摘要
立管是海洋工程中连接海底和上部平台的重要设备。通过立管,可以将石油、天然气等资源从海底输送至海面的平台。立管通常都是细长的结构,并且始终受到海洋环境荷载的作用。当流体经过立管结构物时,会产生周期性的旋涡脱落和流动作用力,引起立管在横流向和顺流向发生振动。这种现象被称之为“涡激振动”。当立管结构的固有频率和涡脱落频率相接近时,会导致横流向及顺流向发生较大振幅的振动。该现象被称之为“锁定”。涡激振动是导致海洋立管发生疲劳破坏的重要因素。因此,随着海洋油气资源的勘探和生产不断向深海发展,具有明显柔性特征的大长细比深水立管的动力响应问题受到了越来越多的关注。
为了研究涡激振动的物理机制,首先针对低雷诺数下圆柱受迫振动问题,在任意拉格朗日-欧拉参考系下建立了基于Navier-Stokes方程的计算流体动力学模型。研究了圆柱在不同振幅和频率下的受力问题。其中,圆柱振动的无量纲振幅为0.2-0.6,频率比(圆柱振动频率与固定圆柱涡脱落频率的比值)为0.4-1.6。数值计算的结果可以看出,当圆柱的振幅为0.6 D时,圆柱后方的尾涡脱落形式为2P,而当圆柱以相对较小的振幅振动时,圆柱后方的尾涡脱落以2S为主。同时,根据数值模拟结果给出了与加速度同相位的流体力和与速度同相位的流体力同约化速度之间的关系。
在上述圆柱受迫振动问题的基础上,进一步建立了圆柱自激振动的计算流体力学模型。此时,允许圆柱在横流向及纵流向发生自由振动。对于质量比(m*=10)情况,数值模型正确模拟了横流向位移的初始分支、上分支及下分支,以及各分支与涡流场模式之间的依赖关系。利用模型,进一步研究了质量比和阻尼比对圆柱自激振动的影响。计算结果表明：低质量比情况下,自激振动发生锁定所对应的约化速度带宽明显增大,但阻尼比的变化不会引起振动系统发生本质上的改变。
虽然计算流体力学模型在认识涡激振动物理机制方面有重要作用,但是由于计算量巨大,目前还远不能满足实际工程的需要。为此,在SHEAR7模型的理论基础上,建立了可用于深水大长细比立管涡激振动动力响应及疲劳损伤预报的经验模型,并开发了相应的分析程序,通过与SHEAR7结果的比较,验证了该经验模型的有效性。
为了研究细长柔性立管在高模态下的涡激振动动力响应问题,并为经验模型提供验证的数据,开展了室内水池拖曳实验,研究均匀流下大长细比立管模型的涡激振动特性,其中立管模型的长度为28.04 m,直径为1.6 cm,长细比为1750。通过光纤光栅传感器测量立管模型在横流向和顺流向的应变,进而通过模态分解的方法,获得振动响应位移。文中研究了位移的频谱特征及位移标准差的空间分布等问题。实验结果发现,顺流向对立管疲劳的贡献基本和横流向是相等的,而在以往的研究工作中,人们往往只关注了横流向振动的作用。
当前广泛使用的涡激振动经验模型如SHEAR7和VIVANA等,其水动力系数主要来源于受迫振动圆柱的实验结果,难以充分考虑大长细比立管的高模态及多模型共同作用的现象。本文以涡激振动试验的实测位移作为输入的数据,结合有限元结构分析,通过数值计算得到了立管模型所受到的流体力沿立管管长的分布。然后,将流体力分解为与速度同相位的项(流体激振力系数)和与加速度同相位的项(附加质量系数)。最终获得了大长细比立管模型发生涡激振动时的水动力学系数。给出了单模态和多模态响应下的水动力学系数并计算了高频响应下对应的水动力学系数。
应用本文建立的经验模型,分析了立管顶部张力、水流速度的空间分布、立管的外径、内径及壁厚对涡激振动的影响。对于工作水深超过1000 m配备浮力块的隔水管涡激振动问题,文中利用所建立的数值模型,研究了不同的浮力块配置方案对涡激振动的影响。数值表明：不合理的浮力块配置方案会给钻井隔水管带来严重的疲劳损伤。当采用连续铺设浮力块的方案时,可以选择40%-60%覆盖的方案；当采用浮力块和裸管交替布置的方案时,裸管和浮力块的空间比值可以选为1：2。
Risers are widely used in the offshore industry to convey fluids, such as oil and gas, from the seabed to the platform. They are slender structures exposed to complex ocean conditions. As the fluid passes risers, the well-known vortex shedding is observed, resulting in the fluctuating forces on the structures and finally inducing the vibrations of the structures in both cross-flow and in-line directions. This phenomenon is commonly called as vortex-induced vibration (VIV). When the natural frequency of the riser is close to the vortex shedding frequency, large amplitude oscillations is observed in both directions. This phenomenon is usually called lock-in. Vortex-induced vibration is one of the most important factors accounted for the fatigue damage of risers in deep water. The dynamic effects of long flexible risers under vortex-induced vibration become of increasing concern.
In order to investigate the physical mechanism of vortex-induced vibration, a Computational Fluid Dynamics (CFD) model based on Navier-Stokes equations under the Arbitrary Lagrangian-Eulerian (ALE) reference coordinate system was established to simulate the forced vibration circular cylinder. In this study, the ratio of displacement amplitude to cylinder diameter is from 0.2 to 0.6, and the frequency ratio (the oscillating frequency of the cylinder and vortex shedding frequency) ranges from 0.4 to 1.6. The numerical results show that when the circular cylinder vibrates at the amplitude of 0.6 D, the vortex structure in the wake of the circular cylinder is 2P mode. Otherwise, the 2S mode can be observed when the circular cylinder oscillates at rather smaller amplitude. According to the numerical results, the fluid forces in phase with acceleration and velocity of the circular cylinder versus reduced velocity are also calculated in this study.
Based on the previous forced oscillating circular cylinder model, a self-excited model is developed. The circular cylinder is free to vibrate in both the cross-flow and in-line directions. For the large mass ratio m*=10.0, the numerical results present the initial branch, upper branch and lower branch for the cross-flow displacement. The relationship between the different branches and the vortex shedding mode is examined. Employing the self-excited model, the influence of mass ratio and damping ratio on the vortex-induced vibration was studied. The numerical results indicate that the decreasing in mass ratio results in the increase of the lock-in range. However, the damping ratio cannot change the essence of the dynamic system.
Though many efforts have been made to research the physical mechanism of vortex-induced vibration with CFD method, it is far from the practical applications due to its huge time consuming. According to the theory of SHEAR7, a mathematical model used to evaluate the dynamic response and fatigue damage of deepwater risers under vortex-induced vibration was developed.
In order to examine the VIV response of a long flexible riser oscillating at rather higher mode and providing the validation data for the empirical model, Laboratory tests were conducted to investigate the multi-mode dynamic responses of riser model subjected to steady uniform flow. The widely used semi-empirical methods in predicting VIV of deepwater risers, such as SHEAR7 and VIVANA, mainly rely on the observations and experimental results of a forced oscillating rigid cylinder under steady currents. Therefore, these empirical models are not able give exact prediction to the dynamic response of the long flexible risers involving higher mode and multi-mode. In this work, by using the available displacements data of VIV experiment as the input data, the time history of total hydrodynamic forces exerted along the axis of the riser model is obtained by the finite element analysis method. The total hydrodynamic forces are further decomposed into a component in phase with velocity (fluid exciting fluid coefficients) and a component in phase with acceleration (added mass coefficients). The results associated with both single mode and multi-mode responses are presented in this work. The hydrodynamic coefficients considering the higher order modes are addressed in this work.
Employing the empirical model developed in this work, the influences of the top tension, the distribution of incident current velocity along the axis of the riser, outer diameter, inner diameter and wall thickness of risers on the dynamic response were investigated. For the problems of deepwater risers equipped with buoyancy modules, the influence of the buoyancy modules on the dynamic VIV response of the riser is studied. The numerical predictions indicate that the unreasonable arrangement of the buoyancy modules may lead to serious fatigue damage of the riser. As for the continuous paving buoyancy modules, the 40%-60% coverage rates are suggested. Otherwise, the space ratio of the buoyancy modules to bare riser should be 1:2 for the alternant paving buoyancy modules used according to the numerical results of this work.
引文
[1]SARPKAYA T. A critical review of the intrinsic nature of vortex-induced vibrations[J]. Journal of Fluids and Structures,2004,18(SUPPL.):389-447.
[2]BLEVINS R D. Flow-induced vibration [M]. New York:NY:Van Nostrand Reinhold,1990.
[3]LIENHARD J H. Synopsis of lift, drag and vortex trail dynamics [J]. Physics of Fluids, 1966,30:991-998.
[4]ACHENBACH E, HEINECKE E. On vortex shedding from smooth and rough cylinders in the Reynolds numbers from 6 X 103 to 5 X 106[J]. Journal of Fluid Mechanics, 1981,109:239-251.
[5]GOVAROHAN R, WILLIAMSON C H K. Critical mass in vortex-induced vibration of a cylinder [J]. European Journal of Mechanics-B/Fluids Bluff Body Wakes and Vortex-Induced Vibrations, 2004,23(1):17-27.
[6]FENG C C. The measurements of vortex-induced effects in flow past stationary and oscillating circular and D-section cylinders. Master's thesis, University of British Columbia:1968.
[7]VANDIVER J K. Dimensionless parameters important to the prediction of vortex-induced vibration of long, flexible cylinders in ocean currents[J]. Journal of Fluids and Structures,1993,7(5):423-455.
[8]BEARMAN P W. Vortex shedding from oscillating bluff bodies [J]. Annual Reviews of Fluid Mechanics,1984,16:195-222.
[9]GABBAI R D, BENAROYA H. An overview of modeling and experiments of vortex-induced vibration of circular cylinders[J]. Journal of Sound and Vibration, 2005,282 (3-5):575-616.
[10]WILLIAMSON C H K, GOVARDHAN R. Vortex-induced vibrations [J]. Annual Reviews of Fluid Mechenics,2004,36:413-455.
[11]WILLIAMSON C H K, GOVARDHAN R. A brief review of recent results in vortex-induced vibrations[J]. Journal of Wind Engineering and Industrial Aerodynamics5th International Colloquium on Bluff Body Aerodynamics and Applications,96(6-7):713-735.
[12]KHALAK A, WILLIAMSON C H K. Motions, forces and mode transitions in vortex-induced vibrations at low mass-damping[J]. Journal of Fluids and Structures, 1999,13(7-8):813-851.
[13]HALSE K H. On vortex shedding and prediction of vortex-induced vibrations of circular cylinders[D]. Norwegian University of Science and TechnologyDepartment of Marine Structures, Faculty of Marine Technology,1997.
[14]PRASANTH T K, MITTAL S. Vortex-induced vibrations of a circular cylinder at.low Reynolds numbers[J]. Journal of Fluid Mechanics,2008,594:463-491.
[15]VlKESTAD K. Multi-frequency response of a cylinder subjected vortex shedding and support motion[D]. Norwegian University of Science and Technology,2000.
[16]VIKESTAD K, VANDIVER J K, LARSEN C M. Added mass and oscillation frequency for a circular cylinder subjected to vortex-induced vibrations and external disturbance [J]. Journal of Fluids and Structures,2000,14(7):1071-1088.
[17]BISHOP E D R, HANSSEN A Y. The lift and drag forces on a circular cylinder oscillating in a flowing fluid, Proceedings of the Royal Society of London Series A,1964[C].
[18]SARPKAYA T. Transverse oscillations of a circular cylinder in uniform flow[R]. Naval Postgraduate School:Naval Postgraduate School,1977.
[19]WILLIAMSON C H K, ROSHKO A. Vortex formation in the wake of an oscillating cylinder [J]. Journal of Fluids and Structures,1988,2(4):355-381.
[20]MORSE T L, WILLIAMSON C H K. Prediction of vortex-induced vibration response by employing controlled motion[J]. Journal of Fluid Mechanics,2004,634:5-39.
[21]MOE G, Wu Z. The lift force on a vibrating cylinder in a current:In Proceedings of the Eighth Int. Offshore Mechanics and Arctic Engineering Symposium, The Hague, 1989[C].
[22]GOPALKRISHNAN R. Vortex-induced forces on oscillating bluff cylinders[D]. Massachusetts Institute of Technology,1993.
[23]SARPKAYA T. Fluid forces on oscillating cylinders[J]. Journal of the Waterway Port Coastal and Ocean Division-ASCE,1978,104(3):275-290.
[24]KAASEN K E, LIE H, SOLAAS F, et al. Norwegian deepwater program:analysis of vortex-induced vibrations of marine risers based on full-scale measurements: Proceedings of the Annual Offshore Technology Conference, Houston, TX, USA,2000[C].
[25]VIKESTAD K, LARSEN C M, VANDIVER J K. Norwegian deepwater program:damping of vortex-induced vibrations:Proceedings of the Annual Offshore Technology Conference, Houston, TX, USA,2000[C].
[26]VENUGOPAL M. Damping and response prediction of a flexible cylinder in a current[D]. Massachusetts Institute of Technology,1996.
[27]SWITHENBANK S B. Dynamic of long flexible cylinders at high-mode number in uniform and sheared flows[D]. Massachusetts Institute of Technology,2007.
[28]TRIM A D, BRAATEN H, LIE H, et al. Experimental investigation of vortex-induced vibration of long marine risers [J]. Journal of Fluids and Structures,2005,21(3 SPEC. ISS.):335-361.
[29]CHAPLIN J R, BEARMAN P W, HUERA HUARTE F J, et al. Laboratory measurements of vortex-induced vibrations of a vertical tension riser in a stepped current[J]. Journal of Fluids and Structures,2005,21(1 SPEC. ISS.):3-24.
[30]HUERA-HUARTE F J, BEARMAN P W. Wake structures and vortex-induced vibrations of a long flexible cylinder--Part 2:Drag coefficients and vortex modes[J]. Journal of Fluids and Structures,2009,25(6):991-1006.
[31]HUERA-HUARTE F J, BEARMAN P W. Wake structures and vortex-induced vibrations of a long flexible cylinder--Part 1:Dynamic response[J]. Journal of Fluids and Structures, 2009,25(6):969-990.
[32]SARPKAYA T. Computational methods with vortices-the 1988 Freeman Scholar Lecture [J]. Journal of Fluids Engineering, Transactions of the ASME,1989,111(1):5-52.
[33]GERRARD J H. Numerical computation of the magnitude and frequency of the lift on a circular cylinder[J]. Philosophical Transactions of the Royal Society of London, 1967,261:137-162.
[34]COTTET G H, KOUMOUTSAKOS P, SALIHI M. Vortex methods with spatially varying cores [J]. Journal of Computational Physics,2000,162(1):164-185.
[35]PLOUMHANS P, WINCKELMANS G S. Vortex methods for high-resolution simulations of viscous flow past bluff bodies of general geometry [J]. Journal of Computational Physics, 2000,165(2):354-406.
[36]PLOUMHANS P, WINCKELMANS G S, SALMON J K, et al. Vortex methods for direct numerical simulation of three-dimensional bluff body flows:Application to the sphere at Re=300, 500, and 1000[J]. Journal of Computational Physics,2002,178(2):427-463.
[37]LAM K, JIANG G D, LIU Y, et al. Grid-free surface vorticity method applied to flow induced vibration of flexible cylinders 2004[J]. International Journal for Numerical Methods In Fluids,2004,46:289-313.
[38]YAMAMOTO C T, MENEGHINI J R, SALTARA F, et al. Numerical simulations of vortex-induced vibration on flexible cylinders[J]. Journal of Fluids and Structures, 2004,19(4):467-489.
[39]吕林.海洋工程小尺度物体的相关水动力数值计算[D].大连理工大学,2006.
[40]LU X, DALTON C, ZHANG J. Application of large eddy simulation to flow past a circular cylinder[J]. Journal of Offshore Mechanics and Arctic Engineering, 1997,119(4):219-225.
[41]TUTAR M, HOLDO A E. Large eddy simulation of a smooth circular cylinder oscillating normal to a uniform flow[J]. Journal of Fluids Engineering-Transactions of the ASME, 2000,122(4):694-702.
[42]BREUER M. A challenging test case for large eddy simulation:High Reynolds number circular cylinder flow:International Journal of Heat and Fluid Flow,2000[C].
[43]KRAVCHENKO A G, MOIN P. Numerical studies of flow over a circular cylinder at Re=3900[J]. Physics of Fluids,2000,12(2):403-417.
[44]Lu X Y, DALTON C. Calculation of the timing of vortex formation from an ocsillating cylinder[J]. Journal of Fluids and Structures,1996,10(5):527-541.
[45]ATLURI S, RAO V K, DALTON C. A numerical investigation of the near-wake structure in the variable frequency forced oscillation of a circular cylinder [J]. Journal of Fluids and Structures,2009,25(2):229-244.
[46]VAN DRIEST E R. On turbulance flow near a wall [J]. Journal of the Aeronautical Sciences, 1956,23:1007-1011.
[47]张兆顺,崔桂香,许春晓.湍流理论与模拟[G].清华大学出版社,2005.
[48]ORSZAG S A, PATTERSON G S. Numerical simulation of three-dimensional homogeneous isotropic turbulance[J]. Physics Review Letters,1972,28:76-79.
[49]MA X, KARAMANOS C S, KARNIADAKIS G E. Dynamics and low-dimensionality of a turbulent near wake[J]. Journal of Fluid Mechanics,2000,410:29-65.
[50]DONG S, KARNIADAKIS G E. DNS of flow past a stationary and oscillating cylinder at Re =10000[J]. Journal of Fluids and Structures,2005,20(4 SPEC. ISS.):519-531.
[51]MARZOUK O A. Direct numerical simulations of the flow past a cylinder moving with sinusoidal and nonsinusoidal profiles [J]. Journal of Fluids Engineering, Transactions of the ASME,2009,131(12):1212011-1212019.
[52]HARTLEN R T, CURRIE I G. Lift-oscillator model of vortex-induced vibration[J]. Journal of the Engineering Mechanics,1970,96((EM5)):577-591.
[53]IWEN W D, BLEVINS R D. A Model for vortex-induced oscillations of structures [J]. Journal Of Applied Mechanics,1974,41 (3):581-586.
[54]IWAN W D. The vortex induced oscillations of elastic structural elements[J]. Journal of Engineering for Industray, 1975,97:1378-1382.
[55]IWAN W D. The vortex-induced oscillation of non-uniform structural systems [J]. Journal of Sound And Vibration,1981,79(2):291-301.
[56]SKOP R A, GRIFFIN 0 M. A model for the vortex-excited resonant response of bluff cylinders[J]. Journal of Sound and Vibration,1973,27(2):225-233.
[57]GRIFFIN O M, SKOP R A, KOOPMANN G H. The vortex-excited resonant vibrations of circular cylinders[J]. Journal of Sound and Vibration,1973,31(2):235-249, N1-N3.
[58]LANDL R. A mathematical model for vortex-excited vibrations of bluff bodies [J]. Journal of Sound and Vibration,1975,42(2):219-234.
[59]BALASUBRAMANIAN S, SKOP R A, HAAN F L, et al. Vortex-excited vibrations of uniform pivoted cylinders in uniform and shear flow[J]. Journal of Fluids and Structures, 2000,14(1):65-85.
[60]KIM W J, PERKINS N C. Two-dimensional vortex-induced vibration of cable suspensions [J]. Journal of Fluids and Structures,2002,16(2):229-245.
[61]FACCHINETTI M L, LANGRE D E, F B. Vortex shedding modeling using fiffusive Van der Pol ocsillators[J]. Comptes Rendus Mecanique,2002,330:451-456.
[62]WILLIAMS R G, SUARIS W. An analytical approach to wake interference effects on circular cylindrical structures[J]. Journal of Sound and Vibration,2006,295(1-2):266-281.
[63]郭海燕,王树青,吴纪宁,et al. Dynamic characteristics of marine risers conveying Fluid[J]. China Ocean Engineering, 2000(2):153-160.
[64]郭海燕,王元斌,傅强.The effect of internal fluid on the response of vortex-induced vibration of marine risers[J]. China Ocean Engineering,2004(1):11-20.
[65]LARSEN C M, HALSE K H, YTTERVIK R, et al. VIVANA, Theory Mannual [R]. Trondheim: MARINTEK, 2001.
[66]BAARHOLM G S, MARTIN LARSEN C, LIE H. Reduction of VIV using suppression devices—An empirical approach[J]. Marine Structures,18(7-8):489-510.
[67]VANDIVER J K, LI L. SHEAR7 program theory mannual [R]. MIT, Department of Ocean Engineering,1999.
[68]CHENG Y, LAMBRAKOS K F. Time domain riser VIV predictions compared to field and laboratory test data:Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering-OMAE, San Diego, CA, United states,2007[C].
[69]董艳秋.波、流联合作用下海洋平台张力腿的涡激非线性振动[J].海洋学报(中文版),1994(3).
[70]马驰,董艳秋,杨丽婷.海洋平台张力腿在两种边界条件下的涡激非线性振动的比较研究[J].船舶力学,2000(1)：56-65.
[71]凌国灿,王东耀.在平台振荡条件下TLP张力腿的涡激非线性响应[J].海洋学报(中文版),1998(3).
[72]Ted Belytschko, Liu Wing Kam, Moran Brian.连续体和结构的非线性有限元[M].庄茁,译.清华大学出版社,2002.
[73]NOH W F. CEL:A time-dependent, two-space-dimensional, coupled Eulerian-Lagrangian code[J]. Methods in Computational Physics,1964,3:117-179.
[74]LIU W K. Finite element procedure for fluid-structure interacitons and application to liquid storage tanks[J]. Nuclear Engineering And Design,1981,65:221-238.
[75]THOMAS HUGHES J R. Larangian-Eulerian finite element formulation for incompressible viscous flows [J]. Computers in Applied Mechanics and Engineering,1981,29(3):329-349.
[76]岳宝曾,王照林,匡金炉.非线性晃动问题的ALE边界元法[J].宇航学报,1998,19(1)：1-7.
[77]王建军,陆明万,张雄等.自由液面流体大晃动有限元方法[J].水动力学研究与进展(A辑),2001,16(3)：390-395.
[78]BATINA J T. Unsteady euler airfoil solutions using unstructured dynamic meshes[J]. AIAA Journal,1990,28(8):1381-1388.
[79]DAI M, SCHMIDT D P. Adaptive tetrahedral meshing in free-surface flow[J]. Journal of Computational Physics, 2005,208:228-252.
[80]JOHNSON A A, TEZDUYAR T E. Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces [J]. Computer Methods in Applied Mechanics and Engineering,1994,119(1-2):73-94.
[81]JOHNSON A A, TEZDUYAR T E. Advanced mesh generation and update methods for 3D flow simulations[J]. Computational Mechanics,1999,23(2):130-143.
[82]SAHIN M, MOHSENI K. An arbitrary Lagrangian-Eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa aequorea victoria[J]. Journal of Computational Physics,2009,228:4588-4605.
[83]LU L, QIN J M, TENG B, et al. Numerical investigations of lift suppression by feedback rotary oscillation of circular cylinder at low Reynolds number[J]. Physics of Fluids, 2011,23(0336013).
[84]WIESELSBERGER C. New data on the law of hydro and aerodynamic resistance [J]. Physikalische Zeitschrift,1921,22:321-382.
[85]BRAZA M, CHASSAING P, HA MINH H. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder[J]. Journal of Fluid Mechanics,1986,165:79-130.
[86]HERFJORD K. A study of two-dimensional separated flow by a combination of the finite element method and Navier-Stokes equations[D]. The Norwegian Institute of Technology, 1995.
[87]HENDERSON RD. Nonlinear dynamics and patterns in turbulent wake transiyion[J]. Journal of Fluid Mechanics,1997,352:65-112.
[88]RENGEL J E, SPHAIER S H. A projection method for unsteady Navier-Stokes equation with finite volume method and collocated grid[J]. Hybrid Methods in Heat and Mass Transfer, 1999,4:1.
[89]HE J W, GLOWINSKI R, METCALFE R, et al. Active control and drag optimization for flow past a circular cylinder: Ⅰ. oscillatory cylinder rotation[J]. Journal of Computational Physics,2000,163(1):83-117.
[90]WANDERLEY J B V, SOUZA GHB, SPHAIER S H, et al. Vortex-induced vibration of an elastically mounted circular cylinder using an upwind TVD two-dimensional numerical scheme[J]. Ocean Engineering,2008,35(14-15):1533-1544.
[91]NORBERG C. Fluctuating lift on a circular cylinder:review and new measurements[J]. Journal of Fluids and Structures,2003,17(1):57-96.
[92]GUILMINEAU E, QUEUTEY P. A numerical simulation of vortex shedding from an ocsillating circular cylinder[J]. Journal of Fluids and Structures,2002,16(6):773-794.
[93]于德介,程军圣,杨宇.机械故障诊断的Hilbert-Huang变换方法[M].科学出版社,2006.
[94]BLACKBURN H M, HENDERSON R D. A study of two-dimensional flow past an oscillating cylinder[J]. Journal of Fluid Mechanics,1999,385:255-286.
[95]SINGH A P, DE A K, CARPENTER V K, et al. Flow past a transversely oscillating square cylinder in free stream at low reynolds numbers [J]. International Journal for Numerical Methods in Fluids,2009,61(6):658-682.
[96]MINHYUNG L, SUNG-YEOUL L. Vortex-induced vibrations of a circular cylinder at low Reynolds Numbers[J]. KSME International Journal,2003,17(11):1628-1637.
[97]VENUGOPAL M. Damping and response prediction of a flexible cylinder in a current[D]. Massachusetts Institute of Technology,1996.
[98]张建侨,宋吉宁,吕林等.质量比对柔性立管涡激振动影响实验研究[J].海洋工程,2009(4)：38-44.
[99]宋吉宁,吕林,张建侨等.三根附属控制杆对海洋立管涡激振动抑制作用实验研究[J].海洋工程,2009(3)：23-29.
[100]陈涛,张嵩.用于桥梁健康监测的光纤光栅解调系统[J].武汉理工大学学报,2009(15)：41-44.
[101]刘晖,瞿伟廉,李功标等.光纤光栅传感系统在结构损伤识别中的应用[J].应用基础与工程科学学报,2009(3)：395-401.
[102]张建侨,宋吉宁,吕林等.柔性立管涡激振动实验的数据分析[J].中国海洋平台,2009(4)：26-32.
[103]WILLDEN R H J, GRAHAM J M R. Multi-modal vortex-induced vibrations of a vertical riser pipe subject to a uniform current profile [J]. European Journal of Mechanics-B/Fluids 2004,23(1):209-218.
[104]SONG J N, Lu L, TENG B, et al. Laboratory tests of vortex-induced vibrations of a long flexible riser pipe subjected to uniform flow[J]. Ocean Engineering, 2011,38:1308-1322.
[105]SREIDE M. Experimental investigation of in-line and cross-flow VIV:Proceedings of the International Offshore and Polar Engineering Conference, Honolulu, HI, United states,2003[C].
[106]HANSEN E A, BRYNDUM M, MAYER S. Interaction of in-line and cross-flow vortex induced vibrations in risers:Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, Oslo, Norway, 2002[C].
[107]HUSE E, NIELSEN F G, SREIDE T. Coupling between in-line and transverse VIV response: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, Oslo, Norway,2002[C].
[108]CHAPLIN J R, BEARMAN P W, CHENG Y, et al. Blind predictions of laboratory measurements of vortex-induced vibrations of a tension riser [J]. Journal of Fluids and Structures, 2005,21(1 SPEC. ISS.):25-40.
[109]张雄,王天舒.计算动力学[M].清华大学出版社,2007.
[110]MYKLEBUST L I, SKALLERUD B. Model reduction methods for flexible structure:The 15th Nordic Seminar on Computational Mechanics, Aalborg, Denmark,2002[C].
[111]施吉林,张宏伟,金光日.计算机科学计算[M].高等教育出版社,2005.
[112]唐国强,吕林,滕斌等.大长细比柔性杆件涡激振动实验[J].海洋工程,2011(1)：18-25.
[113]3000米深水钻井平台“海洋石油981”顺利出坞[J].中国科技信息,2010(5)：6.