混流式水轮机流固耦合振动分析
|
摘要
近年来,国内外一些大型混流式水轮机机组频频出现异常,导致机组振动甚至水力机组结构破坏,降低使用寿命的振动现象,在世界各地普遍存在,严重危及到机组的安全运行。目前,对此问题还没有找到有效的解决方法。
水力机组的振动问题极为复杂。水轮机的振动问题是一个非常复杂多场耦合的非线性动力学问题,特别是流体—固体的耦合作用。混流式水轮机固定部件是主要的水轮机组结构支撑系统。因此,固定部件运行的振动特性对深入了解固定部件的振动机理、避免水力共振、确保机组安全稳定运行具有重要意义。
本文在综述了国内外混流式水轮机组动力特性的研究现状后,主要作了以下工作:
1.借助大型通用有限元分析软件ANSYS,针对混流式水轮机固定部件,组件多,结构各异的特点,在几何造型中采用中心分割,建立各部分几何模型再拼装的方式。建立了混流式水轮机固定部件流固耦合三维有限元分析模型,为水轮机固定部件振动问题的研究奠定基础。
2.对由不可压缩理想流体和固定部件组成的耦合系统,从理论研究出发,采用有限元法的位移—速度势格式,使用加权余量法中的Galerkin法,对耦合系统进行有限元离散,从而导出了系统在流动流体中的流固耦合有限元方程,根据方程中各项的物理意义,详细讨论并分析了附加质量的提出及附加质量的影响因素。
3.根据固定部件在运行时的受力特点及其所要考虑的影响因素,对可压缩理想流体与固定部件组成的线性流固耦合系统,采用有限元方法中的位移—压力格式,应用Galerkin法对流体和固体结构进行离散,建立了系统流固耦合有限元方程。并借助于有限元软件ANSYS中的流固耦合功能分别对两种不同介质下的整体固定部件进行了模态分析,得到固定部件在空气中和静止流体中的自振特性,并对计算结果进行了详细的对比分析,发现一些有价值的振动规律。针对几种特征振源,讨论该水轮机固定部件在运行工况下发生共振的可能性。此外,还讨论了静水压力对水轮机固定部件动力特性的影响,结果表明,对于水轮机固定部件而言,可以不考虑静水压力对其动力特性的影响。
4.根据实际的损坏情况,确定水轮机可能的振动原因:水轮机迷宫环中止漏环径向间隙的不均匀将产生侧向力使转轮与座环发生擦碰。针对这一原因模拟了擦碰力作用下的水轮机固定部件流固耦合系统的动力响应,探究了这一振源对水轮机产生的影响。
5.根据流固耦合系统动力特性分析的模态分析,提出一种基于流体附加质量影响的简化动力特性计算方法——附加质量法。基于振动理论中的能量法与机械振动方法推导建立利用空气和水中不同振动频率确定附加质量的理论方法。并通过ANSYS的二次开发实现了变质量的模态分析得到附加质量模型的模态解,进而讨论了附加质量法的可行性。
The fluid flow induced strong vibrations of Francis hydro turbine unit occur frequently both at domestic and foreign water-power stations. They are ubiquitous that induced structure failure and reduction of turbine operating life, and finally endangered the safety operation of the turbine unit. However, an effective way to solve these problems has not been obtained so far.
As a nonlinear dynamic fluid-structure interaction that coupled multi-fields, the vibration problems of Francis hydro turbine unit are extremely complex. The fixed components of Francis hydro turbine play a main role to keep the system work steadily. Therefore, study on the dynamic characteristics of the fixed components is of great significance to understand the flow-induced vibration mechanism, to prevent resonance of the system, and to ensure the safety and stability of the unit.
The main works of this thesis are as follows:
1. Based on the traits of fixed components of Francis hydro turbine that their geometrical structures are different from each other, this thesis divided the geometry model from its central for several parts to separately build finite element model with software ANSYS. By this way, the whole three-dimensional finite element model can be easily obtained by assembling the separate parts.
2. Described and discretized the coupled system that are composed of fixed components of Francis hydro turbine and the incompressible fluid flow in displacement-velocity finite element formulation. And the fluid-structure interaction governing equation was developed by using the Galerkin method. Then, the advancing of added mass and the effect factors of added mass were discussed in detail in terms of the equation's physical meanings.
3. According to the vibrating features of the fixed components, the linear coupled system that are composed of fixed components and the compressible fluid flow was described in displacement-pressure finite element formulation and discretized by using Galerkin method to develop governing equations. Took advanced use of the fluid-structure interacting analysis function of software ANSYS, the natural frequencies and mode shapes of the whole fixed components both in air and in water were calculated and the compared. For several characteristic vibration sources, the possibilities of the fixed components to occur resonance under normal operating condition were discussed. Moreover, the effects of the hydraulic pressure on the dynamic characteristics of the system were discussed in detail. The results show that the influence of hydrostatic pressure on the dynamic characteristics of the fixed structure were small, and may be neglected.
4. According to the actual damage condition, this thesis reached the conclusion that the possible vibration reason for the turbine is due to the side collision induced by inhomogeneous clearance of the hydro-turbine runner crown seal rings. For this reason, the dynamic responses of fluid-structure interaction system under side collision forces were simulated and analyzed.
5. Based on the modal analysis results of fluid-structure interaction system and the influence of water added mass, a new simplified method to calculate the water added mass, which could be obtained by using the interaction system's frequencies in the air and water, was developed with the energy theory and mechanical vibration theory. Moreover, by secondary development technology of ANSYS, the dynamic characteristics of added mass model with variable-mass modal analysis method were realized and the feasibility of added mass method was also further discussed.
水力机组的振动问题极为复杂。水轮机的振动问题是一个非常复杂多场耦合的非线性动力学问题,特别是流体—固体的耦合作用。混流式水轮机固定部件是主要的水轮机组结构支撑系统。因此,固定部件运行的振动特性对深入了解固定部件的振动机理、避免水力共振、确保机组安全稳定运行具有重要意义。
本文在综述了国内外混流式水轮机组动力特性的研究现状后,主要作了以下工作:
1.借助大型通用有限元分析软件ANSYS,针对混流式水轮机固定部件,组件多,结构各异的特点,在几何造型中采用中心分割,建立各部分几何模型再拼装的方式。建立了混流式水轮机固定部件流固耦合三维有限元分析模型,为水轮机固定部件振动问题的研究奠定基础。
2.对由不可压缩理想流体和固定部件组成的耦合系统,从理论研究出发,采用有限元法的位移—速度势格式,使用加权余量法中的Galerkin法,对耦合系统进行有限元离散,从而导出了系统在流动流体中的流固耦合有限元方程,根据方程中各项的物理意义,详细讨论并分析了附加质量的提出及附加质量的影响因素。
3.根据固定部件在运行时的受力特点及其所要考虑的影响因素,对可压缩理想流体与固定部件组成的线性流固耦合系统,采用有限元方法中的位移—压力格式,应用Galerkin法对流体和固体结构进行离散,建立了系统流固耦合有限元方程。并借助于有限元软件ANSYS中的流固耦合功能分别对两种不同介质下的整体固定部件进行了模态分析,得到固定部件在空气中和静止流体中的自振特性,并对计算结果进行了详细的对比分析,发现一些有价值的振动规律。针对几种特征振源,讨论该水轮机固定部件在运行工况下发生共振的可能性。此外,还讨论了静水压力对水轮机固定部件动力特性的影响,结果表明,对于水轮机固定部件而言,可以不考虑静水压力对其动力特性的影响。
4.根据实际的损坏情况,确定水轮机可能的振动原因:水轮机迷宫环中止漏环径向间隙的不均匀将产生侧向力使转轮与座环发生擦碰。针对这一原因模拟了擦碰力作用下的水轮机固定部件流固耦合系统的动力响应,探究了这一振源对水轮机产生的影响。
5.根据流固耦合系统动力特性分析的模态分析,提出一种基于流体附加质量影响的简化动力特性计算方法——附加质量法。基于振动理论中的能量法与机械振动方法推导建立利用空气和水中不同振动频率确定附加质量的理论方法。并通过ANSYS的二次开发实现了变质量的模态分析得到附加质量模型的模态解,进而讨论了附加质量法的可行性。
The fluid flow induced strong vibrations of Francis hydro turbine unit occur frequently both at domestic and foreign water-power stations. They are ubiquitous that induced structure failure and reduction of turbine operating life, and finally endangered the safety operation of the turbine unit. However, an effective way to solve these problems has not been obtained so far.
As a nonlinear dynamic fluid-structure interaction that coupled multi-fields, the vibration problems of Francis hydro turbine unit are extremely complex. The fixed components of Francis hydro turbine play a main role to keep the system work steadily. Therefore, study on the dynamic characteristics of the fixed components is of great significance to understand the flow-induced vibration mechanism, to prevent resonance of the system, and to ensure the safety and stability of the unit.
The main works of this thesis are as follows:
1. Based on the traits of fixed components of Francis hydro turbine that their geometrical structures are different from each other, this thesis divided the geometry model from its central for several parts to separately build finite element model with software ANSYS. By this way, the whole three-dimensional finite element model can be easily obtained by assembling the separate parts.
2. Described and discretized the coupled system that are composed of fixed components of Francis hydro turbine and the incompressible fluid flow in displacement-velocity finite element formulation. And the fluid-structure interaction governing equation was developed by using the Galerkin method. Then, the advancing of added mass and the effect factors of added mass were discussed in detail in terms of the equation's physical meanings.
3. According to the vibrating features of the fixed components, the linear coupled system that are composed of fixed components and the compressible fluid flow was described in displacement-pressure finite element formulation and discretized by using Galerkin method to develop governing equations. Took advanced use of the fluid-structure interacting analysis function of software ANSYS, the natural frequencies and mode shapes of the whole fixed components both in air and in water were calculated and the compared. For several characteristic vibration sources, the possibilities of the fixed components to occur resonance under normal operating condition were discussed. Moreover, the effects of the hydraulic pressure on the dynamic characteristics of the system were discussed in detail. The results show that the influence of hydrostatic pressure on the dynamic characteristics of the fixed structure were small, and may be neglected.
4. According to the actual damage condition, this thesis reached the conclusion that the possible vibration reason for the turbine is due to the side collision induced by inhomogeneous clearance of the hydro-turbine runner crown seal rings. For this reason, the dynamic responses of fluid-structure interaction system under side collision forces were simulated and analyzed.
5. Based on the modal analysis results of fluid-structure interaction system and the influence of water added mass, a new simplified method to calculate the water added mass, which could be obtained by using the interaction system's frequencies in the air and water, was developed with the energy theory and mechanical vibration theory. Moreover, by secondary development technology of ANSYS, the dynamic characteristics of added mass model with variable-mass modal analysis method were realized and the feasibility of added mass method was also further discussed.
引文
[1]于建华,魏泳涛,曹剑绵.水轮机组结构-液体系统的动态特性分析[J].西南交通大学学报,Vol.36 No.3Jun.2001.
[2]程良骏.水轮机[M].机械工业出版社,1981.
[3]刘大恺.水轮机[M].中国水力电力出版社,1997.
[4]常近时.寿梅华,于希哲,水轮机运行[M].北京:水利电力出版社,1983.
[5]费修渔.100 MW水轮机金属蜗壳裂纹的成因和处理[J].浙江电力,2002.1.
[6]樊世英.混流式水轮机转轮裂纹原因分析及预防措施[J].水力发电,2002,5:38-41.
[7]塞纳M等,胡应德译.混流式水轮机转轮的动力特性改进[M].水力发电与大坝.1999(1):90-95.
[8]菊平.水轮机和发电机振动及主轴摆动的原因和对策[J].东方电气评论,2000,14(2):101-104.
[9]王贵.水轮机振动与稳定性及其试验技术的研究:[博士学位论文].哈尔滨工业大学,2002.
[10]党小建,梁武科,陈千文,水轮机流固耦合振动研究的发展趋势[J].2004.1.
[11]马震岳,沈成能,王溢波,陈婧,等.红石水电站厂房的机组诱发振动及抗振加固研究[J].水力发电学报,2002,76(1)(6).
[12]张双全,韦彩新,肖若富,韩风琴.东江电厂水轮机组对大坝影响的探讨[J].大电机,2002,(3).
[13]Ruprecht A,等非定常流动分析在水利机械中的应用[J].国外大电机,2001,(4).
[14]Vu T C,Shyy W.Performance predition by viscous flow analysis for Francis turbine runner[J].J.of fluid engineering,transaction of the ASME,1994,1.
[15]Moin P and Mahesh Direct numerical simulation:a tool in turbulence research[J].Annual Review of Fluid Mechanic,1998,30:539-578.
[16]周晓泉,瞿伦富,吴玉林.水轮机蜗壳和固定导叶内部流动的数值模拟研究[J].东方电气评论,2001.3:29-34.
[17]张兄文,李国君,李军.离心泵蜗壳内部非定常流动的数值模拟[J].农业机械学报,2006.6:63-68.
[18]李晓峰,王立平,史铁林,扬叔子.考虑非线性油膜力的转子系统稳态响应的研究[J].华中理工大学学报.1999,27(6).
[19]李郁侠,吴子英,原大宁,段凌剑,贺梅.基于传递矩阵法的大型水轮发电机组主轴系统非线瞬态响应数学模型[J].水利水电技术,2002,33(7).
[20]李苹,窦海波,王正.水轮发电机组主轴系统的建模及其非线性瞬态响应[J].清华大学学报,1998,38(6):123-128.
[21]瞿伦富,王正伟,周凌九.轴流转浆机组浆叶液固耦合振动特性仿真计算[J].清华大学学报,1998.38(1):15-18.
[22]谷朝红,姚熊亮.水轮机部件流固耦合振动特性研究[J].大电机技术2001.6:47-52.
[23]肖若富,韦采新,韩风琴,陈秋.流固耦合对水轮机的固定导叶振频振型的影响[J].华中科技大学学报,2001,(4).
[24]陈左一,霍福鹏,刘红.转子叶片在非均匀来流条件下的流体激振特性[J].发电设备,2002,(2).
[25]邢景棠,周盛,崔尔杰.流固祸合力学概述[J].力学进展,1997,27(1):19-37.
[26]Geers T.L.Doubly asymptotic approximations for transient motion of submerged structure,J.Acoust.soc.Am.,1978,64:1500-1508.
[27]戴大农.流固祸合系统动力分析的若干基本问题与数值方法:[博士学位论文].清华大学工程力学系,1988.
[28]Komatsu.K,Fluid-structure interaction,in progress in boundary element method s.Vol.2.Ed.C.A.Brebbia,Pentech press.1th.,1983.
[29]Alfredo B,Rodolfo R.Finite element computation of the vibration modes of a fluid-solid system.compute methods Appl MechEngrg,1994,119:355-370
[30]Alfredo B,Duran R,Rodriguez R,Finite element solution of incompressible fluid-structure vibration problems.International Journal for Numerical Methods in Engineering,1997,40:1435-1448.
[31]Liu W K,Chang H G.Multidisliplinary and interaction problems:a method of computation for fluid structure interaction.Computers & structure,1985,20(1-3):311-320.
[32]戴大农,王歇成,杜庆华.流固祸合系统动力响应的模态分析理论. 固体力学学报,1990,11(4):305-312.
[33]吴一红,谢省宗.水工结构流固藕合动力特性分析.水利学报,1995,1:27-34.
[34]Irons B M.Role of Prt-lversion in Fluid-Sructure Poblems with Mixed Variables.AIAA Joural,1970,8:568-575.
[35]Hamdi M,Ouset Y,Verchery G.A Displacement Methed for the Analysis of Vibration of Coupled Fluid-Structure Systems.Int.J.Numer,Methods Engrg,1978,13:139-150.
[36]Chen H.C.and Taylor R.L.Vibration Analysis of Fluid-Solid Systems Using a Finite Element Displacement Formulation.Int.J.Numer,Methods Engrg,1990,29:683-698
[37]Westergaard H.M.Water pressures on dams during earthquakes.Trans.Amer Soc.Civ.Eng,1993,98:418-433.
[38]Kotsubo S.Dynamic water pressure on dams due to irregular earthquakes.Memoirs Faculty of Engineering,Kyushu university,Fukuoka,Japan,1959,18(4):119-129.
[39]Chopra A.K.Hydrodynamic pressure on dams during earthquake.J.Engng.Me ch.Div,ASCE,1967,93(6):205-223.
[40]]小平清真.不规则地震力所引起的坝上的动水压力.水利译丛,1958.
[41]H.Lamb.On the vibration of an elastic plate in contact with water proceedings of the royal society of London,1920,98.
[42]Blevins R.D.Flow-induced vibration.Van Nostrand-Reinhold,NewYork,1977.
[43]Haskind M D.The hydrodynamic theory of ship oscillations in rolling and pit ching.P rikl,Mat,Mech,1946,10:33-66.
[44]HousnerG.W.Bending vibrations.of a pipe line containing flowing fluid J.Appl,Mech,1952,19:205-208.
[45]Taylor G I.The pressure and impulse of submarine explosion waves on plates.In:Batchelor G K ed.The scientific Papers of G.I.Taylor,Cambridge University Pres s,C ambridge,1963
[46]郑哲敏平板在流体作用下的振动[J].力学学报,1958,2(1):11-16.
[47]居荣初,曾心传.弹性结构与液体祸联振动理论[M].北京:地震出版社,1983.
[48]蒋莉,沈孟育.求解流体与结构相互作用问题的ALE有限体积法[J].水 动力学研究与进展,2000,15(2):148-155.
[49]Zienkiewicz O C.Coupled problems and their numerical solution.In:Lewis R W,Bettess P,Himton E eds.Numerical Methods in coupled synterns.John Wiley and Sons Ltd,New York,1984.
[50]刘正兴,孙雁,谢守国.流体介质中结构的动力特性及响应分析[J].上海交通大学学报,1995,29(4):7-16.
[51]史淑娟,朱礼文,赫崇智等.虑流固耦合的充压膜盒动力学特性分析[J].2006年ansys用户年会论文,北京,2006.
[52]王少波,混流式水轮机转轮动力特性分析及综合优化设计[博士学位论文];北京,机械科学研究院,2003
[53]W.Dettmer,D.Peric.A computational framework for fluid-structure interaction:Finite element formulation and applications.Comput.Methods Appl.Mech.Engrg.195(2006):5754-5779.
[54]Hirt.C.W,Amsden AA,Cook J L.An Arbitrary Lagrangian-Euler computing method for all flow speeds.J.,of computational physics,1974,14(3):27-253.
[55]Bathe K J,zhang Hand Wang M H.Finite element analysis of in compressible and compressible flows with free surfaces and structural interaction.Computers and structures,1995,56(2-3):193-213.
[56]A.T.Chwang and K.H.Wang.Nonlinear impulsive force on an accelerating container.Journal of Fluids Engineering,1984,106(2):223-240.
[57]李遇春,楼梦麟.强震下流体对渡槽槽身的作用[J].水利学报,2000,3:46-52
[58]沈惠明,赵德有.流固祸合振动问题的特征值解法[J].大连理工大学学报,1990,3:15-19.
[59]黄玉盈.复杂外形薄浮板谐祸振问题的边界元一有限元混和解[J].固体力学学报,1991,12(3):255-260.
[60]付作新.水库的库底条件和挡水结构的动水压力[J].水利学报,1987,5:20-25.
[61]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析[J].地震工程与工程振动,1996,16(3):39-47.
[62]张立翔,杨柯.构互动理论及其应用[M].北京:科学出版社,2004.
[63]张升明,吴士冲.流固祸合有限元及储液容器振动问题研究[J].船舶 结构力学论文集(二),1990.
[64]茅春浦,流体力学[M].上海:上海交通大学出版社,1995.
[65]Lindholm US et al.Elastic vibration characteristics of cantilever plates in water.J Ship Res 1965;9(1):11-22.
[66]Meyerhoff WK.Added masses of thin rectangular plates calculatedfrom potential theory.J Ship Res 1970;14(2):100-11.
[67]倪汉根.无限水域中孤立悬臂板的自由振动[J].水动力学研究与进展,1994,9(1):23-29.
[68]吴静萍、王仁康.特种船型的二维水动力计算[J].武汉交通科技大学报,1996,20(3):268-272.
[69]Landweber.L and Shahshahan.A.Added masses and forces on two bodies approaching central impact in an inviscid fluid.Journal of Ship Research,1992,36(2):99-122
[70]宗智、黄鼎良.贴近浅水水底矩形柱体的附加质量和阻尼系数[J].水动力学研究与进展,1990,5(3):1-9.
[71]于洋、周树信.浅水对柱体附加质量与阻尼系数的影响[J].大连海事大学学报,1995,21(1):51-55.
[72]Clarke,David,Calculation of the added mass of circular cylinders in shallow water.Ocean Engineering,2001,28(9):1265-1294
[73]Clarke,David Calculation Of the added mass of elliptical cylinders in shallow water.Ocean Engineeing,2001,28(10):1361-1381
[74]Du JB,He SJ,Wang XC.Dynamic analysis of hydraulic turbine runner and balde system(ii)- analysis of examples.J Tsinghua Univ(Sci& Tech)1998;38(8):72-5.
[75]He SJ,Du JB,Wang XC.Dynamic analysis of hydraulic turbine runner and balde system(i)- mechanics model and formulation.J Tsinghua Univ (Sci& Tech)1998;38(8):68-71.
[76]苏里,李淑娟,唐国安.结构振动诱导流场及附加质量的数值分析[J],应用数学与力学,第26卷第2期,2005.2.
[77]庄茁,刘焕忠,李青.发展附加质量模型分析储液罐的动力响应[J],现代制造工程,2006年第1期.
[78]王自力,蒋志勇,顾永宁.船舶碰撞数值仿真的附加质量模型[J]
[79]王基盛,杨庆山,武岳.薄膜结构附加质量的计算方法[J],空间结构,第9卷第3期2003年9月.
[80]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992
[81]徐芝纶.弹性力学[M].高等教育出版社,1990
[82]张兆顺,崔桂香.流体力学[M].北京:清华大学出版社,1999
[83]章本照.流体力学的有限元方法[M].北京:机械工业出版社,1986
[84]朱伯芳.有限单元法原理与应用[M].北京:水利电力出版社,1979
[85]钱伟长.变分法及有限元[M].北京:科学出版社,1980.
[86]王勖成.有限单元法[M].北京:清华大学出版社,2003
[87]F.T.Doge,F.J.Moody.Fluid transients and fluid-structure interaction.ASME,Wirier A usual Meeting,Boston,1987
[88]Blevins R O.Formulas for natural frequency and mode shape.New York,Van No strand Reinhold Company,1979
[89]Pramila A.Sheet flutter and the interaction between sheet and air.TAPPI-Journal,1986,69:70-74
[90]张升明.流体的可压缩性对弹性结构振动的影响[J].水动力学研究与进展,1994,9(4):429-436.
[91]舒尔曼C.T.著,杨明显等译.水工建筑物的抗震计算[M].北京:水利电力出版社,1980.
[93]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992.
[94]胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981.
[95]许肖梅.声学基础[M].北京:科学技术出版社,2003.
[96]马大猷.现代声学理论基础[M].北京:科学出版社,2004.
[97]何镛.结构振动与声辐射[M].哈尔滨:哈尔滨工程大学出版社,2001.
[98]R.W.克拉夫,J彭津.结构动力学[M].科学出版社,1981
[99]黄玉盈.结构振动分析基础[M].武汉:华中工学院出版社
[100]刘北辰,屈本宁,李国彦等.工程计算力学.北京:机械工业出版社,1994
[101]裴智勇,吴卫国,李晓彬.求解非对称矩阵广义特征问题的Lanczos-QR 方法[J].武汉理工大学学报,2002,6(3):123-125.
[102]L.Lanczos.An interative method for the solution of the eigenvalue problem of linear differential and integral operators.J.Res Nat Bur Standards,1950,45.
[103]徐刚,任文敏,H.G.Reimerdest,A.Dafnist,H.Korsc.储液容器的三维流固耦合动力特性分析[J].力学学报,2004.5.
[104]刘正兴,孙雁,谢守国.计算固体力学.上海:上海交通大学出版社,2000
[105]陈香林,混流式水轮机叶片流固耦合动力特性研究[硕士学位论文],昆明,昆明理工大学,2004.
[106]王珂仑编.水力机组振动[M].北京:水利电力出版社,1984.
[107]晏启详,有衡缝高拱坝的非线性地震响应分析[D],四川大学博士论文,2002
[108]晏启详,刘浩吾,夏春.基于改进的Wilson-θ法的流固耦合迭代算法[J],西南交通大学学报,2002,37(2):204-208.
[109]M.G.Katona,Zienkiewicz.A unified set of single-step algorithms,Part3:the beta-m method,a generalization of the Newmark scheme.International Journal for Numerical methods in Engineering 1985;21:1345-1359.
[110]雷晓燕.岩土工程数值计算[M],北京:中国铁路出版社,1999.
[111]李世芸著ANSYS基础及应用实例[M],北京:中国科学文化出版社,2005
[112]方同 薛璞.振动理论及应用[M].西安:西北工业大学出版社,2002.
[113]覃大清,赵洪田,赵杨.关于混流式水轮机稳定性的几点新认识[J].大电机技术,1998,(3).
[114]刘光宁,等.混流式水轮机的水头变幅和运行工况问题兼论三发电机的若干问题[R].哈尔滨大电机研究所,1995.
[115]刘延柱 陈文良 陈立群.振动力学[M].上海:高等教育出版社,1998.
[116]Liang CC et al.The free vibration analysis of submerged cantilever plates.Ocean Eng 2001;28(9):1225 - 45.
[117]Meirovitch L.Elements of vibration analysis.New York:McGraw-Hill;1986.
[118]Amabili M.Modal properties of annular plates vibrating in water.In:First International Conference on Vibration Measurements by Lasertechniques:Advances and Applications.1994.Ancona,Italy.
[119]Amabili M,Frosali G,Kwak MK.Free vibrations of annular plates coupled with fluids.J Sound Vibrat 1996;191(5):825 - 46.
[120]Q.W.Liang,C.G.Rodriguez,E.Egusquiza.Numerical simulation of fluid added mass effect on a francis turbine runner.Computers & Fluid 36 (2007)1106-1118.
[121]Blevins RD.Formulas for natural frequencies and mode shape.Melbourne:Krieger Publishing Company;1995.
[122]王基盛,杨庆山,武岳.薄膜结构附加质量的计算方法.空间结构,2003,9(3):38-41.
[123]Blevins R O.Formulas for Natural Frequency and Mode Shape EM3.New York:Van Nostrand Reinhold Company,1979.
[124]姜昱汐,三峡升船机中船进出承船厢的附加质量计算[硕士学位论文],大连,大连理工大学,2002
[125]C.G.Rodriguez,E.Egusquiza,X.Escaler,Q.W.Liang,F.Avellan.Experimental investigation of added mass effects on a Francis turbine runner in still water[J].JOURNAL OF FLUIDS AND STRUCTURES,2006,22:699-712.
[2]程良骏.水轮机[M].机械工业出版社,1981.
[3]刘大恺.水轮机[M].中国水力电力出版社,1997.
[4]常近时.寿梅华,于希哲,水轮机运行[M].北京:水利电力出版社,1983.
[5]费修渔.100 MW水轮机金属蜗壳裂纹的成因和处理[J].浙江电力,2002.1.
[6]樊世英.混流式水轮机转轮裂纹原因分析及预防措施[J].水力发电,2002,5:38-41.
[7]塞纳M等,胡应德译.混流式水轮机转轮的动力特性改进[M].水力发电与大坝.1999(1):90-95.
[8]菊平.水轮机和发电机振动及主轴摆动的原因和对策[J].东方电气评论,2000,14(2):101-104.
[9]王贵.水轮机振动与稳定性及其试验技术的研究:[博士学位论文].哈尔滨工业大学,2002.
[10]党小建,梁武科,陈千文,水轮机流固耦合振动研究的发展趋势[J].2004.1.
[11]马震岳,沈成能,王溢波,陈婧,等.红石水电站厂房的机组诱发振动及抗振加固研究[J].水力发电学报,2002,76(1)(6).
[12]张双全,韦彩新,肖若富,韩风琴.东江电厂水轮机组对大坝影响的探讨[J].大电机,2002,(3).
[13]Ruprecht A,等非定常流动分析在水利机械中的应用[J].国外大电机,2001,(4).
[14]Vu T C,Shyy W.Performance predition by viscous flow analysis for Francis turbine runner[J].J.of fluid engineering,transaction of the ASME,1994,1.
[15]Moin P and Mahesh Direct numerical simulation:a tool in turbulence research[J].Annual Review of Fluid Mechanic,1998,30:539-578.
[16]周晓泉,瞿伦富,吴玉林.水轮机蜗壳和固定导叶内部流动的数值模拟研究[J].东方电气评论,2001.3:29-34.
[17]张兄文,李国君,李军.离心泵蜗壳内部非定常流动的数值模拟[J].农业机械学报,2006.6:63-68.
[18]李晓峰,王立平,史铁林,扬叔子.考虑非线性油膜力的转子系统稳态响应的研究[J].华中理工大学学报.1999,27(6).
[19]李郁侠,吴子英,原大宁,段凌剑,贺梅.基于传递矩阵法的大型水轮发电机组主轴系统非线瞬态响应数学模型[J].水利水电技术,2002,33(7).
[20]李苹,窦海波,王正.水轮发电机组主轴系统的建模及其非线性瞬态响应[J].清华大学学报,1998,38(6):123-128.
[21]瞿伦富,王正伟,周凌九.轴流转浆机组浆叶液固耦合振动特性仿真计算[J].清华大学学报,1998.38(1):15-18.
[22]谷朝红,姚熊亮.水轮机部件流固耦合振动特性研究[J].大电机技术2001.6:47-52.
[23]肖若富,韦采新,韩风琴,陈秋.流固耦合对水轮机的固定导叶振频振型的影响[J].华中科技大学学报,2001,(4).
[24]陈左一,霍福鹏,刘红.转子叶片在非均匀来流条件下的流体激振特性[J].发电设备,2002,(2).
[25]邢景棠,周盛,崔尔杰.流固祸合力学概述[J].力学进展,1997,27(1):19-37.
[26]Geers T.L.Doubly asymptotic approximations for transient motion of submerged structure,J.Acoust.soc.Am.,1978,64:1500-1508.
[27]戴大农.流固祸合系统动力分析的若干基本问题与数值方法:[博士学位论文].清华大学工程力学系,1988.
[28]Komatsu.K,Fluid-structure interaction,in progress in boundary element method s.Vol.2.Ed.C.A.Brebbia,Pentech press.1th.,1983.
[29]Alfredo B,Rodolfo R.Finite element computation of the vibration modes of a fluid-solid system.compute methods Appl MechEngrg,1994,119:355-370
[30]Alfredo B,Duran R,Rodriguez R,Finite element solution of incompressible fluid-structure vibration problems.International Journal for Numerical Methods in Engineering,1997,40:1435-1448.
[31]Liu W K,Chang H G.Multidisliplinary and interaction problems:a method of computation for fluid structure interaction.Computers & structure,1985,20(1-3):311-320.
[32]戴大农,王歇成,杜庆华.流固祸合系统动力响应的模态分析理论. 固体力学学报,1990,11(4):305-312.
[33]吴一红,谢省宗.水工结构流固藕合动力特性分析.水利学报,1995,1:27-34.
[34]Irons B M.Role of Prt-lversion in Fluid-Sructure Poblems with Mixed Variables.AIAA Joural,1970,8:568-575.
[35]Hamdi M,Ouset Y,Verchery G.A Displacement Methed for the Analysis of Vibration of Coupled Fluid-Structure Systems.Int.J.Numer,Methods Engrg,1978,13:139-150.
[36]Chen H.C.and Taylor R.L.Vibration Analysis of Fluid-Solid Systems Using a Finite Element Displacement Formulation.Int.J.Numer,Methods Engrg,1990,29:683-698
[37]Westergaard H.M.Water pressures on dams during earthquakes.Trans.Amer Soc.Civ.Eng,1993,98:418-433.
[38]Kotsubo S.Dynamic water pressure on dams due to irregular earthquakes.Memoirs Faculty of Engineering,Kyushu university,Fukuoka,Japan,1959,18(4):119-129.
[39]Chopra A.K.Hydrodynamic pressure on dams during earthquake.J.Engng.Me ch.Div,ASCE,1967,93(6):205-223.
[40]]小平清真.不规则地震力所引起的坝上的动水压力.水利译丛,1958.
[41]H.Lamb.On the vibration of an elastic plate in contact with water proceedings of the royal society of London,1920,98.
[42]Blevins R.D.Flow-induced vibration.Van Nostrand-Reinhold,NewYork,1977.
[43]Haskind M D.The hydrodynamic theory of ship oscillations in rolling and pit ching.P rikl,Mat,Mech,1946,10:33-66.
[44]HousnerG.W.Bending vibrations.of a pipe line containing flowing fluid J.Appl,Mech,1952,19:205-208.
[45]Taylor G I.The pressure and impulse of submarine explosion waves on plates.In:Batchelor G K ed.The scientific Papers of G.I.Taylor,Cambridge University Pres s,C ambridge,1963
[46]郑哲敏平板在流体作用下的振动[J].力学学报,1958,2(1):11-16.
[47]居荣初,曾心传.弹性结构与液体祸联振动理论[M].北京:地震出版社,1983.
[48]蒋莉,沈孟育.求解流体与结构相互作用问题的ALE有限体积法[J].水 动力学研究与进展,2000,15(2):148-155.
[49]Zienkiewicz O C.Coupled problems and their numerical solution.In:Lewis R W,Bettess P,Himton E eds.Numerical Methods in coupled synterns.John Wiley and Sons Ltd,New York,1984.
[50]刘正兴,孙雁,谢守国.流体介质中结构的动力特性及响应分析[J].上海交通大学学报,1995,29(4):7-16.
[51]史淑娟,朱礼文,赫崇智等.虑流固耦合的充压膜盒动力学特性分析[J].2006年ansys用户年会论文,北京,2006.
[52]王少波,混流式水轮机转轮动力特性分析及综合优化设计[博士学位论文];北京,机械科学研究院,2003
[53]W.Dettmer,D.Peric.A computational framework for fluid-structure interaction:Finite element formulation and applications.Comput.Methods Appl.Mech.Engrg.195(2006):5754-5779.
[54]Hirt.C.W,Amsden AA,Cook J L.An Arbitrary Lagrangian-Euler computing method for all flow speeds.J.,of computational physics,1974,14(3):27-253.
[55]Bathe K J,zhang Hand Wang M H.Finite element analysis of in compressible and compressible flows with free surfaces and structural interaction.Computers and structures,1995,56(2-3):193-213.
[56]A.T.Chwang and K.H.Wang.Nonlinear impulsive force on an accelerating container.Journal of Fluids Engineering,1984,106(2):223-240.
[57]李遇春,楼梦麟.强震下流体对渡槽槽身的作用[J].水利学报,2000,3:46-52
[58]沈惠明,赵德有.流固祸合振动问题的特征值解法[J].大连理工大学学报,1990,3:15-19.
[59]黄玉盈.复杂外形薄浮板谐祸振问题的边界元一有限元混和解[J].固体力学学报,1991,12(3):255-260.
[60]付作新.水库的库底条件和挡水结构的动水压力[J].水利学报,1987,5:20-25.
[61]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析[J].地震工程与工程振动,1996,16(3):39-47.
[62]张立翔,杨柯.构互动理论及其应用[M].北京:科学出版社,2004.
[63]张升明,吴士冲.流固祸合有限元及储液容器振动问题研究[J].船舶 结构力学论文集(二),1990.
[64]茅春浦,流体力学[M].上海:上海交通大学出版社,1995.
[65]Lindholm US et al.Elastic vibration characteristics of cantilever plates in water.J Ship Res 1965;9(1):11-22.
[66]Meyerhoff WK.Added masses of thin rectangular plates calculatedfrom potential theory.J Ship Res 1970;14(2):100-11.
[67]倪汉根.无限水域中孤立悬臂板的自由振动[J].水动力学研究与进展,1994,9(1):23-29.
[68]吴静萍、王仁康.特种船型的二维水动力计算[J].武汉交通科技大学报,1996,20(3):268-272.
[69]Landweber.L and Shahshahan.A.Added masses and forces on two bodies approaching central impact in an inviscid fluid.Journal of Ship Research,1992,36(2):99-122
[70]宗智、黄鼎良.贴近浅水水底矩形柱体的附加质量和阻尼系数[J].水动力学研究与进展,1990,5(3):1-9.
[71]于洋、周树信.浅水对柱体附加质量与阻尼系数的影响[J].大连海事大学学报,1995,21(1):51-55.
[72]Clarke,David,Calculation of the added mass of circular cylinders in shallow water.Ocean Engineering,2001,28(9):1265-1294
[73]Clarke,David Calculation Of the added mass of elliptical cylinders in shallow water.Ocean Engineeing,2001,28(10):1361-1381
[74]Du JB,He SJ,Wang XC.Dynamic analysis of hydraulic turbine runner and balde system(ii)- analysis of examples.J Tsinghua Univ(Sci& Tech)1998;38(8):72-5.
[75]He SJ,Du JB,Wang XC.Dynamic analysis of hydraulic turbine runner and balde system(i)- mechanics model and formulation.J Tsinghua Univ (Sci& Tech)1998;38(8):68-71.
[76]苏里,李淑娟,唐国安.结构振动诱导流场及附加质量的数值分析[J],应用数学与力学,第26卷第2期,2005.2.
[77]庄茁,刘焕忠,李青.发展附加质量模型分析储液罐的动力响应[J],现代制造工程,2006年第1期.
[78]王自力,蒋志勇,顾永宁.船舶碰撞数值仿真的附加质量模型[J]
[79]王基盛,杨庆山,武岳.薄膜结构附加质量的计算方法[J],空间结构,第9卷第3期2003年9月.
[80]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992
[81]徐芝纶.弹性力学[M].高等教育出版社,1990
[82]张兆顺,崔桂香.流体力学[M].北京:清华大学出版社,1999
[83]章本照.流体力学的有限元方法[M].北京:机械工业出版社,1986
[84]朱伯芳.有限单元法原理与应用[M].北京:水利电力出版社,1979
[85]钱伟长.变分法及有限元[M].北京:科学出版社,1980.
[86]王勖成.有限单元法[M].北京:清华大学出版社,2003
[87]F.T.Doge,F.J.Moody.Fluid transients and fluid-structure interaction.ASME,Wirier A usual Meeting,Boston,1987
[88]Blevins R O.Formulas for natural frequency and mode shape.New York,Van No strand Reinhold Company,1979
[89]Pramila A.Sheet flutter and the interaction between sheet and air.TAPPI-Journal,1986,69:70-74
[90]张升明.流体的可压缩性对弹性结构振动的影响[J].水动力学研究与进展,1994,9(4):429-436.
[91]舒尔曼C.T.著,杨明显等译.水工建筑物的抗震计算[M].北京:水利电力出版社,1980.
[93]陆鑫森.高等结构动力学[M].上海:上海交通大学出版社,1992.
[94]胡海昌.弹性力学的变分原理及其应用[M].北京:科学出版社,1981.
[95]许肖梅.声学基础[M].北京:科学技术出版社,2003.
[96]马大猷.现代声学理论基础[M].北京:科学出版社,2004.
[97]何镛.结构振动与声辐射[M].哈尔滨:哈尔滨工程大学出版社,2001.
[98]R.W.克拉夫,J彭津.结构动力学[M].科学出版社,1981
[99]黄玉盈.结构振动分析基础[M].武汉:华中工学院出版社
[100]刘北辰,屈本宁,李国彦等.工程计算力学.北京:机械工业出版社,1994
[101]裴智勇,吴卫国,李晓彬.求解非对称矩阵广义特征问题的Lanczos-QR 方法[J].武汉理工大学学报,2002,6(3):123-125.
[102]L.Lanczos.An interative method for the solution of the eigenvalue problem of linear differential and integral operators.J.Res Nat Bur Standards,1950,45.
[103]徐刚,任文敏,H.G.Reimerdest,A.Dafnist,H.Korsc.储液容器的三维流固耦合动力特性分析[J].力学学报,2004.5.
[104]刘正兴,孙雁,谢守国.计算固体力学.上海:上海交通大学出版社,2000
[105]陈香林,混流式水轮机叶片流固耦合动力特性研究[硕士学位论文],昆明,昆明理工大学,2004.
[106]王珂仑编.水力机组振动[M].北京:水利电力出版社,1984.
[107]晏启详,有衡缝高拱坝的非线性地震响应分析[D],四川大学博士论文,2002
[108]晏启详,刘浩吾,夏春.基于改进的Wilson-θ法的流固耦合迭代算法[J],西南交通大学学报,2002,37(2):204-208.
[109]M.G.Katona,Zienkiewicz.A unified set of single-step algorithms,Part3:the beta-m method,a generalization of the Newmark scheme.International Journal for Numerical methods in Engineering 1985;21:1345-1359.
[110]雷晓燕.岩土工程数值计算[M],北京:中国铁路出版社,1999.
[111]李世芸著ANSYS基础及应用实例[M],北京:中国科学文化出版社,2005
[112]方同 薛璞.振动理论及应用[M].西安:西北工业大学出版社,2002.
[113]覃大清,赵洪田,赵杨.关于混流式水轮机稳定性的几点新认识[J].大电机技术,1998,(3).
[114]刘光宁,等.混流式水轮机的水头变幅和运行工况问题兼论三发电机的若干问题[R].哈尔滨大电机研究所,1995.
[115]刘延柱 陈文良 陈立群.振动力学[M].上海:高等教育出版社,1998.
[116]Liang CC et al.The free vibration analysis of submerged cantilever plates.Ocean Eng 2001;28(9):1225 - 45.
[117]Meirovitch L.Elements of vibration analysis.New York:McGraw-Hill;1986.
[118]Amabili M.Modal properties of annular plates vibrating in water.In:First International Conference on Vibration Measurements by Lasertechniques:Advances and Applications.1994.Ancona,Italy.
[119]Amabili M,Frosali G,Kwak MK.Free vibrations of annular plates coupled with fluids.J Sound Vibrat 1996;191(5):825 - 46.
[120]Q.W.Liang,C.G.Rodriguez,E.Egusquiza.Numerical simulation of fluid added mass effect on a francis turbine runner.Computers & Fluid 36 (2007)1106-1118.
[121]Blevins RD.Formulas for natural frequencies and mode shape.Melbourne:Krieger Publishing Company;1995.
[122]王基盛,杨庆山,武岳.薄膜结构附加质量的计算方法.空间结构,2003,9(3):38-41.
[123]Blevins R O.Formulas for Natural Frequency and Mode Shape EM3.New York:Van Nostrand Reinhold Company,1979.
[124]姜昱汐,三峡升船机中船进出承船厢的附加质量计算[硕士学位论文],大连,大连理工大学,2002
[125]C.G.Rodriguez,E.Egusquiza,X.Escaler,Q.W.Liang,F.Avellan.Experimental investigation of added mass effects on a Francis turbine runner in still water[J].JOURNAL OF FLUIDS AND STRUCTURES,2006,22:699-712.