: The recent development on the mechanism and response analysis of vortex-induced vibration (VIV) of flexible cylinders, particularly the slendr risers in deep water, are presented. The main characters of VIV, such as self-excited, self-limited and span coherence and fluid-solid coupling, along with principle influence factors are presented, and different prediction approaches (incluing empirical and numerical methods) and experiments are reviewed. Then we are trying to give our perspectives on some challenging issues, e.g., multi-mode and wide-band VIV, dynamic interaction between top-end motion and submarine riser, VIV suppression, CF and IL motion and large scale experiment at high Reynolds number, of slender riser's VIV so that the future researches on VIV would be focued on those areas.
- vortex-induced vibration /
- interaction between solid and fluid /
- deep-water riser /
- vibration and wave

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图 1 深水平台及其水下立管系统(http://oceanexplorer.noaa.gov/explorations/12lophelia/background/platforms/media/platform_types.html)

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图 2 几种典型海洋立管. (a) 顶张力立管, (b) 钢悬链线立管, (c) 惰性S立管, (d) 陡峭型S立管(e)惰性波浪立管, (f) 惰性型波浪立管

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图 3 涡激振动基本现象的实验观察. (a) 风洞中的弹性支持刚性圆柱的锁频共振 (Feng, 1968), (b) 水中弹性支持刚性圆柱的锁频共振 (Williamson & Govardhan, 2004) (c) 静止圆柱的斯特鲁哈数与雷诺数的关系 (Blevins, 1987)

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图 4 形态各异的圆柱尾迹涡脱落模式.(a) Brika和Laneville(1993) 首次实验展示了不同响应分支对应2S和2P不同的涡脱落模式;(b)铰支的圆柱实验中, 在高响应分支时观察到的2C模式(Flemming & Williamson, 2003);(c)在XY双向振动时观察到的的数值模拟超高响应分支所对应的2T模式(Jauvtis & Williamson, 2003);(d)Williamson和Govardhan(2004)实验结果(在层流中, Re<200);(e)Meneghini & Bearman(1993)的结果(Re<200)

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图 5 不同涡模式对应不同的结构运动幅值 (Wiliamson & Govardhan, 2004)

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图 6 尾迹涡和结构运动的展向不均匀分布显示了涡激振动的展向相关性. (a) 三维CFD计算得到的柔性圆柱尾迹的涡量场(Wiliamson & Govardhan, 2004), (b) 三维结构的响应位移沿展向位置的时间演化(张立武, 2010)

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图 7 驻波、行波以及中间状态的位移响应. (a) 驻波位移时空云图;(b) 行波位移时空云图; (c) 中间位移状态时空云图; (d) 驻波均方根(root mean square, RMS)位移; (e) 行波RMS位移; (f) 中间状态RMS位移

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图 8 出现行波的临界模态阶数n_cri随系统参数的变化关系.(a)n_cri随长径比L/D的变化(b)n_cri随结构阻尼比ζ_sn的变化, (c)n_cri随水动力阻力C_d的变化

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图 9 长度3 000 m变张力、变刚度立管的典型模态. (a)第1阶模态, (b) 第2阶模态, (c)第3阶模态, (d) 第5阶模态(e)第9阶模态, (f) 第13阶模态, (g)第23阶模态, (h) 第29阶模态

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图 10 变刚度立管的涡激振动响应. (a) 位移均方根, (b) 失稳响应

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图 11 不同耦合模型给出的锁频阶段位移、升力系数、相位(加速度耦合模型)响应结果(Facchinetti et al. 2004a). (a) 位移耦合模型, (b) 速度耦合模型, (c) 加速度耦合模型

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图 12 不同模型预测的锁频带宽简缩速度范围以及与实验结果的对比. (a) 非线性模型, (b) 位移耦合模型, (c) 速度耦合模型, (d) 加速度耦合模型

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图 13 简缩速度的变化对涡激振动响应影响的实验结果 (Brika, 1995) . (a) 相位响应, (b) 涡脱落频率, (c) 振幅响应

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图 14 S_G数对振幅峰值的影响

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图 15 不同质量比结构锁频简缩速度范围 (Williamson & Roshko，1988) . (a) 以U_r = U=f_ND衡量锁频范围, (b) 以U_r/f* = U/f_rD衡量锁频范围

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图 16 简缩速度对锁频阶段的附加质量系数和频率比的影响(Sarpkaya, 2004) . (a) 简缩速度对附加质量系数的影响, (b) 简缩速度对频率之比的影响

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图 17 质量比与锁频阶段的频率比的对应关系 (Govardhan & Williamson, 2004) . (a) 不同质量比对应的锁频阶段频率比, (b) 不同质量比对应的下枝频率比

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图 18 质量比μ 对频率比、振幅、升力系数的影响. (a) 频率比;(b) 振幅; (c) 升力系数

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图 19 尾流振子耦合系统示意图

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图 20 涡激振动的升力系数和响应振幅实验结果. (a)升力系数等高线(Govardhan & Williamson, 2004) ; (b) 锁频阶段圆柱振动响应 (Vikestad et al., 2000)

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图 21 基于有限元数值模拟的FR在不同流场的涡激振动响应. (a) 刚性圆柱在均匀流中, (b) 柔性缆索在均匀流中, (c) 柔性缆索在剪切流中, (d) 柔性缆索在阶梯流中

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图 22 剪切流中最大位移/应力响应随流速的变化. (a) 平均RMS振幅(A/D)随速度的变化, (b) 平均RMS应力随速度的变化

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图 23 立管的固有振动频率及St速度曲线

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图 24 基于模态能量法的多模态涡激振动响应的模态加权结果. (a) 最大流速为0.54 m/s, (b) 最大流速为1.14 m/s

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图 25 均匀流和非均匀流中细长FR的多模态涡激振动响应. (a) 均匀流中的RMS 位移响应, (b) 均匀流中的位移时空演化, (c) 剪切流的RMS 位移 (最大流速0.54 m/s), (d) 剪切流的位移时空演化(最大流速0.54 m/s), (e) 剪切流的RMS 位移 (最大流速1.14 m/s), (f) 剪切流的位移时空演化 (最大流速1.14 m/s)

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图 26 平台的横荡运动与水下立管涡激振动的动力耦合响应. (a) 平台横档运动引起的立管振幅放大, (b) 不同平台振荡幅度下的立管振动位移

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图 27 平台的垂荡运动与水下立管涡激振动的动力耦合响应. (a) 考虑与不考虑平台垂荡的立管最大位移, (b) 立管参数激励响应中出现的模态转换

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图 28 悬链线结构示意图. (a) 悬链线结构静力平衡(b)三维系泊系统示意图

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表 1 涡脱落形式与雷诺数的关系

参考文献(283)

[1]	毕勤胜, 陈章耀, 朱玉萍, 邹勇. 2003.参数激励耦合系统的复杂动力学行为分析. 力学学报, 35: 123-127 http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200303018.htm
[2]	Bi Q S, Chen Z Y, Zhu Y P, Zou Y. 2003. Dynamical analysis ofcoupled oscillators with parametrical excitation. ActaMechanica Sinica, 35: 123-127. http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB200303018.htm
[3]	陈伟民, 张立武, 李敏. 2010.采用改进尾流振子模型的柔性海洋立管的涡激振动响应分析. 工程力学,27: 240-246 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201005037.htm
[4]	Chen W M, Zhang L W, Li M. 2010. Prediction ofvortex-induced vibration of flexible riser using improvedwake-oscillator model. Engineering Mechanics, 27:240-246. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201005037.htm
[5]	陈伟民, 郑仲钦, 张立武, 李敏. 2011.内波波致剪切流作用下深海立管的涡激振动. 工程力学, 28:250-256 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201112038.htm
[6]	Chen W M, Zheng Z Q, Zhang L W, Li M. 2011.Vortex-induced vibration of deep water flexible risersexperiencing internal-wave-induced shear flow. EngineeringMechanics, 28: 250-256. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201112038.htm
[7]	陈伟民, 郑仲钦, 郭双喜. 2014.浮式平台的横荡运动对水下柔性立管涡激振动的影响. 海洋工程, 32: 8-13 http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201403002.htm
[8]	Chen W M, Zheng Z Q, Guo S X. 2014. Impact of floatingtop sway on the vortex-induced vibration of submarine riser. The Ocean Engineering, 32: 8-13 http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201403002.htm
[9]	段梦兰, 胡知辉, 曹静, 赵天奉, 房军. 2011.深水钢悬链线立管触地区疲劳实验系统设计. 力学与实践, 33:15-19 http://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201103006.htm
[10]	Duan M L, Hu Z H, Cao J, Zhao T F, Fang J. 2011. The designof fatigue experimental system for steel catenary riser intouchdown zone. Mechanics in Engineering, 33: 15-19. http://www.cnki.com.cn/Article/CJFDTOTAL-LXYS201103006.htm
[11]	付强. 2004. 海洋输液立管动力特性及涡激振动响应理论研究.[硕士论文]. 青岛：中国海洋大学
[12]	Fu Q. 2004. Study on the dynamiccharacteristics and responses of vortex-induced vibration ofmarine risers conveying fluid. [Master Thesis]. Qingdao: OceanUniversity of China.
[13]	葛斐, 惠磊, 洪友士. 2007.水中悬浮隧道锚索在剪切流中的涡激响应.中国科学院研究生院学报, 24: 352-356 http://www.cnki.com.cn/Article/CJFDTOTAL-ZKYB200703012.htm
[14]	Gei F, Hui L, Hong Y S. 2007. vortex-inducedvibration of submarine floating tunnel undergoing shear flow. Journal of University of Chinese Academy of Sciences, 24:352-356. http://www.cnki.com.cn/Article/CJFDTOTAL-ZKYB200703012.htm
[15]	谷家扬, 吕海宁, 杨建民. 2012.随机波浪中张力腿平台耦合运动及系泊系统特性研究. 海洋工程, 30: 42-48 http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201204007.htm
[16]	Gu J Y, Lu H N, Yang J M. 2012. Studies on couplingdynamic response and characteristics mooring system of TLP instochastic waves. The Ocean Engineering, 30: 42-48. http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201204007.htm
[17]	谷斐. 2012. 隔水管涡激振动抑制装置的流动控制实验研究.[博士论文]. 上海: 上海交通大学
[18]	Gu F. 2012. Experimental study onflow control of risers with vortex induced vibration suppressiondevices attached. [PhD Thesis]. Shanghai: Shanghai Jiao TongUniversity.
[19]	郭双喜. 2015. 考虑结构耦合的浮式风机整体系统动响应分析.[硕士论文]. 北京: 中国科学院力学研究所 http://www.irgrid.ac.cn/handle/1471x/475240/handle/1471x/475238/browse?type=title&sort_by=1&order=ASC&year=&rpp=20&offset=60
[20]	Guo S X. 2015. Analysis ondynamic response of floating wind turbine considering couplingbetween elastic components. [Master Thesis]. Beijing: Institute ofMechanics, Chinese Academy of Sciences. http://www.irgrid.ac.cn/handle/1471x/475240/handle/1471x/475238/browse?type=title&sort_by=1&order=ASC&year=&rpp=20&offset=60
[21]	郭海燕, 付强, 娄敏. 2005.海洋输液立管涡激振动响应及其疲劳寿命研究. 工程力学, 22:220-224 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200504039.htm
[22]	Guo H Y, Fu Q, L M. 2005. Vortex-induced vibrations andfatigue life of marine risers conveying flowing fluid. Engineering Mechanics, 22: 220-224. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX200504039.htm
[23]	黄智勇, 潘志远, 崔维成．2007.两向自由度低质量比圆柱体涡激振动的数值计算. 船舶力学, 11:1-9 http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200701000.htm
[24]	Huang Z Y, Pan Z Y, Cui W C. 2007. Numerical simulation ofVIV of a circular cylinder with two degrees of freedom and lowmass-ratio. Journal of Ship Mechanics, 11: 1-9. http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200701000.htm
[25]	菅永军, 鄂学全, 柏威. 2003.参数激励圆柱形容器中的非线性Faraday波. 应用数学和力学, 24:60-66 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200310009.htm
[26]	Jian Y J, E X Q, Bai W. 2003. Nonlinear Faraday waves in aparametrically excited circular cylindeical container. Applied MAthmatics and Mechanics, 24: 60-66. http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX200310009.htm
[27]	雷松,张文首, 赵岩, 岳前进. 2010. FDPSO立管涡激振动响应分析. 工程力学,27: 294-298 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX2010S1065.htm
[28]	Lei S, Zhang W S, Zhao Y, Yue Q J. 2010.Influence of heave motion on vortex-induced vibrations of FDPSOrisers. Engineering Mechanics, 27: 294-298. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX2010S1065.htm
[29]	李曼. 2013. 立管涡激振动模型试验中的尺度效应问题研究.[硕士论文]. 上海: 上海交通大学 Li M. 2013.
[30]	An investigation ofscale effects in the vortex-induced vibration model test ofrisers. [Master Thesis]. Shanghai: Shanghai Jiao Tong University.
[31]	潘志远, 崔维成, 刘应中. 2005.低质量--阻尼因子圆柱体的涡激振动预报模型. 船舶力学, 9:115-124 http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200505013.htm
[32]	Pan Z Y, Cui W C, Liu Y Z. 2005. A predicting model forself-excited VIV of a circular cylinder at low mass-dam ping. Journal of Ship Mechanics, 9: 115-124. http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200505013.htm
[33]	秦伟. 2013. 双自由度涡激振动的涡强尾流振子模型研究.[博士论文].哈尔滨：哈尔滨工程大学 Qin W. 2013.
[34]	Study on vortexinduced vibration in two degrees of freedom using vortex strengthwake oscillator. [PhD Thesis]. Harbin: Harbin EngineeringUniversity.
[35]	邵传平, 陈野军, 王赛, 秦广素. 2014.流向振荡柱体尾流控制研究进展. 力学进展, 44: 188-235 http://lxjz.cstam.org.cn/CN/abstract/abstract144960.shtml
[36]	ShaoC P, Chen Y J, Wang S, Qin G S. 2014. Advances in the control ofwakes behind an in-line oscillating cylinder. Advances inMechanics, 44: 201405. http://lxjz.cstam.org.cn/CN/abstract/abstract144960.shtml
[37]	唐国强, 吕林, 滕斌, 谢彬, 宋吉林, 张建侨, 吴浩. 2001.大长细比柔性杆件涡激振动实验. 海洋工程, 29: 18-25 http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201101002.htm
[38]	Tang G Q,Lü L, Teng B, Xie B, Song J L, Zhang J Q, Wu H. 2001.Laboratory measurement of vortex-induced vibration of longflexible riser. The Ocean Engineering, 29: 18-25. http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201101002.htm
[39]	唐驾时, 贺新柱. 2001. 参数振动系统的共振分析.岳阳师范学院学报自然科学版, 14: 34-40 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSF200101000.htm
[40]	Tang J S, He X Z.2001. Response analysis of parametrically excited system. Journal of Yueyang Normal University (Natural Science,14: 34-40. http://www.cnki.com.cn/Article/CJFDTOTAL-YYSF200101000.htm
[41]	唐友刚, 邵卫东, 张杰, 王丽元, 桂龙. 2013.深海顶张力立管参激--涡激耦合振动响应分析, 工程力学, 30:282-286 http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201305045.htm
[42]	Tang Y G, Shao W D, Zhang J, Wang L Y, Gui L. 2013.Dynamic response analysis for coupled parametric vibration andvortex-induced vibration of top-tensioned riser in deep-sea. Engineering Mechanics, 30: 282-286. http://www.cnki.com.cn/Article/CJFDTOTAL-GCLX201305045.htm
[43]	王东耀, 凌国灿. 1998.在平台振荡条件下TLP张力腿的涡激非线性响应. 海洋学报, 20:119-128 http://www.cnki.com.cn/Article/CJFDTOTAL-SEAC803.016.htm
[44]	Wang D Y, Ling G C. 1998. Vortex-induced nonlinearvibration of TLP tethers under circumstances of platformoscillation. Acta Oceanologica Sinica, 20: 119-128. http://www.cnki.com.cn/Article/CJFDTOTAL-SEAC803.016.htm
[45]	王成官, 王嘉松, 田中旭, 乔信起, 蒋世全, 许亮斌. 2011.海洋隔水管涡激振动的三维数值模拟研究. 水动力学研究与进展, 26: 437-443. http://cdmd.cnki.com.cn/Article/CDMD-10248-1011268154.htm
[46]	Wang C G, Wang J S, Tian Z X, Qiao X Q, Jiang S Q,Xu L B. 2011. Three dimensional numerical simulation of vivonmarine riser. Chinese Journal of Hydrodynamics, 26:437-443. http://cdmd.cnki.com.cn/Article/CDMD-10248-1011268154.htm
[47]	王沣浩, 姜东歌, 罗昔联, 梅雪松. 2006.波状圆柱绕流减阻的实验研究. 西安交通大学学报, 40: 93-96 http://www.cnki.com.cn/Article/CJFDTOTAL-XAJT200601021.htm
[48]	Wang F H, Jiang G D, Luo X L, Mei X S. 2006. Experimentalinvestigation on drag reduction of wavy cylinder in cross flow.Journal of Xi'an Jiaotong University, 40: 93-96. http://www.cnki.com.cn/Article/CJFDTOTAL-XAJT200601021.htm
[49]	王艺. 2010. 均匀来流条件下的圆柱涡激振动研究. [博士论文].北京：中科院力学研究所
[50]	Wang Y. 2010. Study on vortex-inducedvibration of a circular cylinder subjected to steady uniform flow.[PhD Thesis]. Beijing: Institute of Mechanics, Chinese Academy ofSciences.
[51]	肖飞, 杨和振. 2014. 深海钢悬链立管hill不稳定性预测.上海交通大学学报, 48: 583-588 http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201404024.htm
[52]	Xiao F, Yang H Z. 2014. Hillstability prediction of deep-sea steel catenary riser. Journal of Shanghai Jiao Tong University, 48: 583-588. http://www.cnki.com.cn/Article/CJFDTOTAL-SHJT201404024.htm
[53]	徐万海, 曾晓辉, 吴应湘. 2009.深水张力腿平台与系泊系统的耦合动力响应. 振动与冲击, 28:145-150 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200902037.htm
[54]	Xu W H, Zeng X H, Wu Y X. 2009. The coupled dynamicresponses of the tension leg platform and tendon in deep-water.Journal of Vibration and Shock, 28: 145-150. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200902037.htm
[55]	余建星, 许华力, 袁从敏, 王衷畅. 2008.张力腿系缆系统涡激振动疲劳可靠性分析. 船舶力学, 12: 592-598 http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200804014.htm
[56]	Yu J X, Xu H L, Yuan C M, Wang Z C. 2008. Fatigue reliabilityanalysis of vortex induced vibration of TLP tethers in waves andcurrent. Journal of Ship Mechanics, 12: 592-598. http://www.cnki.com.cn/Article/CJFDTOTAL-CBLX200804014.htm
[57]	张杰, 唐友刚, 黄磊, 李伟. 2013.参数激励下深海立管多模态耦合振动特性分析. 振动与冲击, 32:51-56 http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201319011.htm
[58]	Zhang J, Tang Y G, Huang L, Li W. 2013. Multi-mode coupledvibration behavior of a deep-water riser under parametricexcitations. Journal of Vibration and Shock, 32:51-56. http://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ201319011.htm
[59]	张立武. 2010. 深海柔性立管涡激振动响应研究. [硕士论文].北京: 中国科学院力学研究所
[60]	Zhang L W. 2010. Vortex-inducedvibration of long flexible risers in deep water. [Master Thesis].Beijing: Institute of Mechanics, Chinese Academy of Sciences.
[61]	张晓欣. 2007. 美国科学基金委蓝带工作组报告:基于仿真的工程科学. 高性能计算发展与应用, 18: 4-12
[62]	Zhang XX. 2007. Ribbon panel report on simulation-based engineeringscience by NFS blue. Development and Application of HighPerformance Computing, 18: 4-12.
[63]	赵丽刚. 2006. 高温高压条件下海燕立管的动态极值响应研究.[硕士论文]. 哈尔滨: 哈尔滨工程大学
[64]	Zhao L G. 2006. Dynamicextremum response to high temperature and pressure for a riser.[Master Thesis]. Harbin: Harbin Engineering University.
[65]	郑哲敏. 1958. 输水管的振动问题. 力学学报, 2: 100-111 http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB195802002.htm
[66]	Zheng Z M. 1958. Vibration of pipe line. Acta MechanicaSinica, 2: 100-111. http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB195802002.htm
[67]	郑仲钦. 2012a. 平台运动对水下柔性立管动响应的影响分析.[硕士论文]. 北京: 中国科学院力学研究所
[68]	Zheng Z Q. 2012. Analysisof the influence of platform motion on the dynamic response ofmarine flexible riser. [Master Thesis]. Beijing: Institute ofMechanics, Chinese Academy of Sciences.
[69]	郑仲钦, 陈伟民. 2012b. 结构与尾流非线性涡激振动预测模型.海洋工程, 30: 37-41 http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201204006.htm
[70]	Zheng Z Q, Chen W M. 2012. Predictionof vortex-induced vibration of cylinder based on the nonlinearcoupling of structure and wake oscillator. The OceanEngineering, 30: 37-41. http://www.cnki.com.cn/Article/CJFDTOTAL-HYGC201204006.htm
[71]	Aiten J. 1978. An account of some experiment on rigidityproduced by cent force. Philosophical Magazine, 5:81-105.
[72]	Alexander C M. 1981. The complex vibrations and implieddrag of a long oceanographic wire in cross-flow. OceanEngineering, 8: 379-406. https://www.researchgate.net/publication/232338056_The_complex_vibrations_and_implied_drag_of_a_long_oceanographic_wire_in_cross-flow
[73]	Allen D W, Henning D L. 2001. Ultra short fairings forsuppressing vortex-induced vibration. US6223672B1.
[74]	Arcandra T, Kim M H. 2003. Hull/mooring/riser coupleddynamic analysis and sensitivity study of a tanker-based FPSO.Applied Ocean Research, 25: 367-382. doi: 10.1016/j.apor.2003.02.001
[75]	Atsavapranee P, Benaroya H, Wei T. 1998. Vortex dynamics inthe near wake of a freely-oscillating cylinder//The FEDSM'98 ASMEFluids Engineering Division, Summer Meeting, Washington DC, 1-6.
[76]	Baarholm G S, Larsen C M, Lie H. 2005. Reduction of VIVusing suppression devices-An empirical approach. MarineStructures, 18: 489-510. https://www.researchgate.net/publication/229305965_Reduction_of_VIV_using_suppression_devices-An_empirical_approach
[77]	Baarholm G S, Larsen C M, Lie H. 2006. On fatigue damageaccumulation from in-line and cross-flow vortex-induced vibrationson risers. Journal of Fluids and Structures, 22:109-127. doi: 10.1016/j.jfluidstructs.2005.07.013
[78]	Baarholm R, Kristiansen T, Lie H. 2007. Interaction andclashing between bare or straked risers, analyses of experimentaldada//The 26th International Conference on Offshore Mechanics andArctic Engineering, June 10-15 San Diego, CA, US, 803-812.
[79]	Balasubramanian S, Skop R A. 1996. A nonlinear oscillatormodel for vortex shedding from cylinders and cones in uniform andshear flows. Journal of Fluids and Structures, 10:197-214. doi: 10.1006/jfls.1996.0013
[80]	Beaudan P, Moin P. 1994. Numerical experiments on the flowpast a circular cylinder at sub-critical Reynolds number. USA:Department of Mechanical Engineering, Stanford University, ReportTF-62.
[81]	Berger E, Wille R. 1972. Periodic flow phenomena. Annual Reviews of Fluid Mechanics, 4: 313-340. doi: 10.1146/annurev.fl.04.010172.001525
[82]	Birkoff G, Zarantanello E H. 1957. Jets, Wakes andCavities. New York: Academic Press.
[83]	Bishop R E D, Hassan A Y. 1964. The lift and drag forces ona circular cylinder oscillating in a flowing fluid. Mathematical Physical & Engineering Sciences, 277:51-75. http://cn.bing.com/academic/profile?id=11aac16b9718ae965f481d42989a507f&encoded=0&v=paper_preview&mkt=zh-cn
[84]	Blackburn H M, Henderson R D. 1999. A study oftwo-dimensional flow past an oscillating cylinder. Journal ofFluid Mechanics, 385: 255-286. doi: 10.1017/S0022112099004309
[85]	Blackburn H M, Govardhan R N, Williamson C H K. 2001. Acomplementary numerical and physical investigation ofvortex-induced vibration. Journal of Fluids and Structures,15: 481-488. doi: 10.1006/jfls.2000.0345
[86]	Blevins R D. 1987. Flow Induced Vibration. Van NostrandReinhold Company.
[87]	Bosman R L M, Hooker J. 1999. Elastic moduluscharacteristics of polyester mooring ropes//The Annual OffshoreTechnology Conference. 1246-1251.
[88]	Breuer M. 1998. Numerical and modeling influences on largeeddy simulations for the flow past a circular cylinder. International Journal of Heat and Fluid Flow, 19: 512-521. doi: 10.1016/S0142-727X(98)10015-2
[89]	Brika D, Laneville A. 1993. Vortex-induced vibrations of along flexible circular cylinder. Journal of Fluid Mechanics,250: 481-508. doi: 10.1017/S0022112093001533
[90]	Brika D, Laneville A. 1995. An experimental study of theaeolian vibrations of a flexible circular cylinder at differentincidences. J. Fluids Struct, 9: 371-391. doi: 10.1006/jfls.1995.1021
[91]	Carberry J, Govardhan R, Sheridan J, Rockwell D, WilliamsonC H K. 2004. Wake states and response branches of forced andfreely oscillating cylinders. European Journal of Mechanics- B/Fluids, 23: 89-97. doi: 10.1016/j.euromechflu.2003.05.007
[92]	Carberry J, Sheridan J, Rockwell D. 2005. Controlledoscillations of a cylinder: forces and wake modes. Journalof Fluid Mechanics, 538: 31-69. doi: 10.1017/S0022112005005197
[93]	Carl M L, Karl H H. 1997. Comparison of models for vortexinduced vibrations of slender marine structures. MarineStructure, 10: 413-441. https://www.researchgate.net/publication/245185543_Comparison_of_Models_for_Vortex_Induced_Vibrations_of_Slender_Marine_Structures
[94]	Carriere P, Eichelbrenner E A. 1961. Theory of flowreattachment by a tangential jet discharging against a strongadverse pressure gradient//Lachmann GV, ed. Boundary Layer andFlow Control, I: London: Pergamon Press.
[95]	Chandrasekaran S, Chandak N R, Anupam G. 2006. Stabilityanalysis of TLP tethers. Ocean Engineering, 33:471-482. doi: 10.1016/j.oceaneng.2005.04.015
[96]	Chang P K. 1976. Control of Flow Separation. Washington DC:Hemisphere Publication Corporation.
[97]	Chaplin J R, Bearman P W, Huera Huarte F J, Pattenden R J.2005a. Laboratory measurements of vortex-induced vibrations of avertical tension riser in a stepped current. Journal ofFluids and Structures, 21: 3-24. doi: 10.1016/j.jfluidstructs.2005.04.010
[98]	Chaplin J R, Bearman P W, Cheng Y, Fontaine E, Graham J MR, Herfjord M, Isherwood M, Lambrakos K, Larsen C M, Meneghini JR, Moe G, Triantafyllou MS, Willden R H J. 2005b. Blindpredictions of laboratory measurements of vortex-inducedvibrations of a tension riser. Journal of Fluids andStructures, 21: 25-40. doi: 10.1016/j.jfluidstructs.2005.05.016
[99]	Chatjigeorgiou I K. 2004. On the parametric excitation ofvertical elastic slender structures and the effect of damping inmarine applications. Applied Ocean Research, 26:23-33. doi: 10.1016/j.apor.2004.08.001
[100]	Chen S S. 1971. Dynamics stability of tube conveying fluid:Proceedings of the American society of civil engineers. Journal of the Engineering Mechanics Division, 97:1469-1485.
[101]	Chen W M, Li M, Zheng Z Q, Guo S X, Kuan Gan K. 2015.Impacts of top-end vessel sway on vortex-induced vibration of thesubmarine riser for a floating platform in deep water. OceanEngineering, 99: 1-8. https://www.researchgate.net/publication/274140553_Impacts_of_top-end_vessel_sway_on_vortex-induced_vibration_of_the_submarine_riser_for_a_floating_platform_in_deep_water
[102]	Chen W M, Li M, Zhang L W, Tan T C. 2016. Study onMulti-mode VIV of deep water riser in different flow fields byfinite element simulations. J. of Offshore Mechanics andArctic Engineering, 138: 1-8.
[103]	Chen W M, Li M, Guo S X, Gan K. 2014. Dynamic analysis ofcoupling between floating top-end heave and riser's vortex-inducedvibration by using finite element simulations. Applied OceanResearch, 48: 1-9. https://www.researchgate.net/publication/264559813_Dynamic_analysis_of_coupling_between_floating_top-end_heave_and_riser's_vortex-induced_vibration_by_using_finite_element_simulations
[104]	Chen W M, Zhang L W, Li M. 2009. Prediction ofvortex-induced vibration of flexible riser using an improvedwake-oscillator model//The ASME 28th International Conference onOcean, Offshore and Arctic Engineering, Honolulu, Hawaii, 377-383.
[105]	Chen W M, Li M, Zheng Z Q, Tan T C. 2012. DynamicCharacteristics and VIV of deep water riser with axially varyingstructural properties, Ocean Engineering, 42: 7-12. doi: 10.1016/j.oceaneng.2011.12.019
[106]	Chen W M, Zheng Z Q, Li M, Zhang L W. 2011. Effects ofvarying tension and stiffness on dynamic characteristics and VIVof slender riser//Proceeding of the ASME 2011 30th InternationalConference on Ocean. Offshore and Arctic Engineering, Rotterdam,The Netherlands, 207-213(OMEA2011-49295).
[107]	Chen X H, Zhang J, Ma W. 2001. On dynamic coupling effectsbetween a spar and its mooring lines. Ocean Engineering,28: 863-887 doi: 10.1016/S0029-8018(00)00026-3
[108]	Chen X H, Ding Y, Zhang J, Liagre P, Niedzwecki J, TeigenP. 2006. Coupled dynamic analysis of a mini TLP: comparison withmeasurements. Ocean Engineering, 33: 93-117. doi: 10.1016/j.oceaneng.2005.02.013
[109]	Chen X Y, Zha G C, Hu Z J. 2004. Numerical simulation offlow induced vibration based on fully coupled fluid-structuralinteractions//The 34th AIAA Fluid Dynamics Conference and Exhibit,Portland, Oregon, AIAA Paper 2204-2240.
[110]	Chen Z S, Kim W J. 2012. Effect of bidirectional internalflow on fluid-structure interaction dynamics of conveying marineriser model subject to shear current. International Journalof Naval Architecture and Ocean Engineering, 4: 57.
[111]	Chevron Y C, Tran L, Enuganti P, Campbell M. 2011. Steelcatenary riser response identification based on fieldmeasurements//Proceedings of the ASME 2011 30th InternationalConference on Ocean, Offshore and Arctic Engineering, Rotterdam,the Netherlands, OMAE 2011-50148.
[112]	Clarke J H, Menkes H R, Libby P A. 1955. A provisionalanalysis of turbulent boundary layers with injection. Journalof Aeronautical Science, 22: 255-260. doi: 10.2514/8.3322
[113]	Clausen T, D'Souza R. 2001. Dynamic risers key componentfor deep water drilling floating production. Offshore, 61: 89-93.
[114]	Coakley D B, Knutson R K. 2003. Inflatable vibrationreducing fairing. U.S. Patent No.6517589.
[115]	Constantinides Y, Oakley, O H. 2006. Numerical predictionof bare and straked cylinder VIV//The ASME 25th InternationalConference on Offshore Mechanics and Arctic Engineering, 745-753.
[116]	Constantinides Y, Oakley O H, Holmes S. 2007. CFD high L/Driser modeling study//The ASME 26th International Conference onOffshore Mechanics and Arctic Engineering, 715-722.
[117]	Constantinides Y, Oakley O H. 2008. Numerical prediction ofVIV and comparison with field experiments//The ASME 27thInternational Conference on Offshore Mechanics and ArcticEngineering, 577-583.
[118]	Cornut S F A, Vandiver K. 2000. Offshore VIV monitoring atschiehallion-analysis of riser VIV response//The 19th ETCE/OMAE2000 Joint Conference: Energy for the New Millenium, New Orleans,USA, 14-17.
[119]	Dahl J M, Hover F S, Triantafyllou M S. 2006.Two-degree-of-freedom vortex-induced vibrations using a forceassisted apparatus. Journal of Fluids and Structures, 22: 807-818. doi: 10.1016/j.jfluidstructs.2006.04.019
[120]	Dahl J M, Hover F S, Triantafyllou M S. 2007. Resonantvibrations of bluff bodies cause multi vortex shedding and highfrequency forces. Physical Review Letters, 99: 144503. doi: 10.1103/PhysRevLett.99.144503
[121]	Dahl J M, Hover F S, Triantafyllou M S. 2010. Dualresonance in vortex-induced vibrations at subcritical andsupercritical Reynolds numbers. Journal of Fluid Mechanics,643: 395-424 doi: 10.1017/S0022112009992060
[122]	Dai H L, Wang L. 2012. Vortex-induced vibration of pipesconveying fluid using the method of multiple scales. Theoretical & Applied Mechanics Letters, 2: 022006. http://www.cnki.com.cn/Article/CJFDTOTAL-LXKB201202015.htm
[123]	Davies, M.E., 1976. A comparison of the wake structure of astationary and oscillating bluff body. Using a conditionalaveraging technique. Journal of Fluid Mechanics, 75,209-231. doi: 10.1017/S0022112076000189
[124]	Di Silvio G. 1969. Self-controlled vibration of cylinderin fluid stream. Journal of Engineering Mechanics Division,95: 347-361.
[125]	Dickens W R. 1979. The self-induced vibration ofcylindrical structures in fluid flow. Ice Proceedings, 67: 13-30.
[126]	Dong S, Triantafyllou G S, Karniadakis G E. 2008.Elimination of vortex streets in bluff-body flows. PhysicalReview Letters, 100: 204501. doi: 10.1103/PhysRevLett.100.204501
[127]	Evangelinos C, Lucor D, Karniadakis G E. 2000. DNS-derivedforce distribution on flexible cylinders subject to vortex-inducedvibration. Journal of Fluids and Structures, 14:429-440. doi: 10.1006/jfls.1999.0278
[128]	Facchinetti M L, de Langre E, Biolley F. 2004a. Coupling ofstructure and wake oscillators in vortex-induced vibrations. Journal of Fluids and Structures, 19: 123-140. doi: 10.1016/j.jfluidstructs.2003.12.004
[129]	Facchinetti M L, de Langre E, Biolley F. 2004b.Vortex-induced travelling waves along a cable. EuropeanJournal of Mechanics B-Fluids, 23: 199-208. doi: 10.1016/j.euromechflu.2003.04.004
[130]	Feng C C. 1968. The measurement of vortex induced effectsin flow past stationary and oscillating circular and d-sectioncylinders. [Master Thesis]. Canada: Department of MechanicalEngineering, The University of British Columbia.
[131]	Feng L H, Wang J J. 2010. Circular cylindervortex-synchronization control with a synthetic jet positioned atthe rear stagnation point. Journal of Fluid Mechanics, 662: 232-259. doi: 10.1017/S0022112010003174
[132]	Feodosev V P. 1956. Vibrations and stability of a pipe whenliquid flows through it. Inzhenernyi Sbornik, 10:169-170.
[133]	Ferrari J A. 1998. Hydrodynamic loading and response ofoffshore risers. [PhD Thesis]. London: University of London.
[134]	Ferziger J H, Peric M. 1997. Computational Methods forFluid Dynamics. Springer, Berlin-Germany.
[135]	Flemming F, Williamson C H K. 2005. Vortex inducedvibrations of a pivoted cylinder. J. Fluid Mech.,552: 215-252. https://www.researchgate.net/publication/231904312_Vortex-induced_vibrations_of_a_pivoted_cylinder?_sg=qXCtCSE9CiOtgj8MOpbZ7H_iP0f-GVvDxsbH62fU1dAwI_Xhz1i8Q5u3zTn2JefF68l2H-Bwo4zKYK0lo9uKtA
[136]	Franke J, Frank W. 2002. Large eddy simulation of the flowpast a circular cylinder at ReD 3900. Journal of WindEngineering and Industrial Aerodynamics, 90: 1191-1206. doi: 10.1016/S0167-6105(02)00232-5
[137]	Fu S X, Xu Y W, Chen Y. 2014. Seabed effects on thehydrodynamics of a circular cylinder undergoing vortex-inducedvibration at high reynolds number. Journal of Waterway PortCoastal and Ocean Engineering, 140: 04014008. doi: 10.1061/(ASCE)WW.1943-5460.0000241
[138]	Fujarra A L C, Pesce C P, Flemming F, Williamoson C H K.2001. Vortex-induced vibration of a flexible cantilever. Journal of Fluids and Structures, 15: 651-658. doi: 10.1006/jfls.2000.0368
[139]	Furnes G K, Hassanein T, Halse K H, Eriksen M. 1998. Afield study of flow induced vibrations on a deepwater drillingriser//The Annual Offshore Technology Conference, Houston, Texas,USA, OTC 8702.
[140]	Furnes G K, Srensen K. 2007. Flow induced vibrationsmodeled by coupled non-linear oscillators//The 17th InternationalOffshore and Polar Engineering Conference, Lisbon, Portugal,321-329.
[141]	Gad-el-Hak M, Bushnell D M. 1991. Separation control:review. Journal of Fluids Engineering, 113: 5-30. doi: 10.1115/1.2926497
[142]	Garrett D L. 2005. Coupled analysis of floating productionsystems. Ocean Engineering, 32: 802-816. doi: 10.1016/j.oceaneng.2004.10.010
[143]	Ge F, Lu W, Wang L, Hong Y S. 2011. Shear flow inducedvibrations of long slender cylinders with a wake oscillator model.Acta Mechanica Sinica, 27: 330-338. doi: 10.1007/s10409-011-0460-x
[144]	Glezer A, Amitay M. 2002. Synthetic jets. AnnualReview of Fluid Mechanics, 34: 503-529. doi: 10.1146/annurev.fluid.34.090501.094913
[145]	Gopalkrishnan R. 1993. Vortex induced forces on oscillatingbluff cylinders. USA: Woods Hole Oceanographic Institution MA.
[146]	Govardhan R, Williamson C H K. 2004. Critical mass invortex-induced vibration of a cylinder. European Journal ofMechanics B/Fluids, 23: 17-27. doi: 10.1016/j.euromechflu.2003.04.001
[147]	Grant R, Patterson D. 1977. Riser fairing for reduced dragand vortex suppression//The Annual Offshore TechnologyConference. Houston, Texas, USA, OTC 2921 MS.
[148]	Griffin O M, Hall M S. 1991. Review: Vortex sheddinglock-on and flow control in bluff body wakes. Journal ofFluids Engineering, 113: 526-537. doi: 10.1115/1.2926511
[149]	Griffin O M, Skop R A, Ramberg S E. 1975. The resonantvortex excited vibrations of structures and cable systems//Proceedings of Offshore Technology Conference, Houston, Texas,OTC 2319.
[150]	Grundy P, Hewitt M P. 2002. Incremental collapse of tensionlegs and risers//Proceedings of 12th International Offshore andPolar Engineering Conference (ISOPE-2002), Kyushu Japan, 129-132.
[151]	Gu W, Chyu C, Rockwell D. 1994. Timing of vortex formationfrom an oscillating cylinder. Physics of Fluids, 6:3677-3682. doi: 10.1063/1.868424
[152]	Guo H Y, Lou M. 2008. Effect of internal flow onvortex-induced vibration of risers. Journal of Fluids andStructures, 24: 496-504. doi: 10.1016/j.jfluidstructs.2007.10.002
[153]	Halse K H. 2000. Norwegian deep water program: improvedpredictions on vortex-induced vibrations//Proc. of the OTC,Houston, Texas. OTC 11996.
[154]	Hartlen R T, Currie I G. 1970. Lift-oscillator model ofvortex-induced vibration. Journal of the EngineeringMechanics, 96: 577-591.
[155]	He J W, Low Y M. 2010. Probabilistic assessment of theclashing between flexible marine risers//Proceedings of 29thInternational Conference on Ocean, Offshore and ArcticEngineering, OMAE, 2010-20046, 41-49.
[156]	Herlianto I, Chen Q, Karunakaran D. 2012. Lateral bucklinginduced by trawl gears pull-over loads on high temperature/highpressure subsea pipeline//The ASME 31st International Conferenceon Ocean Offshore and Arctic Engineering, Rio de Janeiro, Brazil,235-240.
[157]	Heurtier J M, Biollcy F, Berhault C. 1998. Fully coupleddynamic analysis of rigid lines and floater behaviors in deepwater//Proceedings of the Eighth (1998) International Offshore andPolar Engineering Conference Montrkal, Canada, May 24-29.
[158]	Heurtier J M, Le Buhan P, Fontaine E F, Mer L S S, Cunff FC L. 2001. Coupled dynamic response of moored FPSO withrisers//Proceedings of the Eleventh (2001) International Offshoreand Polar Engineering Conference Stavanger, Norway, June 17-22.
[159]	Holmes S, Constantinides Y, Oakley O H. 2006. Simulation ofriser VIV using fully three dimensional CFD simulations//The ASME25th International Conference on Offshore Mechanics and ArcticEngineering, Hamburg, Germany. 563-570.
[160]	Hong N, Huh T. 1999. Effect of internal flow onvortex-induced vibration of riser//The Ninth InternationalOffshore and Polar Engineering Conference, Brest, France, 688-693.
[161]	Hover F S, Davis J T, Triantafyllou M S. 2004.Three-dimensionality of mode transition in vortex-inducedvibrations of a circular cylinder. European Journal ofMechanics B/Fluid, 23: 29-41. doi: 10.1016/j.euromechflu.2003.04.002
[162]	Hover F S, Techet A H, Triantafyllou M S. 1998. Forces onoscillating uniform and tapered cylinders in cross flow. Journal of Fluid Mechanics, 363: 97-114. doi: 10.1017/S0022112098001074
[163]	Huarte F J H, Bearman P W, Chaplin J R. 2006. On the forcedistribution along the axis of a flexible circular cylinderundergoing multi-mode vortex-induced vibrations. Journal ofFluids and Structures, 22: 897-903. doi: 10.1016/j.jfluidstructs.2006.04.014
[164]	Huerre P. 2002. Global nonlinear instabilities in wakeflows//The Conference on Bluff Body Wakes and Vortex-InducedVibrations (BBVIV3), Port Douglas, Australia.
[165]	Huse E, Kleiven G, Nielsen F G. 1998. Large scale modeltesting of deep sea risers//The Offshore Technology Conference,Houston, Texas. OTC 8701.
[166]	Huse E, Kleiven G, Nielsen F G. 1999. VIV-induced axialvibration on deep sea risers//The Offshore Technology Conference,Houston, Texas, OTC 10932.
[167]	Iwan W D, Blevins R D. 1974. A model for vortex inducedoscillation of structures. Journal of Applied Mechanics,41: 581-586. doi: 10.1115/1.3423352
[168]	Iwan W D. 1981. The Vortex-induced oscillation ofnon-uniform structure analysis. Journal of Sound andVibration, 79: 291-301. doi: 10.1016/0022-460X(81)90373-4
[169]	Jauvtis N, Williamson C H K. 2003. Vortex induced vibrationof a cylinder with two degrees of freedom. J. Fluids Struct,17: 1035-1042. doi: 10.1016/S0889-9746(03)00051-3
[170]	Jauvtis N, Williamson C H K. 2004. The effect of twodegrees of freedom on vortex-induced vibration at low mass anddamping. Journal of Fluid Mechanics, 509: 23-62. doi: 10.1017/S0022112004008778
[171]	Kaasen K E, Lie H, Solaas F, Vandiver J K. 2000. Norwegiandeep water program: Analysis of vortex-induced vibrations ofmarine risers based on full-scale measurements//The OffshoreTechnology Conference, Houston, Texas, OTC 11997.
[172]	Kaasen K E. 2001. Optimizing sensor locations foridentification of riser VIV modes//The 11th International Oceanand Polar Engineering Conference, Stavanger, Norway, 23-28.
[173]	Karayaka M, Chen J H, Blankenship C, Chevron E T C, Ruf W.2009. 2H Offshore Inc. Mat Podskarbi, Schlumberger Tahiti onlinemonitoring system for steel catenary risers and flowlines//Offshore Technology Conference, Houston, Texas, OTC 19860.
[174]	Keber M, Wiercigroch M. 2008. Dynamics of a vertical riserwith weak structural nonlinearity excited by wakes. Journalof Sound and Vibration, 315: 685-699. doi: 10.1016/j.jsv.2008.03.023
[175]	Ketar M, Patil K D. 2014. Review of subsea pipeline forminimizing thermal and pressure expansion. Journal ofPetroleum Engineering and Technology, 4: 10-22. https://www.researchgate.net/publication/263327195_Review_of_Subsea_Pipeline_for_Minimizing_Thermal_and_Pressure_Expansion
[176]	Khalak A, Williamson C H K. 1999. Motions, orces and modetransitions in vortex-induced vibrations at low mass-damping. Journal of Fluids and Structures, 13: 813-851. doi: 10.1006/jfls.1999.0236
[177]	Kim Y H, Vandiver J K, Holler R. 1986. Vortex-inducedvibration and drag coefficients of long cables subjected tosheared flows. Journal of Energy Resources Technology, 108: 77-83. doi: 10.1115/1.3231245
[178]	Korkischko I, Meneghini J R. 2010. Experimentalinvestigation of flow-induced vibration on isolated and tandemcircular cylinders fitted with strakes. Journal of Fluids andStructures, 26: 611-625. doi: 10.1016/j.jfluidstructs.2010.03.001
[179]	Kravchenko A G, Moin P. 1998. B-spline methods and zonalgrids for numerical simulations of turbulent flows. USA:Department of Mechanical Engineering, Stanford University, ReportTF-73.
[180]	Kumar R A, Sohn C H, Gowda B H L. 2008. Passive control ofvortex-induced vibrations. An Overview Recent Patents onMechanical Engineering, 1: 1-11. https://www.researchgate.net/publication/237455935_Passive_Control_of_Vortex-Induced_Vibrations_An_Overview
[181]	Lam K, Wang F H, Li J Y, So R M C. 2004. Experimentalinvestigation of the mean and fluctuating forces of wavy(varicose) cylinders in a cross-flow. Journal of Fluids andStructures, 19: 321-334. doi: 10.1016/j.jfluidstructs.2003.12.010
[182]	Lam K, Lin Y F, Zou L, Liu Y. 2010. Investigation ofturbulent flow past a yawed wavy cylinder. Journal of Fluidsand Structures, 26: 1078-1097. doi: 10.1016/j.jfluidstructs.2010.07.005
[183]	Larsen C M, Halse K H. 1997. Comparison of models forvortex-induced vibrations of slender marine structures. Marine Structures, 10: 413-441. doi: 10.1016/S0951-8339(97)00011-7
[184]	Larsen C M, Vikestad K, Yttervik R, Passano E. 2001.Empirical model for analysis of vortex induced vibrations---theoretical background and case studies//The ASME 20thInternational Conference on Offshore Mechanics and ArcticEngineering, Rio de Janeiro. OMAE2001/OFT-1203.
[185]	Layek G C, Midya C, Gupta A S. 2008. Influences of suctionand blowing on vortex shedding behind a square cylinder in achannel. International Journal of Non-Linear Mechanics, 43: 979-984. doi: 10.1016/j.ijnonlinmec.2008.07.006
[186]	Lee S J, Kim H B. 1997. The effect of surface protrusionson the near wake of a circular cylinder. Journal of WindEngineering and Industrial Aerodynamics, 71: 351-361.
[187]	Lee H H, Wang P W. 2000. Analytical solution on the surgemotion of tension-leg twin platform structural systems. OceanEngineering, 27: 393-415. https://www.researchgate.net/publication/279142892_Analytical_solution_on_the_surge_motion_of_tension-leg_twin_platform_structural_systems
[188]	Li B B, Ou J P, Teng B. 2010. Fully coupled effects ofhull. Mooring and risers model in time domain based on aninnovative deep draft multi-spar. China Ocean Engineering,24: 219-233. http://d.wanfangdata.com.cn/Periodical_zghygc-e201002002.aspx
[189]	Liao J C. 2002. Vortex-induced vibration of slenderstructure in unsteady flow. [PhD Thesis]. Massachusetts:Massachusetts Institute of Technology.
[190]	Lie H, Kaasen K E. 2006. Modal analysis of measurementsfrom a large-scale VIV model test of a riser in linearly shearedflow. Journal of Fluids and Structures, 22: 557-575. doi: 10.1016/j.jfluidstructs.2006.01.002
[191]	Lie H, Larsen C M, Vandiver J K. 1997. Vortex inducedvibrations of long marine risers; model test in a rotatingrig//The ASME16th International Conference on Offshore Mechanicsand Arctic Engineering, Yokohama, Japan, 241-252.
[192]	Lim H C, Lee S J. 2004. Flow control of a circular cylinderwith O-rings. Fluid Dynamics Research, 35: 107-122. doi: 10.1016/j.fluiddyn.2004.05.001
[193]	Lubbad R K, Loset S, Moe G. 2011. Experimentalinvestigations of the efficiency of round-Sectioned helicalstrakes in suppressing vortex induced vibrations. Journal ofOffshore Mechanics and Arctic Engineering, 133:041102.1-041102.10. doi: 10.1115/1.4002732
[194]	Lucor D, Imas L, Karniadakis G E. 2001. Vortex dislocationsand force distribution of a long flexible cylinders subjected tosheared flows. Journal of Fluids and Structures Mechanics,15: 641-650. doi: 10.1006/jfls.2000.0366
[195]	Lucor D, Triantafalou M S, Ma X, Karniadakis G E. 2003.Vortex-induced vibrations of long marine risers in sheared flows:DNS studies//The 4th ASME/JSME Joint Fluids EngineeringConference, Honolulu, Hawaii, USA.
[196]	Lucor D, Foo J, Karniadakis G E. 2005. Vortex modeselection of a rigid cylinder subject to VIV at low mass-damping.Journal of Fluids and Structures, 20: 483-503. doi: 10.1016/j.jfluidstructs.2005.02.002
[197]	Lyons G J, Patel M H. 1986. A prediction technique forvortex induced transverse response of marine risers and tethers.Journal of Sound and Vibration, 11: 467-487. https://www.researchgate.net/publication/223088996_A_prediction_technique_for_vortex_induced_transverse_response_of_marine_risers_and_tethers?_sg=l_JYjtW7RiZgFCT8nONSm69ab1Ja-6TYMrxhDwc06JdnbdQlYa4Ufs-nM5KLxBf4aQ4ZTKll9xaluAPOKDIlBw
[198]	Lyons G J, Vandiver J K, Larsen C M, Ashcombe G T. 2003.Vortex induced vibrations measured in service in the Foinavendynamic umbilical and lessons from prediction. Journal ofFluids and Structures, 17: 1079-1094. doi: 10.1016/S0889-9746(03)00072-0
[199]	Machado R Z, Mourelle M M, Franciss R, Silva R M, Lima C S,Eisemberg R, Oliveira D. 1992. Monitoring program for the firststeel catenary riser installed in a moored floating platform indeep water//Oceans Conference Record (IEEE), 801-810.
[200]	Mandini R V. 1961. Kinematics of vortices in the early wakeof vibrating circular cylinders. [Master Thesis]. USA: Universityof California, Berkeley.
[201]	Marcollo H, Chaurasia H, Vandiver J K. 2007. Phenomenaobserved in VIV bare riser field tests//THE ASME 26thInternational Conference on Offshore Mechanics and ArcticEngineering, 989-995.
[202]	Masters R H, Griffith B L. 2012. Apparatus and method forsecuring a fairing around a marine element. US2012/0243944.
[203]	Mathelin L, de Langre E. 2005. Vortex-induced vibrationsand waves under shear flow with a wake oscillator model. European J. of Mechanics B/Fluids, 24: 478-490. doi: 10.1016/j.euromechflu.2004.12.005
[204]	Meneghini J R, Bearman P W. 1993. Numerical simulation ofhigh amplitude oscillator-flow about a circular cylinder using adiscrete vortex method//Shear Flow Conf. Orlando, FL, AIAA Paper93-3288.
[205]	Meneghini J R, Saltara F, Fregonesi R A, Yamamoto C T,Casaprima E, Ferrari J A. 2004. Numerical simulations of VIV onlong flexible cylinders immersed in complex flow fields. European Journal of Mechanics B/Fluids, 23: 51-63. doi: 10.1016/j.euromechflu.2003.09.006
[206]	Meng D, Chen L. 2011. Nonlinear free vibrations andvortex-induced vibrations of fluid-conveying steel catenary riser.Applied Ocean Research, 34: 52-67. https://www.researchgate.net/publication/251508857_Nonlinear_free_vibrations_and_vortex-induced_vibrations_of_fluid-conveying_steel_catenary_riser
[207]	Mittal R, Moin P. 1997. Suitability of upwind-biasedfinite-difference schemes for large-eddy simulation of turbulentflows. AIAA Journal, 35: 1415-1417. doi: 10.2514/2.253
[208]	Mittal S, Kumar V. 2001. Flow-induced vibrations of a lightcircular cylinder at Reynolds numbers 10³ to 10⁴. Journal of sound and vibration, 245: 923-946. doi: 10.1006/jsvi.2001.3612
[209]	Moe G, Wu Z J. 1990. The lift force on a vibrating cylinderin a current. Journal of Offshore Mechanics and ArcticEngineering, 112: 297-303. doi: 10.1115/1.2919870
[210]	Moe G, Chucheepsakul S. 1998. The effect of internal flowon marine risers//The 7th International Conference on OffshoreMechanics and Arctic Engineering, 375-382.
[211]	Morse T L, Govardhanb R N, Williamson C H K. 2008. Theeffect of end conditions on the vortex-induced vibration ofcylinders. Journal of Fluids and Structures, 24:1227-1239. doi: 10.1016/j.jfluidstructs.2008.06.004
[212]	Morse T L, Williamson C H K. 2006. Employing controlledvibrations to predict fluid forces on a cylinder undergoingvortex-induced vibration. Journal of Fluids and Structures,22: 877-884. doi: 10.1016/j.jfluidstructs.2006.04.004
[213]	Murrin D, Ordonez M, Stone G, Bose N, Qiu W. 2007. Highmode vortex induced vibration (VIV) experiments on a large-scaleriser//The 2007 IEEE Oceans, Vancouver, Canada, 1-7.
[214]	Narzul P, Marion A. 1986. Static and dynamic behavior offlexible catenary risers//The ASME 5th International OffshoreMechanics and Arctic Engineering Symposium, 378-386.
[215]	Newman D J, Karniadakis G E. 1997. A direct numericalsimulation study of flow past a freely vibrating cable. Journal of Fluid Mechanics, 344: 95-136. doi: 10.1017/S002211209700582X
[216]	Okajima A, Nakamura A, Kosugi T, Uchida H. 2002.Flow-induced in-line oscillation of a circularcylinder//Conference on Bluff Body Wakes and Vortex-InducedVibrations (BBVIV3), Port Douglas, Australia.
[217]	OrcaFlex Manual of Version 9.3a. Orcina Ltd. 1998.
[218]	Ordonez M, Sonnaillon M O, Murrin D, Bose N, Qiu W. 2007.An advanced measurement system for vortex-induced-vibrationscharacterization in large-scale risers//The 2007 IEEE Oceans,Vancouver, 1-5. http://www.academia.edu/11053410/An_Advanced_Measurement_System_for_Vortex-Induced-Vibrations_Characterization_in_Large-Scale_Risers
[219]	Paidoussis M P, Issid N T. 1974. Dynamic stability of pipesconveying fluid. Journal of Sound and Vibration, 33:267-294. doi: 10.1016/S0022-460X(74)80002-7
[220]	Patel M H, Park H I. 1995. Combined axial and lateralresponses of tensioned buoyant platform tethers. EngineeringStructures, 17: 687-695. https://www.researchgate.net/publication/245077319_Combined_axial_and_lateral_responses_of_tensioned_buoyant_platform_tethers
[221]	Patel M H, Witz J A. 1991a. Compliant Offshore Structures.Butterworth-Heinemann.
[222]	Patel M H, Park H I. 1991. Dynamics of tension leg platformtethers at low tension. Part I - Mathieu stability at largeparameters. Marine Structures, 4: 257-273. https://www.researchgate.net/publication/256633933_Dynamics_of_tension_leg_platform_tethers_at_low_tension_Part_I_-_Mathieu_stability_at_large_parameters
[223]	Pesce C P, Fujarra A L C. 2000. Vortex-induced vibrationsand jumping phenomenon: An experimental investigation with aclamped flexible cylinder in water. International Journal ofOffshore and Polar Engineering, 420: 26-33.
[224]	Pontaza J P, Chen H C. 2007. Three-dimensional numericalsimulations of circular cylinders undergoing two degree-of-freedomvortex-induced vibrations. Journal of Offshore Mechanics andArctic Engineering, 129: 158-164. doi: 10.1115/1.2746396
[225]	Pontaza J P, Chen C, Chen H. 2005. Chimerareynolds-averaged navier-stokes simulations of vortex-inducedvibration of circular cylinders. Civil Engineering in theOceans, 2014: 166-176.
[226]	Prasad A, Williamson C H K. 1997. Three dimensional effectsin turbulent bluff-body wakes. Journal of Fluid Mechanics,343: 235-264. doi: 10.1017/S002211209700579X
[227]	Rao Z B, Fu S X, Yang J M. 2011. Vortex-induced vibrationanalysis of steel catenary riser. Journal of Ship Mechanics,15: 245-258. https://www.researchgate.net/publication/286940807_Vortex-induced_vibration_analysis_of_steel_catenary_riser
[228]	Sainsbury R N, King R. 1971. The flow induced oscillationof marine structures. Ice Proceedings, 49: 269-302. https://www.researchgate.net/publication/237903174_The_flow_induced_oscillation_of_marine_structures
[229]	Sanchis A. 2009. Two degrees of freedom vortex-inducedvibrations of a rigid circular cylinder with varying naturalfrequencies in the X and Y directions//The ASME 28th InternationalConference on Ocean, Offshore and Arctic Engineering. Honolulu HI,USA, 889-894.
[230]	Sarpkaya T. 1977. In-Line and transverse forces oncylinders in oscillatory flow at high reynolds numbers. Journal of Ship Research, 21: 200-216. https://www.researchgate.net/publication/259945764_In-line_and_transverse_forces_on_cylinders_in_oscillatory_flow_at_high_Reynolds_numbers
[231]	Sarpkaya T. 1978. Fluid forces on oscillating cylinders.Journal of Waterway Port Coastal and Ocean Division, 104: 275-290. https://www.researchgate.net/publication/234196852_Fluid_Forces_on_Oscillating_Cylinders
[232]	Sarpkaya T. 1995. Hydrodynamic damping flow-inducedoscillations and biharmonic response. Journal of OffshoreMechanics and Arctic Engineering, 117: 232-238. doi: 10.1115/1.2827228
[233]	Sarpkaya T. 1979. Vortex-induced oscillations a selectivereview. Journal of Applied Mechanics, 46: 241-258. doi: 10.1115/1.3424537
[234]	Sarpkaya T. 2004. A critical review of the intrinsic natureof vortex-induced vibrations. Journal of Fluids andStructure, 19: 389-447. doi: 10.1016/j.jfluidstructs.2004.02.005
[235]	Simos A N, Pesce C P. 1997. Mathieustability in the dynamics of TLP's tethers considering variabletension along the length. Transactions on the BuiltEnvironment, 29: 41-48.
[236]	Skop R A, Griffin O M. 1973. A model for the vortex-excitedresonant response of bluff cylinders. Journal of Sound andVibration, 27: 225-233. doi: 10.1016/0022-460X(73)90063-1
[237]	Slaouti A, Gerrard J H. 1981. An experimental investigationof the end effects on the wake of a circular-cylinder towedthrough water at low reynolds numbers. Journal of FluidMechanics, 122: 297-314. https://www.researchgate.net/publication/231926882_An_experimental_investigation_of_the_end_effects_on_the_wake_of_a_circular_cylinder_towed_through_water_at_low_Reynolds_numbers?_sg=cvx6vlLeFbIlNNik8FzceRWVPGJQySvj57gCbT0_KyreMzC8y9_BMyHGWw6NxPeJnC0WP9ptoA6Ko81RZvz-ew
[238]	So R M C, Liu Y, Chan S T, Lam K. 2001. Numerical studiesof a freely vibrating cylinder in a cross flow. Journal ofFluids and Structures, 15: 845-866. doi: 10.1006/jfls.2000.0377
[239]	Song J N, Lü L, Zhang J Q, Hao W V, Tang G Q. 2009.Experimental investigation of suppression of vortex-inducedvibration of marine risers by three control rods. The OceanEngineering, 27: 23-29.
[240]	Spanos P D, Ghosh R, Finn L D. 2005. Coupled analysis of aspar structure: Monte Carlo and statistical linearizationsolutions. Journal of Offshore Mechanics and ArcticEngineering, 127: 11-16. doi: 10.1115/1.1862253
[241]	Srinil N, Wiercigroch M, O'Brien P. 2009. Reduced-ordermodeling of vortex-induced vibration of catenary riser. OceanEngineering, 36: 1404-1414.
[242]	Srinil N, Zanganeh H. 2012. Modelling of coupledcross-flow/in-line vortex-induced vibrations using double duffingand van der Pol oscillators. Ocean Engineering, 53:83-97. doi: 10.1016/j.oceaneng.2012.06.025
[243]	Stansberg C T, Ormberg H, Oritsland O. 2002. Challenges indeep water experiments: Hybrid approach. Journal of OffshoreMechanics and Arctic Engineering, 124: 91-96. https://www.researchgate.net/publication/245363573_Challenges_in_Deep_Water_Experiments_Hybrid_Approach
[244]	Sugimoto T, Saito S, Matsuda K, Okajima A, Kiwata T, KosugiT. 2002. Water tunnel experiments on in-line oscillation of acircular cylinder with a finite span length//Conference on BluffBody Wakes and Vortex-Induced Vibrations (BBVIV3), Port Douglas,Australia.
[245]	Sun J, Shi H, Jukes P. 2011. Upheaval buckling analysis ofpartially buried pipeline subjected to high pressure and hightemperature//The ASME 30th International Conference on Ocean,Offshore and Arctic Engineering, Rotterdam, The Netherlands,487-494.
[246]	Szepessy S, Bearman P W. 1992. Aspect ratio and end plateeffects on vortex shedding from a circular cylinder. Journalof Fluid Mechanics, 234: 191-217. doi: 10.1017/S0022112092000752
[247]	Tahara A, Kim M H. 2008. Coupled-dynamic analysis offloating structures with polyester mooring lines. OceanEngineering, 35: 1676-1685. https://www.researchgate.net/publication/223300103_Coupled-dynamic_analysis_of_floating_structures_with_polyester_mooring_lines
[248]	Tezduyar T E, Behr M, Liou J. 1992. A new strategy forfinite element computations involving moving boundaries andinterfaces---the deforming-spatial-domain/space-time procedure: I.The concept and the preliminary tests. Computer Methods inApplied Mechanics and Engineering, 94: 339-351. http://www.doc88.com/p-192575994260.html
[249]	Tognarelli M A, Slocum S T, Frank W R, Campbell R B. 2004.VIV response of a long flexible cylinder in uniform and linearlysheared currents//Offshore Technology Conference, OTC-16338,1-12. https://www.onepetro.org/download/conference-paper/OTC-16338-MS?id=conference-paper%2FOTC-16338-MS
[250]	Trim A D, Braaten H, Lie H, Tognarelli M A. 2005.Experimental investigation of vortex-induced vibration of longmarine risers. Journal of Fluids and Structures, 21:335-361. doi: 10.1016/j.jfluidstructs.2005.07.014
[251]	Trarieux F, Lyons G J, Patel M H. 2006. Investigations witha bandwidth measure for fatigue assessment of the Foinaven dynamicumbilical including VIV. Engineering Structures, 28:1671-1690. doi: 10.1016/j.engstruct.2006.03.014
[252]	Triantafyllou M S, Techet A H, Hover F S. 2004. Review ofexperimental work in biomimetic foils. IEEE Journal ofOceanic Engineering, 29: 585-594. doi: 10.1109/JOE.2004.833216
[253]	Vandiver J K, Allen D, Li L. 1996. The occurrence oflock-in under highly sheared conditions. Journal of Fluidsand Structures, 10: 555-561. doi: 10.1006/jfls.1996.0037
[254]	Vandiver J K. 1998. Research challenges in thevortex-induced vibration prediction of marine risers//The 1998Offshore Technology Conference. Houston, Texas, the USA, OTC8698.
[255]	Vandiver J K. 2002. A universal reduced damping parameterfor prediction of vortex-induced vibration//Proceedings of the20th International Conference on Offshore Mechanics and ArcticEngineering, Oslo, Norway.
[256]	Vandiver J K, Jaiswal V, Jhingran V. 2009. Insights onvortex-induced traveling waves on long risers. Journal ofFluids and Structures, 25: 641-653. doi: 10.1016/j.jfluidstructs.2008.11.005
[257]	Vandiver J K, Mazel C H. 1976. A field study ofvortex-excited vibrations of marine cables//The 8th AnnualOffshore Technology Conference, Dallas, Texas, the USA, OTC 2491.
[258]	Vandiver J K. 1983. Drag coefficients of long flexiblecylinders//15th Annual Offshore Technology Conference, Houston,Texas.
[259]	Vandiver J K, Li L. 1999. SHEAR7 program theorymanual//MIT, Department of Ocean Engineering, MIT, Boston, USA.
[260]	Vandiver J K, Marcollo H, Swithenbank S, Jhingran V. 2005.High mode number vortex-induced vibration fieldexperiments//Offshore Technology Conference, Houston, Texas. https://www.onepetro.org/download/conference-paper/OTC-17383-MS?id=conference-paper%2FOTC-17383-MS
[261]	Vikestad K. 1998. Multi-frequency response of a cylindersubjected to vortex shedding and support motions. [PhD Thesis].Norwegia: Department of Marine Structures Faculty of MarineTechnology, Norwegian University of Science and Technology.
[262]	Vikestad K, Vandiver J K, Larsen C M. 2000. Added mass andoscillation frequency for a circular cylinder subjected tovortex-induced vibrations and external disturbance. Journalof Fluids and Structures, 14: 1071-1088. doi: 10.1006/jfls.2000.0308
[263]	Wang J G, Fu S X, Baarholm R, Wu J, Larsen C M. 2014.Fatigue damage of a steel catenary riser from vortex-inducedvibration caused by vessel motions. Marine Structures, 39: 131-156. doi: 10.1016/j.marstruc.2014.07.002
[264]	Wang Y, Chen W M, Lin M. 2007. Study on the variation ofadded mass and its application to the calculation of amplituderesponse for a circular cylinder at lock-in. China OceanEngineering, 21: 429-437.
[265]	Wichers J E W, Voogt H J, Roelofs H W, Driessen P C M.2001. DeepStar-CTR 4401 Benchmark Model Test. MARIN, Netherlands,Technical Report No. 16417-1-OB.
[266]	Williamson C H K, Govardhan R. 2008. A brief review ofrecent results in vortex-induced vibrations. Journal of WindEngineering and Industrial Aerodynamics, 96: 713-735. doi: 10.1016/j.jweia.2007.06.019
[267]	Williamson C H K. 1996. Vortex dynamics in the wake. Annual Review of Fluid Mechanics, 28: 477-539. doi: 10.1146/annurev.fl.28.010196.002401
[268]	Williamson C H K, Govardhan R. 2004. Vortex-inducedvibrations. Annu.Rev.Fluid Mech, 36: 413-455. doi: 10.1146/annurev.fluid.36.050802.122128
[269]	Williamson C H K, Roshko A. 1988. Vortex formation in thewake of an oscillating cylinder. J. Fluids Struct., 2:355-381. doi: 10.1016/S0889-9746(88)90058-8
[270]	Willden R H J, Graham J M R. 2001. Numerical prediction ofVIV on long flexible circular cylinders. Journal of Fluidsand Structures, 15: 659-66. doi: 10.1006/jfls.2000.0359
[271]	Willis N R T, Thethi K S. 1999. Stride JIP: Steel risers indeep water environments-progress summary//The Offshore TechnologyConference, Houston, USA, OTC 10974.
[272]	Wu M C, Lou J Y K. 1991. Effect of rigidity and internalflow on marine riser dynamics. Applied Ocean Research, 13: 235-244. doi: 10.1016/S0141-1187(05)80047-1
[273]	Wu X D, Ge F, Hong Y H. 2012a. A review of recent studieson vortex-induced vibrations of slender cylinders. J FluidsStruct., 28: 292-308. https://www.researchgate.net/publication/257281882_A_review_of_recent_studies_on_vortex-induced_vibrations_of_long_slender_cylinders
[274]	Wu X M, Huang W P. 2012b. Study on analysis method for deepwater TTR coupled vibration of parameter vibration andvortex-induced vibration. Journal of Vibroengineering, 24: 977-983. http://www.jve.lt/Vibro/JVE-2012-14-3/JVE-2012-14-3-821-Wu.pdf
[275]	Xu W H, Gao X F, Du J. 2012. The prediction on in-linevortex-induced vibration of slender marine structures. ActaMechanica Sinica, 28: 1303-1308. doi: 10.1007/s10409-012-0098-3
[276]	Xu Y W, Fu S X, Chen Y, Zhong Q, Fan D X. 2013. Experimentinvestigation on vortex induced forces of oscillating cylinder athigh reynolds number. Ocean System Engineering, 3: 167-180. doi: 10.12989/ose.2013.3.3.167
[277]	Yamamoto C T, Fregonesi R A, Meneghini J R, Saltara F,Ferrari J A. 2004. Numerical simulations of vortex-inducedvibration of flexible cylinders. Fluids Struct., 19:467-489. doi: 10.1016/j.jfluidstructs.2004.01.004
[278]	Yang H Z, Xiao F. 2014. Instability analyses of atop-tensioned riser under combined vortex and multi-frequencyparametric excitations. Ocean Engineering, 81: 12-28. doi: 10.1016/j.oceaneng.2014.02.006
[279]	Yu M H, Lin T K. 2005. A numerical study on fluid elasticvibrations of multiple cylinders in cross flow. Journal ofthe Chinese Institute of Engineers, 28: 101-110. doi: 10.1080/02533839.2005.9670976
[280]	Zdravkovich M M. 1981. Review and classification of variousaerodynamic and hydrodynamic means for suppressing vortexshedding. Journal of Wind Engineering and IndustrialAerodynamics, 7: 145-189. http://www.doc88.com/p-7048974026517.html
[281]	Zdravkovich M M. 1997. Flow Around Circular Cylinders. Vol.1: Fundamentals. Oxford: Oxford Science Publications. https://www.researchgate.net/publication/231987425_Flow_around_Circular_Cylinders_Volume_1_Fundamentals_By_M_M_Zdravkovich_Oxford_Science_Publications_1997_672_pp_120
[282]	Zhang H, Han Y, Chen F. 2011. Experimental investigation onthe vortex-induced vibration of the cylinders with helicalstrakes. Applied Mechanics and Materials, 117-119: 747-750.
[283]	Zhang L W, Chen W M. 2010. Controlling parameter for wavetypes of long flexible riser undergoing vortex-inducedvibration//Proceedings of 1st International Symposium onArchimedes Bridge, 161-170.