仿鱼类摆动尾鳍推进系统的水动力研究
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摘要
鱼类等水下生物具有高效游动和准确定位的能力。同鱼类的游动相比较，应用在无人水下航行器上（Underwater Unmaned Vehicle, UUV）的传统推进系统由许多螺旋桨组成。这些螺旋桨分布在多个方向上，用来推进和操纵艇体。传统的推进系统往往占用较大的空间消耗较多的能量。近年来，越来越多的仿生推进系统样机被开发出来。在这些系统中，鱼体-尾鳍（Body and Caudal Fin, BCF）模式最为普遍。因此，BCF模式的鱼类游动引起了众多学者的关注。本文以研究仿鱼类摆动尾鳍推进系统的水动力性能为目的，在研究过程中，以计算流体力学方法（Computational Fluid Dynamics, CFD）为主要工具，分析了仿鱼类摆尾推进系统的推进性能。
首先，为了研究摆尾推进系统在复杂流场中的推进性能，采用求解RANS方程的方法计算了二维摆动水翼在振动半圆柱扰动流场中的水动力性能。分析了来流旋涡和水翼摆动生成旋涡之间的相互作用模式。计算结果显示来流旋涡对水翼的水动力影响很大，水翼能够从来流旋涡中吸收能量，提高推进效率。
其次，研究了尾鳍形状和柔性变形对摆尾推进系统水动力性能的影响。一方面，对三种不同形状（仿金枪鱼、仿海豚、仿白鲸尾鳍）摆动尾鳍的水动力性能进行了计算。计算结果和实验结果的比较表明非定常面元法和求解RANS方程的方法都是有效的。尾鳍形状特别是投影面积对摆动尾鳍的水动力性能有重要影响。通过对三种不同形状尾鳍的水动力性能进行比较发现：仿金枪鱼摆动尾鳍的脱落涡分布范围最小，推进效率最高。另一方面，研究了具有弦向变形的柔性摆动尾鳍的推进性能。讨论了弦向变形相位角对柔性摆动尾鳍水动力性能的影响。研究表明弦向变形相位角能够减小输入功率，提高推进效率。通过调整弦向变形相位角可以节省能量。
再次，研究了非对称运动对仿鱼类摆尾推进系统的影响。分别计算了非对称纯摇摆运动、非对称纯升沉运动、摇摆偏移非对称摆动运动和升沉偏移非对称摆动运动这四种非对称运动下摆尾推进系统的水动力性能。研究表明非对称运动的尾鳍在一个运动周期内产生非对称的水动力。摇摆偏移能够导致侧向力在一个运动周期内的平均值非零。升沉偏移引起了水动力变化的不连续。因此，对原来的升沉偏移非对称模型进行了改进，以消除水动力的跳跃。此外，脱落涡也受到非对称运动的影响，其分布也不再对称。
最后，采用求解RANS方程的方法数值模拟了以“仿生-I”为原型的仿金枪鱼水下机器人的自主游动过程。提出了一种解决流体-运动耦合问题的方法。以弹簧原理为基础的动网格技术结合网格重构技术保证了计算网格的质量。计算结果和实验结果的比较表明这种计算方法是有效的。此外，研究表明尾鳍的摆动频率、侧向运动振幅和摇摆运动振幅对金枪鱼的巡游速度、水动力性能以及脱落涡有很大的影响。
Fish and cetaceans have an outstanding capability to swim efficiently and locate preciselyunder water by flow control. By contrary, the traditional propulsion systems used in UnmannedUnderwater Vehicles (UUVs) always have many screw propellers distributed in variousdirections for both propulsion and maneuvering, which take large room and consume highenergy. In recent years, many kinds of bio-propulsion systems have been develped. Amongthese bio-propulsion systems, the BCF (Body and Caudal Fin) mode is widely used. Therefore,fish swimming in BCF mode are paid more attention by researchers. This paper presents studyon hydordynamic performance of biomemetic fish flapping caudal fin propulsion system. Inthe study, Computational Fluid Dynamics (CFD) method is applied to analyze propulsionperformance of the flapping caudal fin propulsion system.
Firstly, in order to study the propulsion perfromance of the hydrofoil in complex flowfield, hydrodynamic performance of a two-dimensional flapping hydrofoil behind anoscillating semi cylinder is calculated based on RANS equations. Interaction modes betweenincoming vortices and foil vortices are analyzed. The results show that incoming vorticesmake large influence on hydrodynamics of the hydrofoil. The hydrofoil could absorb energyfrom incoming vortices so that the propulsion efficiency is enhanced.
Secondly, effects of caudal fin shapes and flexibility are studied. First of all, thepropulsion performance of flapping caudal fins with three different shapes (the tuna caudal fin,the dolphin caudal fin and the whale caudal fin) is calculated by both the unsteady panel methodand the RANS equations based method. The comparison between calculation results andexperimental results indicates that the two numerical methods are both validated. It is alsoshown that the caudal fin shape especially as far as its projected area has a crucial influence onthe propulsion performance of a flapping caudal fin. The tuna caudal fin produces the smallestvortices distribution and has the largest propulsion efficiency. Then, the propulsion performanceof a flapping caudal fin with chordwise flexibility is studied. The effects of chordwise deflectionphase angle on propulsion performance are discussed. It is figured out that some chordwisedeflection phase angles make import power smaller, propulsion efficiency higher. Energycould be saved by adjusting chordwise deflection phase angle.
Thirdly, effects of asymmetric motions are studied. Numerical simulations on a flapping caudal fin under asymmetric motions are performed by the panel method and RANSequations based method. Four kinds of asymmetric motions are discussed, includingasymmetric pitch motion, asymmeric heave motion, flapping motion with pitch bias andflapping motion with heave bias. The study indicates that under asymmetric motions,unsymmetrical hydrodynamics in one motion period can be produced. It is indicated that thepitch bias makes the mean lateral force non-zero. Meanwhile, hydrodynamics varying inmotion period is not continuous under heave bias. Thus, Modifications are done so as to getrid of the jump of hydrodynamics. Besides that, shedding vortices are also influenced byasymmetric motions.
Finally, the self-propelled swimming of a bio-mimetic UUV called “FangSheng-I” iscalculated by RANS equations based method. An algorithm of fluid-motion coupling isdesigned and implemented in the CFD code. Spring based dynamic mesh and remeshtechniques are used to keep grid quality. The comparison between calculating results andexperimental results shows that the numerical method is validated. After that, it is indicatedthat that motion parameters including motion frequency, heave amplitude and pitch amplitudemakes an important effects on cruising velocity, hydrodynamic performance and sheddingvortices.
首先，为了研究摆尾推进系统在复杂流场中的推进性能，采用求解RANS方程的方法计算了二维摆动水翼在振动半圆柱扰动流场中的水动力性能。分析了来流旋涡和水翼摆动生成旋涡之间的相互作用模式。计算结果显示来流旋涡对水翼的水动力影响很大，水翼能够从来流旋涡中吸收能量，提高推进效率。
其次，研究了尾鳍形状和柔性变形对摆尾推进系统水动力性能的影响。一方面，对三种不同形状（仿金枪鱼、仿海豚、仿白鲸尾鳍）摆动尾鳍的水动力性能进行了计算。计算结果和实验结果的比较表明非定常面元法和求解RANS方程的方法都是有效的。尾鳍形状特别是投影面积对摆动尾鳍的水动力性能有重要影响。通过对三种不同形状尾鳍的水动力性能进行比较发现：仿金枪鱼摆动尾鳍的脱落涡分布范围最小，推进效率最高。另一方面，研究了具有弦向变形的柔性摆动尾鳍的推进性能。讨论了弦向变形相位角对柔性摆动尾鳍水动力性能的影响。研究表明弦向变形相位角能够减小输入功率，提高推进效率。通过调整弦向变形相位角可以节省能量。
再次，研究了非对称运动对仿鱼类摆尾推进系统的影响。分别计算了非对称纯摇摆运动、非对称纯升沉运动、摇摆偏移非对称摆动运动和升沉偏移非对称摆动运动这四种非对称运动下摆尾推进系统的水动力性能。研究表明非对称运动的尾鳍在一个运动周期内产生非对称的水动力。摇摆偏移能够导致侧向力在一个运动周期内的平均值非零。升沉偏移引起了水动力变化的不连续。因此，对原来的升沉偏移非对称模型进行了改进，以消除水动力的跳跃。此外，脱落涡也受到非对称运动的影响，其分布也不再对称。
最后，采用求解RANS方程的方法数值模拟了以“仿生-I”为原型的仿金枪鱼水下机器人的自主游动过程。提出了一种解决流体-运动耦合问题的方法。以弹簧原理为基础的动网格技术结合网格重构技术保证了计算网格的质量。计算结果和实验结果的比较表明这种计算方法是有效的。此外，研究表明尾鳍的摆动频率、侧向运动振幅和摇摆运动振幅对金枪鱼的巡游速度、水动力性能以及脱落涡有很大的影响。
Fish and cetaceans have an outstanding capability to swim efficiently and locate preciselyunder water by flow control. By contrary, the traditional propulsion systems used in UnmannedUnderwater Vehicles (UUVs) always have many screw propellers distributed in variousdirections for both propulsion and maneuvering, which take large room and consume highenergy. In recent years, many kinds of bio-propulsion systems have been develped. Amongthese bio-propulsion systems, the BCF (Body and Caudal Fin) mode is widely used. Therefore,fish swimming in BCF mode are paid more attention by researchers. This paper presents studyon hydordynamic performance of biomemetic fish flapping caudal fin propulsion system. Inthe study, Computational Fluid Dynamics (CFD) method is applied to analyze propulsionperformance of the flapping caudal fin propulsion system.
Firstly, in order to study the propulsion perfromance of the hydrofoil in complex flowfield, hydrodynamic performance of a two-dimensional flapping hydrofoil behind anoscillating semi cylinder is calculated based on RANS equations. Interaction modes betweenincoming vortices and foil vortices are analyzed. The results show that incoming vorticesmake large influence on hydrodynamics of the hydrofoil. The hydrofoil could absorb energyfrom incoming vortices so that the propulsion efficiency is enhanced.
Secondly, effects of caudal fin shapes and flexibility are studied. First of all, thepropulsion performance of flapping caudal fins with three different shapes (the tuna caudal fin,the dolphin caudal fin and the whale caudal fin) is calculated by both the unsteady panel methodand the RANS equations based method. The comparison between calculation results andexperimental results indicates that the two numerical methods are both validated. It is alsoshown that the caudal fin shape especially as far as its projected area has a crucial influence onthe propulsion performance of a flapping caudal fin. The tuna caudal fin produces the smallestvortices distribution and has the largest propulsion efficiency. Then, the propulsion performanceof a flapping caudal fin with chordwise flexibility is studied. The effects of chordwise deflectionphase angle on propulsion performance are discussed. It is figured out that some chordwisedeflection phase angles make import power smaller, propulsion efficiency higher. Energycould be saved by adjusting chordwise deflection phase angle.
Thirdly, effects of asymmetric motions are studied. Numerical simulations on a flapping caudal fin under asymmetric motions are performed by the panel method and RANSequations based method. Four kinds of asymmetric motions are discussed, includingasymmetric pitch motion, asymmeric heave motion, flapping motion with pitch bias andflapping motion with heave bias. The study indicates that under asymmetric motions,unsymmetrical hydrodynamics in one motion period can be produced. It is indicated that thepitch bias makes the mean lateral force non-zero. Meanwhile, hydrodynamics varying inmotion period is not continuous under heave bias. Thus, Modifications are done so as to getrid of the jump of hydrodynamics. Besides that, shedding vortices are also influenced byasymmetric motions.
Finally, the self-propelled swimming of a bio-mimetic UUV called “FangSheng-I” iscalculated by RANS equations based method. An algorithm of fluid-motion coupling isdesigned and implemented in the CFD code. Spring based dynamic mesh and remeshtechniques are used to keep grid quality. The comparison between calculating results andexperimental results shows that the numerical method is validated. After that, it is indicatedthat that motion parameters including motion frequency, heave amplitude and pitch amplitudemakes an important effects on cruising velocity, hydrodynamic performance and sheddingvortices.
引文
[1]童秉纲,孙茂,尹协振.飞行和游动生物流体力学的国内研究进展概述.自然杂志.2005,27(4):191–199.
[2]王天然,王越超,曲道奎.机器人技术新进展.中国科学院科学与社会系列报告-2004高技术发展报告,北京:科学出版社,2004.
[3] Gray J. Studies in animal locomotion. IV. The propulsive powers of thedolphin. Journal of Experimental Biology.1936,13:192-199.
[4] M.S. Triantafyllou, G.S. Triantafyllou, D.K.P. Yue, Hydrodynamics offish-like swimming. Annual Reviews of Fluid Mechanics.2000,32:33–53.
[5] Fish F. E., Lauder G. V. Passive and Active Flow Control by Swimming Fishesand Mammals. Annual Reviews of Fluid Mechanics.2006,38:193–224.
[6] Weihs D. Hydrodynamics of fish schooling. Nature.1973,241:290-291.
[7] Wu T. Y. T. On Theoretical Modeling of Aquatic and Aerial Locomotion.Advance Applied Mechanics.2001,38:291-353.
[8] Triantafyllou M. S., Triantafyllou G. S., Yue D. K. P. Hydrodynamics ofFish like Swimming. Annual Reviews on Fluid Mechanics.2000,32:33–53.
[9] Triantafyllou M. S., Hover F. S., Techet A. H., et al. Review ofHydrodynamic Scaling Laws in Aquatic Locomotion and Fishlike Swimming.Applied MechanicsReviews.2005,58(4):225–237.
[10]刘军考.仿鱼水下推进器理论与实验研究.哈尔滨工业大学工学博士学位论文.2002.
[11] M.S.Triantafyllou，G.S.Triantafyllou. An efficient swimming machine.Scientific.1995，272(3):64-70P.
[12] Breder C.M.The Locomotion of Fishes.Zoological.1926，4：159–291.
[13] J.L.Lighthill. Mathematical biofluiddynamics. Society for Industrial andApplied Mathematics， Philadelphia，1975
[14] Webb P.W. The biology of fish swimming in Mechanics and physiology ofanimal swimming. Cambridge: U.K.Cambridge University Press.1994：45-62.
[15] C.C.Lindsey. Form function and locomotory habits in fish. Fish Physiology.New York: Academic Press.1978(7):1-100.
[16]陈维山，夏丹，刘军考，石胜君.鲹科和鲔科仿鱼机器人自主游动机理的分析与比较.机械工程学报.
[17] C.Pozrikidis. A practical guide to boundary elements methods.CHAPMAN&HALL/CRC,2002.
[18] R.J.Leveque. Finite difference methods for ordinary and partialdifferential equations. Society for Industrial and Applied Mathematics,1997.
[19] M.S.Gockenbach. Understanding and implementing the finite element method.Society for Industrial and Applied Mathematics,2006.
[20] J.H.Ferziger, M.Peric. Computational methods for fluid dynamics.Springer,2002.
[21] J.Lighthill. Note on the swimming of slender fish. J. Fluid Mech.1960，9:305-317.
[22] J.Lighthill. Aquatic animal propulsion of high hydromechanicalefficiency. J. Fluid Mech.1970，44:265-301.
[23] Lighthill M.J. Large-Amplitude Elongated-Body Theory of Fish Locomotion.Proceeding of the Royal Society of London Series B,1971,179:125-138.
[24] Weihs D. A Hydrodynamical Analysis of Fish Turning Manoeuvres. Proceedingof the Royal Society of London Series B,1972,182:59-72.
[25] Weihs D. The Mechanism of Rapid Starting of Slender Fish. Biorheology,10:343-350.
[26] T.Y.Wu. Swimming of a waving plate. J. Fluid Mech.1961，10:321-344.
[27] T.Y.Wu. Hydrodynamics of swimming propulsion. Part1. Swimming of atwo-dimension flexible plate at variable forward speeds in an inviscidfluid. J. Fluid Mech.1971，46(2):337-355.
[28] T.Y. Wu. Hydrodynamics of swimming propulsion. Part2. Some optimum shapeproblems. J. Fluid Mech.1971，46(3):521-544.
[29] T.Y. Wu. Hydrodynamics of swimming propulsion. Part3. Swimming andoptimum movements of slender fish with side fins. J. Fluid Mech.1971，46(3):545-568.
[30] J.N.Newman，T.Y.Wu. A generalized slender-body theory for fish-like forms.J. Fluid Mech.1973，57(4):673-693.
[31] J. Y. Cheng, L. X. Zhuang, B. G. Tong. Analysis of Swimming ThreeDimensional Waving Plate. Journal of Fluid Mechanics.1991,232:341-355.
[32]程健宇，庄礼贤，童秉纲.三维变幅波板的游动.水动力学研究与进展.1991增刊，1-11页
[33]程健宇，庄礼贤，童秉纲.鱼类鳗鲡模式推进的游动性能分析.水动力学研究与进展.1998，3(3):87-97页
[34]童秉纲，庄礼贤.描述鱼类波状游动的流体力学模型及其应用.自然杂志.1998，20(1):1-7页.
[35] C. Zhang, L. X. Zhuang, X. Y. Lu. Analysis of Hydrodynamics forTwo-dimensional Flowaround Waving Plates. Journal of Hydrodynamics.2002,29(1):18-22.
[36] J. Y. Cheng, T. J. Pedley, J. D. Altringham. A Continuous Dynamic BeamModel for Swimming Fish. Phil Trans Roy Soc Lond B,1998,353:981-997.
[37] D.S.Betteridge，R.D.Archer. A study of the mechanics of flapping wings.Aer. Quart.1974.
[38] R.D.Archer， J.Sapup， D.S.Betteridge. Propulsive characteristics offlapping wings. J. Aero.1979:355-371P.
[39] A.R.Ahmadi. An asymptotic unsteady lifting-line theory with energeticsand optimum motion of thrust-producing lifting surfaces. Ph.D. thesis.MIT.
[40] M. G. Chopra. Large Amplitude Lunate-Tail Theory of Fish Locomotion.Journal of Fluid Mechanics.1976,74:161-182.
[41] M. G. Chopra, T. Kambe. Hydrodynamics of Lunate-Tail Swimming Propulsion:Part2. Journal of Fluid Mechanics.1977,79:49-69..
[42] K. D. Jones，M. F. Platzer. Numerical computation of flapping-wingpropulsion and power extraction. AIAA-97-0826.
[43] JONES, K. D., CASTRO, B. D., MAHMOUND, O., PLATZER, M. F., NEEF, M. F.,GOENT, K., AND HUMMEL, D. A Collaborative Numerical and ExperimentalInvestigation of Flapping-Wing Propulsion, AIAA paper,2002-0706.
[44] P. Liu, N. Bose. Propulsive Performance From Oscillating propulsors withspanwise flexibility. Proceeding of the Royal Society of London SeriesA,1997,453:1763-1770.
[45] Pengfei Liu. A time-domain panel method for oscillating propulsors withboth chordwise and spanwise flexibility. PhD Thesis. Memorial Universityof Newfoundland， Canada.1997.
[46]苏玉民，黄胜，庞永杰等.仿鱼尾潜器推进系统的水动力分析.海洋工程，2002，20(2):54-59.
[47] Q. J. Qian, M. Q. Liu, L. Sun, D. J. Sun. The Optimal Motion ofTwo-Dimensional Undlating Plate Swimming in Fluid Flow. Journal ofHydrodynamics23(1):12-20.
[48] Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS. Three-dimensional flowstructures and vorticity control in fish-like swimming. Journal of FluidMech,2002,468:1-28
[49] Wolfgang M. J. Hydrodynamics of Flexible-Body Swimming Motions. PhDthesis, M.I.T., Boston, MA, U.S.A.,1999.
[50] Wolfgang M. J., Anderson J. M., Grosenbaugh M., Yue D., Triantafyllou M.Nearbody Flow Dynamics in Swimming Fish. Journal of Experimental Biology,202:2303-2327..
[51]吴辅兵.振动翼推进及干扰效应非定常流体动力研究.哈尔滨工程大学工学博士论文.2004.
[52] Liu H., Wassersug R., Kawachi K. A Computational Fluid Dynamics Study ofTadpole Swimming. Journal of Experimental Biology.1996,199(6):1245-1260.
[53] Liu H., Wassersug R., Kawachi K. The Three Dimensional Hydrodynamics ofTadpole Locomotion. Journal of Experimental Biology.1997,200(6):2807-2819.
[54] Liu H., Katsumata Y. Computation of Self-Propelled Swimming in LarvaFishes. Journal of Computational Physics.2006,28:219-232.
[55] Carling J., Williams T. L., Bowtell G. Self-Propelled AnguilliformSwimming: Simultaneous Solution of the Two-Dimensioanl Navier-StokesEquations and Newton’s Laws of Motion. Journal of Experimental Biology.1998,201:3143-3166.
[56]胡文蓉.鱼类单向机动运动二维流动特征的数值研究.中国科学院研究生院博士论文.2004.
[57] W. R. Hu, B. G. Tong, H. Liu. A Computational Study on Backeard SwimmingHydrodynamics in the Eel. Journal of Hydrodynamics,2005,17(4):438-447.
[58]夏全新，鲁传敬，吴磊.鱼类波状摆动推进的数值模拟.水动力学研究与进展A辑.2005，20：921-928.
[59] S. Kern, P. Koumoutsakos.Simulations of Optimized AnguilliformSwimming.Journal of Experimental Biology.2006，209：4841-4857.
[60] A. Leroyer, M. Visonneau. Numerical Methods for RANSE Simulation of aSelf-Propelled Fish-Like Body. Journal of Fluids and Structures.2005,20:975-991.
[61] W.C.Sandberg，R.Ramamurti. Unsteady flow computations for oscillatingfins: a status report. Papers of11thInternational symposium on UUStechnology. Autonomous Undersea Systems Institute.1999:182-194.
[62]董根金.波状摆动变形体非定常粘性绕流的数值研究.中国科学技术大学博士论文.2006.
[63]王亮.仿生鱼群自主游动及控制的研究.河海大学博士论文.2007.
[64]邵雪明.二维波动板绕流场的DLM/FD.模拟中国力学学会技术大会2005.
[65]邓见.含运动物体三维复杂流场数值模拟和尾流结构研究.浙江大学博士论文.2007.
[66]张来平，常兴华，段旭鹏，张涵信.三鱼群游流动干扰及其减阻机理的数值研究.水动力学研究与进展.2007，22(6)：753-760.
[67]杨焱.锦鲤常规自由游动的流动物理研究.中国科技大学博士论文.2008.
[68]夏丹.鲔科仿生原型自主游动机理的研究.哈尔滨工业大学博士论文.2010.
[69]徐晓锋.仿生鱼游动与运动控制的数值分析技术.上海交通大学硕士论文.2011.
[70]张晓庆,王志东,张振山二维摆动水翼仿生推进水动力性能研究.水动力学研究与进展.200621（5），632-639.
[71]王志东，丛文超，张淋，李立军.自主航行模式下二维摆动尾鳍的推进性能研究.江苏科技大学学报（自然科学版）.2010,24(6):523-528.
[72] Wang Z. D., Lao Y. J., LI L. J., Cong W. C. Experiment on the Characteristicof3D Vortex Ring Behind a Flexible Oscillating Caudal Fin. Journal ofHydrodynamics, Ser. B,2010,22(3):393-4014.
[73]杨亮.仿金枪鱼摆动尾鳍的水动力性能与推进机理研究.哈尔滨工程大学博士论文.2009.
[74] I. Borazjani, F. Sotiropoulos. Numerical Investigation of theHydrodynamics of Carangiform Swimming in the Transitional and inertialFlow Regimes. Journal of Experimental Biology.2008,211:1541-1558.
[75] I. Borazjani, F. Sotiropoulos. Numerical Investigation of theHydrodynamics of Anguilliform Swimming in the Transitional and inertialFlow Regimes. Journal of Experimental Biology.2009,212:576-592.
[76] I. Borazjani, F. Sotiropoulos. On the Role of Form and Kinematics on theHydrodynamics of Self-Propelled Body/Caudal Fin Swimming. Journal ofExperimental Biology.2010,213:89-107.
[77] L. Schouveiler, F. S. Hover, M. S. Triantafyllou. Performance of FlappingFoil Propulsion. Journal of Fluids and Structures.2005,20:949-959.
[78] F. S. Hover, Φ. Haugsdal, M. S. Triantafyllou. Effect of Angle of AttackProfiles in Flapping Foil Propulsion. Journal of Fluids and Structure.2004,19:37-47.
[79] Gopalkrishnan R, Triantafyllou MS, Triantafyllou GS et al. ActiveVorticity Control in a Shear Flow Using a Flapping Foil. Journal of FluidMechanics,1994,27(4):1-21.
[80] A. H. Techet. Experimental Visualization of the Near-BoundaryHydrodynamics about Fish-Like Swimming Bodies. Massachusetts Institutesof Technology, Cambridge,2001.
[81] George V Lauder, E. Drucker. Forces, fishes, and fluids: hydrodynamicmechanisms of aquatic locomotion. News Phsiol. Sci.2002,17:235-240
[82] J. C. Nauen, G. V. Lauder. Three-Dimensional Analysis of Finlet Kinematicsin the Chub Mackerel. Biol.Bull.2001,200:9-19.
[83]陈宏，竺长安，尹协振，邢晓正.仿生机器人C形起动的动力学分析.哈尔滨工业大学学报.2009,41(1):113-117.
[84]吴燕峰，贾来兵，尹协振.斑马鱼S型起动运动学研究.实验力学.2007,22(5):519-526.
[85]周萌，尹协振，童秉纲.鲫鱼皮肤和肌肉的力学性能研究.实验力学.2010,25(5):536-545.
[86]贾来兵.二维流场中板状柔性体与流体相互作用的研究.中国科学技术大学博士论文.2009.
[87]吴冠豪，曾理江.用于自由游动鱼三维测量的视频跟踪方法.中国科学G辑，2007,37(6):760-766.
[88]老轶佳，王志东，张振山，李力军.摆动柔性鳍尾涡流场的实验测试与分析.水动力学研究与进展A.2009,24(1):106-112.
[89] Hui Yan, Yu-min Su, Liang Yang. Experimentation of Fish Swimming Basedon Tracking Locomotion Locus. Journal of Bionic Engineering,2008,5(3):258-263.
[90]苏玉民，杨亮，赵士奇，王晓飞.仿鱼尾鳍推进系统的水动力性能实验研究.华中科技大学学报.2009，37(9)：82-85.
[91] D. S. Barrett. The Design of a Flexible Hull Undersea Vehicle Propelledby an Oscillating Foil. Massachusetts Institutes of Technology, Cambridge,1994.
[92] H. Hu, Biologically inspired design of autonomous robotic fish at essex, Proceedingsof the IEEE SMC UK-RI Chapter Conference, on Advances in Cybernetic Systems,Sheffield,2006,3-8.
[93] http://www.nmri.go.jp/eng/khirata/fish
[94] Guo S X, Fukuda T, Asaka K. Fish-like underwater microrobot with3DOF.Proceedings of the IEEE International Conference on Robotics and Automation,2002(1):738-743.
[95]梁建宏，邹丹，王松等. SPC-II机器鱼平台及其自主航行实验.北京航空航天大学学报.2005,31(7):709-713.
[96]夏丹，陈维山，刘军考，韩路辉.基于Kane方法的仿鱼机器人波状游动的动力学建模.机械工程学报.2009,45(6):41-49.
[97]张志刚，喻俊志，王硕，桑海泉，谭民.多关节仿鱼运动推进机构的设计与实现.中国造船.2005,46(1):22-28.
[98]陈尔奎，喻俊志，王硕，谭民.一种基于视觉的仿生机器鱼实时避障综合方法.控制与决策.2004，19(4)：452-458.
[99]喻俊志，陈尔奎，王硕，谭民.基于颜色信息的多机器鱼并行视觉跟踪算法.中国科学院研究生院学报.2003,20(4):433-440.
[100]成巍，苏玉民，秦再白，秦仔白，万磊，徐玉如.一种仿生水下机器人的研究进展.船舶工程.2004，26(1):5-8.
[101] Stephen Licht Victor Polidoro Melissa Flores, Franz Hover, and MichaelTriantafyllou Design and Projected Performance of a Flapping Foil AUV.Proceedings of the13thInternational Symposium on Unmanned UntetheredSubmersible Technology.2003.
[102]胡天江.仿生长鳍波动适应性理论与控制方法研究.国防科技大学工学博士论文.2008.
[103] George V. Lauder and Eliot G. Drucker. Morphology And ExperimentalHydrodynamic Of Fish Fin Control Surface. Proceedings of the13thInternational Symposium on Unmanned Untethered Submersible Technology.2003.
[104] Eliot G. Drucker And Geoger V. Lauder. Locomoter Forces on A Swimming Fish:Three-Dimensional Vortex Wake Dynamics Quantified Using Digital ParticleImage Velocimetry. The Journal of Experimental Biology202,2393–2412(1999) Printed in Great Britain The Company of Biologists Limited1999.
[105] Streitlien K, Triantafyllou GS.Efficient foil propulsion through vortexcontrol. AIAA Journal,1996,34(11):2315-2318.
[106] Beal DN. Propulsion through wake synchronization using flapping-foil.Massachusetts Institutes of Technology, Cambridge,2003.
[107] Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS. Three-dimensional flowstructures and vorticity control in fish-like swimming. Journal of FluidMech,2002,468:1-28.
[108] J. Liao. Neuromuscular control of trout swimming in a vortex street:implications for energy economy dring the Karman gait. Journal ofExperimental Biology.2004,207:3495-3506.
[109] Florian R. Menter. Improved Two-Equation k Turbulence Models forAerodynamic Flows. NASA Technical Memorandum103975.1992
[110] Simmons JEL. Phase-angle measurements between hot-wire signals in theturbulent wake of a two-dimensional bluff body. Journal of Fluid Mechanics,1974,64:599-609.
[111] Anderson JM. Vorticity control for efficiency propulsion. MassachusettsInstitutes of Technology, Cambridge,1996.
[112] Anderson JM, Kerrebrock P A. The Vorticity Control Unmanned UnderseaVehicle (VCUUV): An Autonomous Robot Tuna. Proceedings of the11thInternational Symposium on Unmanned Untethered Submersible Technology,Durham, USA,1999:63-70.
[113] Nakashima M, Ono K. Experimental study of two-joint dolphin robot.Proceedings of the11thInternational Symposium on Unmanned UntetheredSubmersible Technology, Durham, USA,1999,82-89.
[114] P.Liu，N.Bose. Hydrodynamic characteristics of a lunate shape oscillatingpropulsor. Ocean Eng.1999，26:519-529.
[115]程健宇,庄礼贤,童秉纲.新月形尾鳍推进的流体力学分析.力学学报,1992,24(4)：458-465.
[116]刘军考,陈维山,陈在礼.尾鳍的形状与运动参数对推进速度的影响.高技术通信,2001,4：86-88
[117]李龙,尹协振.鲹科类鱼尾模型的巡游推进特性实验研究.实验流体力学,2008,22(1)：1-6.
[118] J Katz, D Weihs. Hydrodynamic propulsion by large amplitude oscillation of an airfoilwith chordwise flexibility. J. Fluid Mech,1978,88,485-497.
[119] P Prempraneerach, F Hover, M S Triantafyllou. The effect of chordwiseflexibility on the thrust and efficiency of a flapping foil. Proceedingsof the13thInternational symposium on Unmanned Untethered SubmersibleTechnology, Durham, USA,2003:120-128.
[120] Qiang Zhu. Numerical simulation of a flapping foil with chordwise orspanwise flexibility. AIAA Journal,2007,45(10):2448-2458.
[121]王志东，张晓庆，丛文超.柔性摆动水翼弦向变形模式及其对推进性能影响的研究[J].船舶力学，2010，14(7)：609-707.
[122]成巍，苏玉民，秦再白等.柔性仿金枪鱼月牙形尾鳍水动力分析[J].海洋工程，2004，22(4)：73-79.
[123]杨亮苏玉民.粘性流场中摆动尾鳍的水动力性能分析.哈尔滨工程大学学报，2007，28(10):1073-1078.
[124] Read D A, Hover F S, Triantafyllou M S. Forces on oscillating foils forpropulsion and maneuvering. Journal of Fluids and Structures,2003,17(1):163-183.
[125]赵士奇.仿鱼尾鳍推进系统实验研究.哈尔滨工程大学硕士学位论文2008.
[126] LIU Zhen, HYUN Beom-soo, KIM Moo-rong, JIN Ji-yuan. Experimental andNumerical study for hydrodynamic characteristics of an oscillatinghydrofoil. Journal of hydrodynamics, Ser. B,2008,20(3):280-287.
[127] Q. Xiao, W. Liao. Numerial study of asymmetric effect on pitching foil.International Journal of Modern Physics C.2009,20:1663-1680.
[128]颜翚.鱼类游动观测实验及运动分析哈尔滨工程大学硕士学位论文.2008.
[129]成巍.仿生水下机器人仿真与控制技术的研究.哈尔滨工程大学博士学位论文.2004.
[2]王天然,王越超,曲道奎.机器人技术新进展.中国科学院科学与社会系列报告-2004高技术发展报告,北京:科学出版社,2004.
[3] Gray J. Studies in animal locomotion. IV. The propulsive powers of thedolphin. Journal of Experimental Biology.1936,13:192-199.
[4] M.S. Triantafyllou, G.S. Triantafyllou, D.K.P. Yue, Hydrodynamics offish-like swimming. Annual Reviews of Fluid Mechanics.2000,32:33–53.
[5] Fish F. E., Lauder G. V. Passive and Active Flow Control by Swimming Fishesand Mammals. Annual Reviews of Fluid Mechanics.2006,38:193–224.
[6] Weihs D. Hydrodynamics of fish schooling. Nature.1973,241:290-291.
[7] Wu T. Y. T. On Theoretical Modeling of Aquatic and Aerial Locomotion.Advance Applied Mechanics.2001,38:291-353.
[8] Triantafyllou M. S., Triantafyllou G. S., Yue D. K. P. Hydrodynamics ofFish like Swimming. Annual Reviews on Fluid Mechanics.2000,32:33–53.
[9] Triantafyllou M. S., Hover F. S., Techet A. H., et al. Review ofHydrodynamic Scaling Laws in Aquatic Locomotion and Fishlike Swimming.Applied MechanicsReviews.2005,58(4):225–237.
[10]刘军考.仿鱼水下推进器理论与实验研究.哈尔滨工业大学工学博士学位论文.2002.
[11] M.S.Triantafyllou，G.S.Triantafyllou. An efficient swimming machine.Scientific.1995，272(3):64-70P.
[12] Breder C.M.The Locomotion of Fishes.Zoological.1926，4：159–291.
[13] J.L.Lighthill. Mathematical biofluiddynamics. Society for Industrial andApplied Mathematics， Philadelphia，1975
[14] Webb P.W. The biology of fish swimming in Mechanics and physiology ofanimal swimming. Cambridge: U.K.Cambridge University Press.1994：45-62.
[15] C.C.Lindsey. Form function and locomotory habits in fish. Fish Physiology.New York: Academic Press.1978(7):1-100.
[16]陈维山，夏丹，刘军考，石胜君.鲹科和鲔科仿鱼机器人自主游动机理的分析与比较.机械工程学报.
[17] C.Pozrikidis. A practical guide to boundary elements methods.CHAPMAN&HALL/CRC,2002.
[18] R.J.Leveque. Finite difference methods for ordinary and partialdifferential equations. Society for Industrial and Applied Mathematics,1997.
[19] M.S.Gockenbach. Understanding and implementing the finite element method.Society for Industrial and Applied Mathematics,2006.
[20] J.H.Ferziger, M.Peric. Computational methods for fluid dynamics.Springer,2002.
[21] J.Lighthill. Note on the swimming of slender fish. J. Fluid Mech.1960，9:305-317.
[22] J.Lighthill. Aquatic animal propulsion of high hydromechanicalefficiency. J. Fluid Mech.1970，44:265-301.
[23] Lighthill M.J. Large-Amplitude Elongated-Body Theory of Fish Locomotion.Proceeding of the Royal Society of London Series B,1971,179:125-138.
[24] Weihs D. A Hydrodynamical Analysis of Fish Turning Manoeuvres. Proceedingof the Royal Society of London Series B,1972,182:59-72.
[25] Weihs D. The Mechanism of Rapid Starting of Slender Fish. Biorheology,10:343-350.
[26] T.Y.Wu. Swimming of a waving plate. J. Fluid Mech.1961，10:321-344.
[27] T.Y.Wu. Hydrodynamics of swimming propulsion. Part1. Swimming of atwo-dimension flexible plate at variable forward speeds in an inviscidfluid. J. Fluid Mech.1971，46(2):337-355.
[28] T.Y. Wu. Hydrodynamics of swimming propulsion. Part2. Some optimum shapeproblems. J. Fluid Mech.1971，46(3):521-544.
[29] T.Y. Wu. Hydrodynamics of swimming propulsion. Part3. Swimming andoptimum movements of slender fish with side fins. J. Fluid Mech.1971，46(3):545-568.
[30] J.N.Newman，T.Y.Wu. A generalized slender-body theory for fish-like forms.J. Fluid Mech.1973，57(4):673-693.
[31] J. Y. Cheng, L. X. Zhuang, B. G. Tong. Analysis of Swimming ThreeDimensional Waving Plate. Journal of Fluid Mechanics.1991,232:341-355.
[32]程健宇，庄礼贤，童秉纲.三维变幅波板的游动.水动力学研究与进展.1991增刊，1-11页
[33]程健宇，庄礼贤，童秉纲.鱼类鳗鲡模式推进的游动性能分析.水动力学研究与进展.1998，3(3):87-97页
[34]童秉纲，庄礼贤.描述鱼类波状游动的流体力学模型及其应用.自然杂志.1998，20(1):1-7页.
[35] C. Zhang, L. X. Zhuang, X. Y. Lu. Analysis of Hydrodynamics forTwo-dimensional Flowaround Waving Plates. Journal of Hydrodynamics.2002,29(1):18-22.
[36] J. Y. Cheng, T. J. Pedley, J. D. Altringham. A Continuous Dynamic BeamModel for Swimming Fish. Phil Trans Roy Soc Lond B,1998,353:981-997.
[37] D.S.Betteridge，R.D.Archer. A study of the mechanics of flapping wings.Aer. Quart.1974.
[38] R.D.Archer， J.Sapup， D.S.Betteridge. Propulsive characteristics offlapping wings. J. Aero.1979:355-371P.
[39] A.R.Ahmadi. An asymptotic unsteady lifting-line theory with energeticsand optimum motion of thrust-producing lifting surfaces. Ph.D. thesis.MIT.
[40] M. G. Chopra. Large Amplitude Lunate-Tail Theory of Fish Locomotion.Journal of Fluid Mechanics.1976,74:161-182.
[41] M. G. Chopra, T. Kambe. Hydrodynamics of Lunate-Tail Swimming Propulsion:Part2. Journal of Fluid Mechanics.1977,79:49-69..
[42] K. D. Jones，M. F. Platzer. Numerical computation of flapping-wingpropulsion and power extraction. AIAA-97-0826.
[43] JONES, K. D., CASTRO, B. D., MAHMOUND, O., PLATZER, M. F., NEEF, M. F.,GOENT, K., AND HUMMEL, D. A Collaborative Numerical and ExperimentalInvestigation of Flapping-Wing Propulsion, AIAA paper,2002-0706.
[44] P. Liu, N. Bose. Propulsive Performance From Oscillating propulsors withspanwise flexibility. Proceeding of the Royal Society of London SeriesA,1997,453:1763-1770.
[45] Pengfei Liu. A time-domain panel method for oscillating propulsors withboth chordwise and spanwise flexibility. PhD Thesis. Memorial Universityof Newfoundland， Canada.1997.
[46]苏玉民，黄胜，庞永杰等.仿鱼尾潜器推进系统的水动力分析.海洋工程，2002，20(2):54-59.
[47] Q. J. Qian, M. Q. Liu, L. Sun, D. J. Sun. The Optimal Motion ofTwo-Dimensional Undlating Plate Swimming in Fluid Flow. Journal ofHydrodynamics23(1):12-20.
[48] Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS. Three-dimensional flowstructures and vorticity control in fish-like swimming. Journal of FluidMech,2002,468:1-28
[49] Wolfgang M. J. Hydrodynamics of Flexible-Body Swimming Motions. PhDthesis, M.I.T., Boston, MA, U.S.A.,1999.
[50] Wolfgang M. J., Anderson J. M., Grosenbaugh M., Yue D., Triantafyllou M.Nearbody Flow Dynamics in Swimming Fish. Journal of Experimental Biology,202:2303-2327..
[51]吴辅兵.振动翼推进及干扰效应非定常流体动力研究.哈尔滨工程大学工学博士论文.2004.
[52] Liu H., Wassersug R., Kawachi K. A Computational Fluid Dynamics Study ofTadpole Swimming. Journal of Experimental Biology.1996,199(6):1245-1260.
[53] Liu H., Wassersug R., Kawachi K. The Three Dimensional Hydrodynamics ofTadpole Locomotion. Journal of Experimental Biology.1997,200(6):2807-2819.
[54] Liu H., Katsumata Y. Computation of Self-Propelled Swimming in LarvaFishes. Journal of Computational Physics.2006,28:219-232.
[55] Carling J., Williams T. L., Bowtell G. Self-Propelled AnguilliformSwimming: Simultaneous Solution of the Two-Dimensioanl Navier-StokesEquations and Newton’s Laws of Motion. Journal of Experimental Biology.1998,201:3143-3166.
[56]胡文蓉.鱼类单向机动运动二维流动特征的数值研究.中国科学院研究生院博士论文.2004.
[57] W. R. Hu, B. G. Tong, H. Liu. A Computational Study on Backeard SwimmingHydrodynamics in the Eel. Journal of Hydrodynamics,2005,17(4):438-447.
[58]夏全新，鲁传敬，吴磊.鱼类波状摆动推进的数值模拟.水动力学研究与进展A辑.2005，20：921-928.
[59] S. Kern, P. Koumoutsakos.Simulations of Optimized AnguilliformSwimming.Journal of Experimental Biology.2006，209：4841-4857.
[60] A. Leroyer, M. Visonneau. Numerical Methods for RANSE Simulation of aSelf-Propelled Fish-Like Body. Journal of Fluids and Structures.2005,20:975-991.
[61] W.C.Sandberg，R.Ramamurti. Unsteady flow computations for oscillatingfins: a status report. Papers of11thInternational symposium on UUStechnology. Autonomous Undersea Systems Institute.1999:182-194.
[62]董根金.波状摆动变形体非定常粘性绕流的数值研究.中国科学技术大学博士论文.2006.
[63]王亮.仿生鱼群自主游动及控制的研究.河海大学博士论文.2007.
[64]邵雪明.二维波动板绕流场的DLM/FD.模拟中国力学学会技术大会2005.
[65]邓见.含运动物体三维复杂流场数值模拟和尾流结构研究.浙江大学博士论文.2007.
[66]张来平，常兴华，段旭鹏，张涵信.三鱼群游流动干扰及其减阻机理的数值研究.水动力学研究与进展.2007，22(6)：753-760.
[67]杨焱.锦鲤常规自由游动的流动物理研究.中国科技大学博士论文.2008.
[68]夏丹.鲔科仿生原型自主游动机理的研究.哈尔滨工业大学博士论文.2010.
[69]徐晓锋.仿生鱼游动与运动控制的数值分析技术.上海交通大学硕士论文.2011.
[70]张晓庆,王志东,张振山二维摆动水翼仿生推进水动力性能研究.水动力学研究与进展.200621（5），632-639.
[71]王志东，丛文超，张淋，李立军.自主航行模式下二维摆动尾鳍的推进性能研究.江苏科技大学学报（自然科学版）.2010,24(6):523-528.
[72] Wang Z. D., Lao Y. J., LI L. J., Cong W. C. Experiment on the Characteristicof3D Vortex Ring Behind a Flexible Oscillating Caudal Fin. Journal ofHydrodynamics, Ser. B,2010,22(3):393-4014.
[73]杨亮.仿金枪鱼摆动尾鳍的水动力性能与推进机理研究.哈尔滨工程大学博士论文.2009.
[74] I. Borazjani, F. Sotiropoulos. Numerical Investigation of theHydrodynamics of Carangiform Swimming in the Transitional and inertialFlow Regimes. Journal of Experimental Biology.2008,211:1541-1558.
[75] I. Borazjani, F. Sotiropoulos. Numerical Investigation of theHydrodynamics of Anguilliform Swimming in the Transitional and inertialFlow Regimes. Journal of Experimental Biology.2009,212:576-592.
[76] I. Borazjani, F. Sotiropoulos. On the Role of Form and Kinematics on theHydrodynamics of Self-Propelled Body/Caudal Fin Swimming. Journal ofExperimental Biology.2010,213:89-107.
[77] L. Schouveiler, F. S. Hover, M. S. Triantafyllou. Performance of FlappingFoil Propulsion. Journal of Fluids and Structures.2005,20:949-959.
[78] F. S. Hover, Φ. Haugsdal, M. S. Triantafyllou. Effect of Angle of AttackProfiles in Flapping Foil Propulsion. Journal of Fluids and Structure.2004,19:37-47.
[79] Gopalkrishnan R, Triantafyllou MS, Triantafyllou GS et al. ActiveVorticity Control in a Shear Flow Using a Flapping Foil. Journal of FluidMechanics,1994,27(4):1-21.
[80] A. H. Techet. Experimental Visualization of the Near-BoundaryHydrodynamics about Fish-Like Swimming Bodies. Massachusetts Institutesof Technology, Cambridge,2001.
[81] George V Lauder, E. Drucker. Forces, fishes, and fluids: hydrodynamicmechanisms of aquatic locomotion. News Phsiol. Sci.2002,17:235-240
[82] J. C. Nauen, G. V. Lauder. Three-Dimensional Analysis of Finlet Kinematicsin the Chub Mackerel. Biol.Bull.2001,200:9-19.
[83]陈宏，竺长安，尹协振，邢晓正.仿生机器人C形起动的动力学分析.哈尔滨工业大学学报.2009,41(1):113-117.
[84]吴燕峰，贾来兵，尹协振.斑马鱼S型起动运动学研究.实验力学.2007,22(5):519-526.
[85]周萌，尹协振，童秉纲.鲫鱼皮肤和肌肉的力学性能研究.实验力学.2010,25(5):536-545.
[86]贾来兵.二维流场中板状柔性体与流体相互作用的研究.中国科学技术大学博士论文.2009.
[87]吴冠豪，曾理江.用于自由游动鱼三维测量的视频跟踪方法.中国科学G辑，2007,37(6):760-766.
[88]老轶佳，王志东，张振山，李力军.摆动柔性鳍尾涡流场的实验测试与分析.水动力学研究与进展A.2009,24(1):106-112.
[89] Hui Yan, Yu-min Su, Liang Yang. Experimentation of Fish Swimming Basedon Tracking Locomotion Locus. Journal of Bionic Engineering,2008,5(3):258-263.
[90]苏玉民，杨亮，赵士奇，王晓飞.仿鱼尾鳍推进系统的水动力性能实验研究.华中科技大学学报.2009，37(9)：82-85.
[91] D. S. Barrett. The Design of a Flexible Hull Undersea Vehicle Propelledby an Oscillating Foil. Massachusetts Institutes of Technology, Cambridge,1994.
[92] H. Hu, Biologically inspired design of autonomous robotic fish at essex, Proceedingsof the IEEE SMC UK-RI Chapter Conference, on Advances in Cybernetic Systems,Sheffield,2006,3-8.
[93] http://www.nmri.go.jp/eng/khirata/fish
[94] Guo S X, Fukuda T, Asaka K. Fish-like underwater microrobot with3DOF.Proceedings of the IEEE International Conference on Robotics and Automation,2002(1):738-743.
[95]梁建宏，邹丹，王松等. SPC-II机器鱼平台及其自主航行实验.北京航空航天大学学报.2005,31(7):709-713.
[96]夏丹，陈维山，刘军考，韩路辉.基于Kane方法的仿鱼机器人波状游动的动力学建模.机械工程学报.2009,45(6):41-49.
[97]张志刚，喻俊志，王硕，桑海泉，谭民.多关节仿鱼运动推进机构的设计与实现.中国造船.2005,46(1):22-28.
[98]陈尔奎，喻俊志，王硕，谭民.一种基于视觉的仿生机器鱼实时避障综合方法.控制与决策.2004，19(4)：452-458.
[99]喻俊志，陈尔奎，王硕，谭民.基于颜色信息的多机器鱼并行视觉跟踪算法.中国科学院研究生院学报.2003,20(4):433-440.
[100]成巍，苏玉民，秦再白，秦仔白，万磊，徐玉如.一种仿生水下机器人的研究进展.船舶工程.2004，26(1):5-8.
[101] Stephen Licht Victor Polidoro Melissa Flores, Franz Hover, and MichaelTriantafyllou Design and Projected Performance of a Flapping Foil AUV.Proceedings of the13thInternational Symposium on Unmanned UntetheredSubmersible Technology.2003.
[102]胡天江.仿生长鳍波动适应性理论与控制方法研究.国防科技大学工学博士论文.2008.
[103] George V. Lauder and Eliot G. Drucker. Morphology And ExperimentalHydrodynamic Of Fish Fin Control Surface. Proceedings of the13thInternational Symposium on Unmanned Untethered Submersible Technology.2003.
[104] Eliot G. Drucker And Geoger V. Lauder. Locomoter Forces on A Swimming Fish:Three-Dimensional Vortex Wake Dynamics Quantified Using Digital ParticleImage Velocimetry. The Journal of Experimental Biology202,2393–2412(1999) Printed in Great Britain The Company of Biologists Limited1999.
[105] Streitlien K, Triantafyllou GS.Efficient foil propulsion through vortexcontrol. AIAA Journal,1996,34(11):2315-2318.
[106] Beal DN. Propulsion through wake synchronization using flapping-foil.Massachusetts Institutes of Technology, Cambridge,2003.
[107] Zhu Q, Wolfgang MJ, Yue DKP, Triantafyllou MS. Three-dimensional flowstructures and vorticity control in fish-like swimming. Journal of FluidMech,2002,468:1-28.
[108] J. Liao. Neuromuscular control of trout swimming in a vortex street:implications for energy economy dring the Karman gait. Journal ofExperimental Biology.2004,207:3495-3506.
[109] Florian R. Menter. Improved Two-Equation k Turbulence Models forAerodynamic Flows. NASA Technical Memorandum103975.1992
[110] Simmons JEL. Phase-angle measurements between hot-wire signals in theturbulent wake of a two-dimensional bluff body. Journal of Fluid Mechanics,1974,64:599-609.
[111] Anderson JM. Vorticity control for efficiency propulsion. MassachusettsInstitutes of Technology, Cambridge,1996.
[112] Anderson JM, Kerrebrock P A. The Vorticity Control Unmanned UnderseaVehicle (VCUUV): An Autonomous Robot Tuna. Proceedings of the11thInternational Symposium on Unmanned Untethered Submersible Technology,Durham, USA,1999:63-70.
[113] Nakashima M, Ono K. Experimental study of two-joint dolphin robot.Proceedings of the11thInternational Symposium on Unmanned UntetheredSubmersible Technology, Durham, USA,1999,82-89.
[114] P.Liu，N.Bose. Hydrodynamic characteristics of a lunate shape oscillatingpropulsor. Ocean Eng.1999，26:519-529.
[115]程健宇,庄礼贤,童秉纲.新月形尾鳍推进的流体力学分析.力学学报,1992,24(4)：458-465.
[116]刘军考,陈维山,陈在礼.尾鳍的形状与运动参数对推进速度的影响.高技术通信,2001,4：86-88
[117]李龙,尹协振.鲹科类鱼尾模型的巡游推进特性实验研究.实验流体力学,2008,22(1)：1-6.
[118] J Katz, D Weihs. Hydrodynamic propulsion by large amplitude oscillation of an airfoilwith chordwise flexibility. J. Fluid Mech,1978,88,485-497.
[119] P Prempraneerach, F Hover, M S Triantafyllou. The effect of chordwiseflexibility on the thrust and efficiency of a flapping foil. Proceedingsof the13thInternational symposium on Unmanned Untethered SubmersibleTechnology, Durham, USA,2003:120-128.
[120] Qiang Zhu. Numerical simulation of a flapping foil with chordwise orspanwise flexibility. AIAA Journal,2007,45(10):2448-2458.
[121]王志东，张晓庆，丛文超.柔性摆动水翼弦向变形模式及其对推进性能影响的研究[J].船舶力学，2010，14(7)：609-707.
[122]成巍，苏玉民，秦再白等.柔性仿金枪鱼月牙形尾鳍水动力分析[J].海洋工程，2004，22(4)：73-79.
[123]杨亮苏玉民.粘性流场中摆动尾鳍的水动力性能分析.哈尔滨工程大学学报，2007，28(10):1073-1078.
[124] Read D A, Hover F S, Triantafyllou M S. Forces on oscillating foils forpropulsion and maneuvering. Journal of Fluids and Structures,2003,17(1):163-183.
[125]赵士奇.仿鱼尾鳍推进系统实验研究.哈尔滨工程大学硕士学位论文2008.
[126] LIU Zhen, HYUN Beom-soo, KIM Moo-rong, JIN Ji-yuan. Experimental andNumerical study for hydrodynamic characteristics of an oscillatinghydrofoil. Journal of hydrodynamics, Ser. B,2008,20(3):280-287.
[127] Q. Xiao, W. Liao. Numerial study of asymmetric effect on pitching foil.International Journal of Modern Physics C.2009,20:1663-1680.
[128]颜翚.鱼类游动观测实验及运动分析哈尔滨工程大学硕士学位论文.2008.
[129]成巍.仿生水下机器人仿真与控制技术的研究.哈尔滨工程大学博士学位论文.2004.