用户名: 密码: 验证码:
舵机电液伺服调节器耦合振动特性及其控制研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
随着造船技术的发展,船舶日益趋向大型化、高速化,船舶液压舵机由电液伺服调节器进行控制,要求调节器稳定性、可靠性和动态性能好。电液伺服调节器是一个电液伺服系统,当伺服阀进行启闭动作时,系统内产生的水击经过管路的传输,在活塞端引起较大的振动幅值,容易产生跑舵现象。液压水击现象是系统的非恒定流动,是流动参数阶跃变化时的动态过渡过程,特别是电液伺服调节器的阀芯、阀套为互动关系,对水击的影响更加复杂。本文以REG260型调节器为例,对电液伺服调节器的水击诱发振动机理和特性及其相关因素的影响规律进行深入的研究,以便采取相应的控制措施来减小或抑制水击振动,保障系统有较好的动态性能。
     首先对电液伺服调节器的静动态特性进行了分析,利用对称阀控非对称缸的理论,定义了系统的负载流量和压力,考虑对称阀存在零位间隙和泄漏,建立了系统的数学模型,进行仿真,得到系统的稳定性能、阶跃响应和跟踪性能指标。
     然后考虑油液与结构耦合作用,对激振源――反馈阀套式伺服阀的耦合水击振动特性进行研究,利用油液粘度较大的瞬变流摩阻模型,推导了完备的伺服阀耦合水击运动微分方程,运用特征线法获得了系统激振力的特性;对刚性管路以及动边界液压缸,采用拉格朗日网格法处理动边界条件,进行活塞端的水击传输特性频域的计算分析,表明忽略动边界对管路系统的影响会造成很大的误差,在动边界条件下,泊松耦合的对水击压力幅值的影响不明显,连接耦合在伺服阀开启较快时,管路中水击效应明显;伺服阀开启较慢时,管路轴向振动以应力波频率振动的受迫振动占主导地位,水击振动中高频成分增加;伺服阀启闭动作结束后,活塞端仍有较大的压力振动幅值。
     伺服阀的启闭规律对水击振动的影响比较显著,根据调节器的水击耦合振动方程,运用非线性规划算法,得到系统耦合水击振动的优化伺服阀启闭规律曲线。在此规律作用下计算得到水击压力衰减率近似达7dB;从实际工程应用出发,对优化启闭规律采用两阶段、三阶段线性化处理,水击压力下降率可达18.2%;采用自适应神经模糊推理方法控制优化启闭动作,取得了较好的效果。
     根据调节器的水击振动响应计算结果,从调整系统阻抗和减小激振源影响两个方面进行了振动控制研究。结果表明,调整管路长度是从频域分析避开谐振频率点的简单有效的方法,将REG260型电液伺服调节器的管长改进为0.73m,压力振动衰减率可达6dB;根据负载阻抗、活塞面积以及容腔初始长度等参数的影响规律,应用非线性规划方法优化了结构参数,调整了系统的阻抗,压力振动衰减率近似可达6dB,有效的减小了水击压力幅值。
     最后通过REG260型电液伺服调节器的实验,对其静动态以及水击耦合振动特性进行了实验研究,表明利用对称阀控非对称缸理论所建立的数学模型,可以有效的进行系统的稳定性判别以及输入信号与输出位移的关系研究;利用耦合水击振动模型在伺服阀控制口水击压力振动的计算结果与实验测试值偏差为2.87%,实验得到的液压缸无杆腔压力变化趋势与计算结果基本一致,验证了耦合振动模型的正确性;运用伺服阀的两阶段启闭规律,测得活塞无杆腔的压力下降了13.04%,验证了控制措施的有效性。
Along with the development of shipbuilding, ship the growing tendency of large, high-speed, steering the movement controlled by electro-hydraulic servo control regulator, so the regulator required stability, reliability and easy to control. REG260 type of electro-hydraulic servo steering regulator system is a typical electro-hydraulic servo system, servo valve open-shut moves, oil within the system have been rapid alternating movements of the pressure wave process is water hammer, flowed in the transmission line, it cought be cause the larger vibration amplitude in piston area, deviate the mandate direction of the rudder, the ship sailed to the security threat. Hydraulic water hammer phenomenon is the unsteady flow; flow parameters vary is the dynamic changes in the transition process. In particular, it is interaction between valve spool, valve sleeve of electro-hydraulic servo system regulator, the system of water hammer effects more complicated in the pipeline network. It is necessary to research the servo system of water-induced vibration mechanism and the characteristics and the law related to the influence of factors deeply, in order to take appropriate control measures to reduce or suppress the vibration of water hammer, to protect the safety of the system operation.
     First, the electro-hydraulic servo steering Regulator REG260 for static and dynamic characteristics were analyzed for symmetric asymmetric cylinder valve control theory, redefines the load flow and pressure, and consider the existence of symmetric zero valve clearance and leaked to establish a system of model. Simulations show that the system is stable and has good step response and tracking performance.
     Then, account structure coupled with the oil, the vibrate source -- the servo valve coupled vibration of water hammer is studied, whereas viscosity of hydraulic system is the larger transient flow model, the proposed model is a complete servo valve coupled differential equations of motion of water hammer. Use the method of characteristics derived characteristics of vibration force of the water hammer; laid the study foundation of pipeline transmission characteristics and control; In numerical calculation using Lagrangian grid handling moving boundary conditions. Frequency - domain analysis shows that neglected the impact of moving boundary condition, the error will be great with the boundary changes; Since moving boundary conditions, for junction coupling, when the servo valve opened quickly, pipeline water hammer effect obviously, on the contrary, servo valve opened slowly, pipeline to axial vibration frequency vibration stress wave dominated, the bigger frequency composition of water hammer vibration increases. There is still a larger vibration amplitud after servo valve open-shut moves;
     Servo valve open-shut law of the water hammer effects were more marked, under the system vibration coupling water hammer equation, using of nonlinear programming algorithm, by the study of water hammer process, the optimal curve law coupling water hammer calculation wree derived, the optimization law of water hammer pressure decay rate of approximately 7dB. From a practical application, for the optimization using the law includes a two-stage and three-stage linear, the rate of pressure decline is 18.2% and using adaptive neuro-fuzzy logic control, and achieved good results.
     According to water hammer vibration response calculation results of the analysis, vibration controls of REG260 the servo system wree proposed from two aspects of the adjustment of system impedance and reduce the vibration source. The results show that the adjustment of the length of pipe from the frequency domain analysis may avoid resonant frequency of pipe, it is simple and effective method to improve the management of long to 0.73 m, pressure vibration attenuation rate should be 6dB; Load impedance of the piston area and the capacity cavity length of the initial parameters to be improved, application of nonlinear programming method for the optimization of system impedance, the optimization of the structure parameters, adjusted the system impedance, effectively reduced the amplitude of water hammer pressure, the pressure vibration attenuation approximate rate of up to 6 dB.
     Finally, adoption of REG260 electro-hydraulic servo steering regulator experiments, studied its static and dynamic characteristics and the water hammar coupling vibration characteristics, the experiments showed that the use of symmetric asymmetric cylinder valve control theory established by the mathematical model can be effective for system stability discrimination, and relationship of input drift the output displacement signal analysis; consider oil and structure coupling model, through the pressure oscillation experiment of the servo valve port and calculation results deviation is 2.87%; and the hydraulic cylinder with a rear-chamber pressure trend consistent with the calculation results, verified coupling vibration model is correctness; the use of servo valve open-shut law two stages of testing rear-chamber pressure is 13.04% decline, proved the control measures is effectiveness.
引文
[1] Jean BErtheas. G Moresco. P Dufourco. Linear hydrophonic antenna and electronic device to remove right/left ambiguity, associated with the antenna. United States Patent, Patent Number: 5058082,1991.10
    [2] Sun J C, Liu S, Li D P. Study and realization of design and simulation system of ship stance control [A]. Proceedings of the 3rd Word Congress on Intelligent Control and Automation, 2000, 4:2889-2892
    [3]黄雪梅.转叶式舵机的特点和价值分析[J].广船科技.2001,4:17-20
    [4] Yang Shu-xing, Zhong Ping. On the Parametric Design of Electromechanical Actuators. Journal of Beijing Institute of Technology, 1997, vol.6, 2 :138-144
    [5]张礼华,卢道华,刘芳华.船舶舵机个体Agent的研究与构建[J].船电技术,2004,6:26-29
    [6] N Joukowsky. On the hydraulic hammer in water supply pipes [A]. 1898, English translation by O Simin: Water hammer. Proceedings of the American Water Works Association [C].1904.24:341-424
    [7] R Skalak. An extension of the theory of water hammer [J]. Transactions of the ASME.1956, 78(1):105-116
    [8] G Herrmann and I Mir K. Three-dimensional and shell-theory analysis of axially symmetric motion of cylinders [J]. ASME Journal of Applied Mechanics, 1956, 23(4): 563-568
    [9] Sharp.D.B, jt.auth, water hammer. Practical solutions, London: Amold, 1996, 12: 234-238
    [10] R P Dearmond and W T Rouleau. Wave propagation in viscous, compressible liquids confined in elastic tubes [J]. ASME Journal of Basic Engineering. December 1972, 811-817
    [11] S I Rubinow and J B Keller. Wave propagation in a viscous elastic tube containing a viscous fluid [J]. Journal of Fluid Mechanics, 1978, 88, Part1: 181-203
    [12] G D Ckuiken. Approximate dispersion equations for thin walled liquid-filled tubes [J]. Applied Scientific Research, 1984, 41:37-53
    [13] G D Ckuiken. Wave propagation in fluid line [J]. Applied Scientific Research, 1984,41: 69-91
    [14] G D Ckuiken. Wave propagation in a thin-walled liquid-filled initially stressed tube [J]. Journal of Fluid Mechanics, 1984, 141:289-308
    [15] G D Ckuiken. Amplification of pressure fluctuation due to fluid-structure interaction [J]. Journal of Fluid and Structures, 1988, 2:425-435
    [16] F T Brown. The transient response of fluid lines [J]. Journal of Basic Engineering, 1962, 84:546-553
    [17] F T Brown. A quasi method of characteristics with application to fluid lines with frequency dependent wall shear and heat transfer [J]. ASME Journal of Basic Engineering, June 1969:423-432
    [18] A F D′souza and R Oldenburger. Dynamic response of fluid lines [J]. Journal of Basic Engineering, 1964, 86:589-598
    [19] E L Holmboe and W T Rouleau. The effect of viscous shear on transients in liquid lines [J]. ASME Journal of Basic Engineering, 1967, 89:174-180
    [20] S C Tentarelli. Propagation of Noise and Vibration in Complex Hydraulic Tubing Systems [D]. Ph.D. Thesis of Lehing University, Department of Mechanical Engineering, Bethlehem, USA.1990
    [21] J D Regetz. An Experimental Determination of the Dynamic Response of a Long Hydraulic Line[R]. National Aeronautics & Space Administration, Technical Notes D-576, December1960
    [22] S E Jones and D J wood. The Effect of axial boundary motion on pressure surge generation [J].ASME Journal of Basic Engineering, 1972, 94:441-446
    [23] J A ELLIS. Study of pipe-liquid interaction following pump-trip and check-valve closure in a pumping station [A]. Proceedings of the 3rd International Conference on Pressure Surges[C]. BHRA Canterbury. March1980:203-220
    [24] A S Tijsseling, A E Vardy and D fan. Fluid structure interaction in a T-pipce pipe [J]. Journal of Fluids and Structures, 1996, 10:763-786
    [25] A S Tijsseling, A E Vardy and D fan. Fluid structure interaction and cavitation in a single-elbow pipe system [J]. Journal of Fluids Structures, 1996, 10: 395-420
    [26] R A Clark, I R Gilroy and E Reissner. Stresses and deformations of toriodal shells of elliptical cross section with applications to the problems of bending of curved tubes and bourdon gage[J].of Applied Mechanics, Transactions of ASME, March 1954,21:37-48
    [27] J F Watham. The shell analysis of noncircular pipe bends [J]. Journal of Nuclear Engineering and Design, 1981, 67:287-296
    [28] J F Wathan. Analysis of pipe bends with symmetrical noncircular cross section [J]. Journal of Applied Mechanics, 1987, 54:604-610
    [29] Wiggert D C, Hatfield F J, Shtckenbruck S .Analysis of liquid and strctural transients in piping by the method of characteristics. In Fluid Transients in Fluid-structureinteraction-1985 [J], ASME-FED 1985b, 30: 97-102
    [30] Budny D D, Hatfteld F J, Wiggert D C .An experimental study on the influence of structural damping on internal fluid pressure during a transient flow [J]. ASME Journal of Pressure Vessel Technology, 1990, 112: 284-290
    [31] Wiggert D C, Hatfield F J, Stuckenbruck S .Analysis of liquid and structural transients by the method of charaeteristics [J]. ASME Journal of Fluids Engineering, 1987, 100: 161-165
    [32] Elansany A S, Contractor D N .Valve Closure: Method for Controlling Transients [J]. Journal of Pressure Vessel Technology, 1994, 116: 437-442
    [33] Tijessing A S, Vardy A E and Fan D. Fluid Structure Interaction and Cavitation in a single-elbow Pipe System [J]. Journal of Fluids and Structure, 1996, 10: 395-420
    [34] Vardy A E, Fan D .Fluid-structure interaction in a T-piece pipe [J]. Journal of Fluids and Structures, 1996, 10: 763-786
    [35]蔡亦钢.流体传输管道动力学[M].浙江:浙江大学出版社,1990:91-99
    [36]王学芳,叶宏开,汤荣铭.工业管道中的水锤[M].北京:科学出版社, 1995:31-34
    [37] Lee U, Joohong K .Dynamics of branched pipline systems conveying internal unsteady flow [J]. Journal of vibration and Acoustics, 1999, 121: 114-122
    [38] Soliman H O, Datta T K .The Seismic Response of a Piping System to Non-stationary Random Ground Motion [J]. Journal of Sound and Vibration, 1995, 180(3): 459-473
    [39] Misra A K, Paidoussis M P, Van K S .On the Dynamics of Curved Pipes Transporting Fluid. Part I: Inextensible Theory [J]. Journal of Fluids and Structures, 1988, 2: 221-244
    [40] Lavooij C S W, Tijsseling A S .Fluid-structure Interaction in Liquid-filled Piping Systems [J]. Journal of Fluids and Structure, 1991, 5: 573-595
    [41] Heinsbroek A G T J, Lavooij C S W, and Tijsseling A S .Fluid-structure interaction in non-rigid piping-a numerical investigation [A]. Transactions of SMiRT 11, Tokyo, Japan, 1991, Paper B12/1, 309–314
    [42] Gorman D G., Reese J M , and Zhang Y L .Vibration of a Flexible Pipe Conveying Viscous Pulsating Fluid Flow [J]. Journal of Sound and Vibration. 2000, 230(2): 379-392
    [43] Meng Fanhua. Frequency Characteristic of an Electro一hydraulic Servomechanism with a Nonsymmetrical Cylinder. Report of Department of Mechanical Engineering, Sophia University, 1984.11
    [44]李洪人.液压控制系统[M].国防工业出版社,1981:191-199
    [45] atoru Hayashi, Emeritus. Nonlinear phenomenon in hydraulic system[J]. Journal offluid control. 1998, 18(4): 48-52
    [46] Bret R.Givens. An engineering design simulator for advanced distributed simulation.IEEE, 1996:565-571
    [47] M. R. Sirouspoun, S. E. Salcudean. Nonlinear control of a hydraulic parallel manipulator. Processing of the 2001 IEEE: 3760-3765
    [48]王学芳,叶宏开,汤荣铭等.工业管道中的水锤[M].北京:科学出版社,1995.6:71-75
    [49]赵喜容,任德志.管道对液压系统静动特性的影响[J].机床与液压.1997,(5):41-42
    [50]岑豫皖.液压管道对电液伺服系统稳定性影响的研究[J].机床与液压.1998,(4):58-60
    [51]孙以泽.管道网络自动建模方法研究[J].机床与液压.1998,(3):39-40
    [52] D D Budny, D C Wiggert and F J Hatfield. The influence of structural damping on internal pressure during a transient flow [J]. ASME Journal of Fluid Engineering, 1991, 113(3):424-429
    [53] D C Wiggert. Fluid transients in flexible piping systems (a perspective on recent developments) [A].Proceedings of the 18th IAHR Symposium on Hydraulic Machinery and Cavitation[C]. Valencia, Spain, September 1996: 58-67
    [54] A E Vardy and D fan. Method of characteristics analysis of one-dimensional members [J].Journal of Sound and Vibration, 1989, 129(3):477-487
    [55] A E Vard and K L Hwan. A characteristic model of transient friction in pipes [J]. IAHR Journal of Hydraulic Research, 1991, 29(5):669-678
    [56] A E vardy and A T alsarraj. Coupled axial and flexural vibration of 1-Dmembers [J]. Journal of Sound and Vibration, 1991, 148(1):25-39
    [57] Pobradovic. Analysis of hydrodynamic loads on piping structures-FSI theory applied on pipe support design [A]. International Conference on Engineering Design[C]. Dubrivnik, Yugoslavia, August1990
    [58]张翔林.液固相互作用下管道流体瞬变的研究[D].华中理工大学博士论文,1996
    [59] Yang Ke, Zhang Lixiang and Li Guiqing. Variational principles for FSI in liquid-filled piping systems [A]. First International Conference on Structural Engineering[C]. October1999, Kunming, China
    [60] G Pavic. Vibroacoustical energy flow through straight pipes [J]. Journal of Sound and Vibration, 1992, 154:411-429
    [61] C A FDEJONG. Analysis of Pulsation and Vibrations in Fluid-filled Pipe Systems [D]. Ph.D. Thesis of Eindhoven University of Technology, Eindhoven, The Netherlands, 1994
    [62] L X Zhang, A S Tijsseling and A Evardy. Frequency response analysis in internal flows [J]. Journal of Hydrody namics.1995, 7(3):39-49
    [63] L X Zhang, W H Huang, A S Tijsseling and A Evardy. Normal modal of fluid-structure interaction in internal flows [J]. Journal of Hydrody namics.1998, 10(4):71-89
    [64] Kolsky H .Stress Waves in Solids [M]. Oxford: Clarendon Press, 1953:51-54
    [65] M P Paidoussis and G X LI. Pipe conveying fluid: a model dynamical problem [J]. Journal of Fluid and Structures.1993, 7:137-204
    [66]刘延柱,陈文良,陈立群.振动力学[M].北京:高等教育出版社,1998:54-59
    [67] Lee U, Pak C H and Hong S C. The dynamic of a piping system with internal unsteady flow [J]. Journal of sound and vibration.1995,182:297-311.
    [68]陈一鸣,赵永凯,赵静一等.液压管流的振动问题[J].东北重型机械学院学报,1994, 18(3): 275-282
    [69] JIAO Xiu-wen, YAN Xiang-an, ZHANG Cheng-pu. a method of calculating pressure distribution of p eriodic pulsation fluid transported in piping network[J]. Transactions of Tianjin University, 1996, 2(2): 56-59
    [70]焦秀稳,曹玉平,石晓庆等.传输管网流体脉动研究[J].海洋学报, 1996, 18(6): 114-118
    [71]焦宗夏,华清,于凯.传输管道流固耦合振动的模态分析[J].航空学报,1999, 20(4):316-320
    [72]张智勇,沈荣瀛.充液直管管系统中的固-液耦合振动响应分析[J].振动工程学报, 2000,13(3):455-461
    [73]杨春犁.一种空间管路的复模态模型及流固耦合振动分析[J].排灌机械, 2000,18(2):38-39
    [74]张立翔,黄文虎, A. S. Tijsseling.水锤诱发弱约束管道流固棍合振动频谱分析[J].工程力学, 2000,17(1): 1-12
    [75] Backe, W. The present and future of fluid power Proceedings of the Institution of Mechanical Engineers, London, 1993, 80th Thomas Hawksley Memorial Lecture
    [76] M. Borghi, M. Milani, R. Paoluzzi. Stationary Axial Flow Force Analysis on Compensated Spool Valves. Internationa1 Journal of Fluid Power I .2000(1): 17-25
    [77]程文辉.用正交曲线网格及冻结法计算河道流速场[J].水利学报,1988(6):12-14
    [78]彭凯.在二维流动计算中应用河床切削技术处理动边界问题[J].水利学报,1992(2):35-38
    [79] Numerical methods in Heat Transfer, Edited by R.W.Lewis,Jhon Wiley &Sons Ltd, 1981
    [80] JIMA. The penetration rate of solid-liquid phase-change heat transfer interface with different kinds of boundary conditions. Int, J. Heat Mass Transfer. 1995,38(11):2135-2138
    [81] J.V.Miller. J.Inst.Math. heat transfer interface with solid-liquid phase-change. Applic, 1978,22:467-477
    [82] P.Jamet. Siam.J.Num. heat transfer interface with different kinds of boundary conditions. Anal. 1978,5:912-928
    [83] Hirose, Koichi. Numerical study of natural-convection heat transfer in eccentric horizontal cylindrical annuli. Heat Transfer--Japanese Research, 1994,23(5):427-439
    [84] Masaaki Kawahashi. Nonlinear Phenomena Induced by Finite-Amplitude Oscillation of Air Column in Closed Duct. JSME. International Journal Series B, 1996, 39(2): 27-39
    [85] Otani A, Kobayashi H, Kobayashi N, Tadaishi Y. Performance of a viscous damper using electrorheological fluid. In:Ma D C ed. Proceedings of the 1994 ASME Pressure Vessel and Piping Conference,Minneapolis,Minnesota,1994-06. New York: ASME, 1994. PVP-Vol. 287, MD-Vol. 47, 93~97
    [86] Tijsseling A S, Vardy A E. On the suppression of coupled liquid/pipe vibrations. In: Thomassen E. ed. Proc 18th International Symposium on Hydraulic Machinery and Cavitation, Valencia, Spain, 1996-09. Netherlands: IAHR 1996. 945~954
    [87] Tsai Y K, Lin Y H. Adaptive modal vibration control of a fluid-conveying cantilever pipe. Journal of Fluid and Structure. 1997. 11:535~547
    [88] Chen Y Q, Fan Q S, Zhu Z G.. Acquiring appropriate objective functions during optimal vibration design of the piping system. In: Chien Wei-Zang Eds. Proceedings of the 4th international conference on nonlinear mechanics, ICNM 4, China, 2002-08. Shanghai: Shanghai University Press, 2002, 544~549
    [89]陈刚,朱石坚.管壁不连续对管路结构振动传递的影响[J].海军工程大学学报,2004,16(2):40-43
    [90]谢坡岸,王强.蓄能器对管路流体脉动消减作用的研究[J].噪声与振动控制,2000,4:2-5
    [91]李爱社.油田注水系统压力脉动滤波器结构参数仿真分析[J].机床与液压,1998,2:23-25
    [92]简炎钧,王义,杨凤珍等.舰船蒸汽动力管系的振动分析及其解决对策的研究[J].船舶,1998,2:19-21
    [93]王强,胡明,姚本炎等.船用往复泵管路减振技术研究[J].船舶工程,2002,1:27-31
    [94]王强,沈荣瀛,姚本炎等.管路消振器降低管路振动与脉动压力[J].中国造船,2003,44(1):39-45
    [95]王栋梁,李洪人,张景春.非对称阀控制非对称缸的分析研究[J].山东建材学院学报.2001,15(2):123-127
    [96]刘长年,液压伺服系统优化设计理论[M].北京:冶金工业出版社.1989:163-164
    [97]赵继云,钟廷修.零开口非对称四通阀特性的理论研究[J].机床与液压1998,(2):35-37
    [98] Meng Fanhua. Frequency Characteristic of an Electro一hydraulic Servo mechanism with a Nonsymmetrical Cylinder. Report of Department of Mechanical Engineering, Sophia University,1984.1
    [99] Ravi N.Banavar, Vineet Aggarwal. A loop transfer recovery approach to the control of an electro-hydraulic actuator. Control Engineering Practice, 1998, 6(7):837-845
    [100] Brunone B, Ferrante M, Calabresi F. High Reynolds number transients in a pump rising main, field tests and numerical modeling [C]. 4th International Conference on Wate, Pipeline Systems, York, UK, BHR Group, 200l
    [101] Vardy A E, Brown J M B. Transient turbulent friction in smooth pipe flows [J].Journal of Sound and Vibration, 2003, 259(5): 1011-1036
    [102] Ghidaoui M S, Mansour S. Efficient treatment of the Vardy-Brown unsteady shear in pipe transients [J].Journal of Hydraulic Engineering, American Society ofCivil Engineers,2002, 128: 102-112
    [103] Axworthy D H, Ghidaoui M, Mclnnes D A. Extended thermodynamics derivation of energy dissipation in unstesdy pipe flow [J]. Joumal of Hydraulic Engineering,American Society of Civil Engineers, 2000, 126: 276 -287
    [104] Silva-Araya W F, Chaudhry M H. Unsteady friction in rough pipe [J]. Journal of Hydraulic Engineering, Amenican Society of Civil Engineers, 2001, 127:607-617
    [105] Ming Zhao, Ghidaoui M S. Efficient quasi-two-dimensional mode1 for water hammer problems [J]. Journal of Hydraulic Engineering,American Society of Civil Engineers,2002, 129: 1007– 1013
    [106] Bergant A, Simpson A R, Vitkovsky J. Developments in unsteady pipe flow friction modeling [J]. Journal of Hydraulic Research .2001, 39:249-257

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700