覆冰导线气动及舞动特性研究
|
摘要
输电线路的舞动是低频高幅的自激振动，产生的巨大的能量对输电线路的安全运行造成极大的隐患和危害，随着输电塔高度的增加及输电线路档距的增大，架空输电线高柔的特点更突出，舞动引起的断线及倒塔等严重电力事故频发，对舞动及其控制的研究对输电线路的安全运行具有重要的意义。本文从气动力风洞试验、数值模拟两个方面对覆冰导线的舞动进行了研究，主要内容如下：
覆冰引起的气动不稳是输电线路舞动的直接诱因，对覆冰导线气动特性的研究是解决舞动问题的基本，本文首先针对输电线路的经典覆冰类型和风场特性设计了覆冰导线气动特性测力风洞试验，分别进行了均匀流和紊流风场下的测力试验，得到了新月形、扇形、冠形在不同覆冰厚度下的气动特性，并研究了平均风速大小，紊流效应及二维流场效应等因素对覆冰导线气动特性的影响。
其次针对目前覆冰导线气动力特性数据匮乏的特点，采用FLUENT软件进行了新月形、扇形、冠形三种覆冰截面在五种覆冰厚度下的气动特性仿真，基于风洞试验结果验证了数据的可靠性。然后对气动力结果进行了曲线拟合，得出了各覆冰截面在不同覆冰厚度及初始凝冰角下的竖向升力系数公式，丰富了风洞试验的结果，建立了详细的覆冰导线气动力特性数据库。
然后本文建立了输电线的单自由度振子数学模型，基于准定常理论采用多尺度方法推导了舞动振幅的解析解，并采用Runge-Kutta方法编制了求解舞动时程的数值仿真程序，与解析结果进行了对比。本文系统的研究了覆冰截面、覆冰厚度、初始凝冰角以及升力曲线阶数等参数对舞动振幅的影响。针对舞动过程中振幅大等特点，提出了一种利用舞动现象进行能量获取的思路，并对不同覆冰形状的截面的能量获取率进行了分析。基于单自由度和两自由度振子系统，给出了舞动稳定性的判别公式。
最后采用有限元程序ANSYS/LS-DYNA，建立非线性粘性阻尼器单元来模拟覆冰导线的气动特性，同时在输电塔上施加脉动风时程，进行了输电线舞动以及输电塔随机振动的显式有限元计算。采用本文方法对500kV海门到汕头榕江大跨越工程进行了风振计算，提出了施加防屈曲耗能支撑的控制方案，并对控制方案进行了优化。对压重防舞技术和相间间隔棒防舞技术进行了探讨，给出了防舞方案的优化设计思路，并对Port Credit线路进行了防舞设计。
Galloping is one type of flow-induced vibration under the condition of non-circularcross section. Galloping of ice-coated transmission conductors is a high-amplitude andlow-frequency self-excited vibration. The large displacements induced by the phenomenonof galloping can produce great energy and cause huge harm to the power grid operation.Rapid growth of electricity transmission capacity in China necessitates conductors forhigh-capacity and long-distance and the properties of high flexible of the conductors areeven more prominent. So galloping could bring the conductors of a transmission line closetogether and cause flashovers, even the line breakage or tower crash recently. So, it is veryimportant to study on the galloping for the safe power grid operation. The aerodynamic andgalloping characteristics of the ice-coated lines were studied through the wind tunnel testand numerical simulation. The main contests are as follows:
The unstable aerodynamic characteristics which caused by the icing is the culprit ofthe transmission conductors galloping while the research on the icing is essential to solvethe matters.Firstly, the wind tunnel test of the aerodynamic characteristics of the ice-coatedlines was projected according to the typical icing types and the wind field characteristics.The tests were carried out under the uniform flow and the turbulent flow. The differenticing types such as crescent, fan and corona shapes were tested. The influences of theaverage velocity and the two-dimensional flow effect were investigated. The fittingfunctions of the lift coefficients and drag ones were given finally.
Secondly, on the issues that the data of the ice-coated transmission conductors, thesimulation of three different icing cross sections under five different icing thicknesses wereproceed based on the Fluent. The reliability of the simulation data was verified according tothe wind tunnel test results. The vertical formulas of different icing cross sections and icingthickness were obtained through the curve fitting technology. The aerodynamiccharacteristics data base of the ice-coated transmission lines were set up.
The mathematical model of the one-degree-freedom oscillator of the transmission linewas modeling on account of the theory of quasi-steady state. The multiple scale method was used to solve the amplitude of the oscillator. The numerical simulation program solvingthe time-histories displacement of the oscillator galloping was worked out on account of theRunge-Kutta method. The galloping amplitude results of the multiple scales and theRunge-Kutta method were compared and the accuracy of the multiple scales was satisfied.The influence of the icing cross sections, the icing thickness and the orders of the verticalaerodynamic coefficient functions on the galloping amplitude were discussed. Aiming thehigh-amplitude phenomenon of the galloping, an idea of energy harvesting from thegalloping of the oscillator was proposed. The energy conversion efficiency factor ofdifferent cross section shapes was discussed. Also, the instability of galloping of theone-degree-freedom and two-degree-freedom oscillator models was studied. The formula ofdiscrimination of stability was obtained and the instability of galloping of various cases wasanalyzed.
Finally, the finite element model was established which the non-linear dampingelement was fixed to simulate the aerodynamic forces in the ANSYS/LS-DYNA. Thefluctuating wind force was applied on the model and the analysis was carried out to get theresponse of the lines galloping and the towers random vibration. According to the explicitfinite element method proposed above, the wind-induced vibration analysis of the500kVlong span transmission line from Hai-men to Shan-tou was carried out. The bucklingrestrained braces were fixed on the tower for the anti-vibration and different optionalschemes were prosed, then the optimized scheme was got. Also, the anti-gallopingtechnology was investigated, such as the mass block and interphase spacer devices. On thePort Credit test lines, the anti-galloping schemes were proposed and the optimized schemeswere got.
覆冰引起的气动不稳是输电线路舞动的直接诱因，对覆冰导线气动特性的研究是解决舞动问题的基本，本文首先针对输电线路的经典覆冰类型和风场特性设计了覆冰导线气动特性测力风洞试验，分别进行了均匀流和紊流风场下的测力试验，得到了新月形、扇形、冠形在不同覆冰厚度下的气动特性，并研究了平均风速大小，紊流效应及二维流场效应等因素对覆冰导线气动特性的影响。
其次针对目前覆冰导线气动力特性数据匮乏的特点，采用FLUENT软件进行了新月形、扇形、冠形三种覆冰截面在五种覆冰厚度下的气动特性仿真，基于风洞试验结果验证了数据的可靠性。然后对气动力结果进行了曲线拟合，得出了各覆冰截面在不同覆冰厚度及初始凝冰角下的竖向升力系数公式，丰富了风洞试验的结果，建立了详细的覆冰导线气动力特性数据库。
然后本文建立了输电线的单自由度振子数学模型，基于准定常理论采用多尺度方法推导了舞动振幅的解析解，并采用Runge-Kutta方法编制了求解舞动时程的数值仿真程序，与解析结果进行了对比。本文系统的研究了覆冰截面、覆冰厚度、初始凝冰角以及升力曲线阶数等参数对舞动振幅的影响。针对舞动过程中振幅大等特点，提出了一种利用舞动现象进行能量获取的思路，并对不同覆冰形状的截面的能量获取率进行了分析。基于单自由度和两自由度振子系统，给出了舞动稳定性的判别公式。
最后采用有限元程序ANSYS/LS-DYNA，建立非线性粘性阻尼器单元来模拟覆冰导线的气动特性，同时在输电塔上施加脉动风时程，进行了输电线舞动以及输电塔随机振动的显式有限元计算。采用本文方法对500kV海门到汕头榕江大跨越工程进行了风振计算，提出了施加防屈曲耗能支撑的控制方案，并对控制方案进行了优化。对压重防舞技术和相间间隔棒防舞技术进行了探讨，给出了防舞方案的优化设计思路，并对Port Credit线路进行了防舞设计。
Galloping is one type of flow-induced vibration under the condition of non-circularcross section. Galloping of ice-coated transmission conductors is a high-amplitude andlow-frequency self-excited vibration. The large displacements induced by the phenomenonof galloping can produce great energy and cause huge harm to the power grid operation.Rapid growth of electricity transmission capacity in China necessitates conductors forhigh-capacity and long-distance and the properties of high flexible of the conductors areeven more prominent. So galloping could bring the conductors of a transmission line closetogether and cause flashovers, even the line breakage or tower crash recently. So, it is veryimportant to study on the galloping for the safe power grid operation. The aerodynamic andgalloping characteristics of the ice-coated lines were studied through the wind tunnel testand numerical simulation. The main contests are as follows:
The unstable aerodynamic characteristics which caused by the icing is the culprit ofthe transmission conductors galloping while the research on the icing is essential to solvethe matters.Firstly, the wind tunnel test of the aerodynamic characteristics of the ice-coatedlines was projected according to the typical icing types and the wind field characteristics.The tests were carried out under the uniform flow and the turbulent flow. The differenticing types such as crescent, fan and corona shapes were tested. The influences of theaverage velocity and the two-dimensional flow effect were investigated. The fittingfunctions of the lift coefficients and drag ones were given finally.
Secondly, on the issues that the data of the ice-coated transmission conductors, thesimulation of three different icing cross sections under five different icing thicknesses wereproceed based on the Fluent. The reliability of the simulation data was verified according tothe wind tunnel test results. The vertical formulas of different icing cross sections and icingthickness were obtained through the curve fitting technology. The aerodynamiccharacteristics data base of the ice-coated transmission lines were set up.
The mathematical model of the one-degree-freedom oscillator of the transmission linewas modeling on account of the theory of quasi-steady state. The multiple scale method was used to solve the amplitude of the oscillator. The numerical simulation program solvingthe time-histories displacement of the oscillator galloping was worked out on account of theRunge-Kutta method. The galloping amplitude results of the multiple scales and theRunge-Kutta method were compared and the accuracy of the multiple scales was satisfied.The influence of the icing cross sections, the icing thickness and the orders of the verticalaerodynamic coefficient functions on the galloping amplitude were discussed. Aiming thehigh-amplitude phenomenon of the galloping, an idea of energy harvesting from thegalloping of the oscillator was proposed. The energy conversion efficiency factor ofdifferent cross section shapes was discussed. Also, the instability of galloping of theone-degree-freedom and two-degree-freedom oscillator models was studied. The formula ofdiscrimination of stability was obtained and the instability of galloping of various cases wasanalyzed.
Finally, the finite element model was established which the non-linear dampingelement was fixed to simulate the aerodynamic forces in the ANSYS/LS-DYNA. Thefluctuating wind force was applied on the model and the analysis was carried out to get theresponse of the lines galloping and the towers random vibration. According to the explicitfinite element method proposed above, the wind-induced vibration analysis of the500kVlong span transmission line from Hai-men to Shan-tou was carried out. The bucklingrestrained braces were fixed on the tower for the anti-vibration and different optionalschemes were prosed, then the optimized scheme was got. Also, the anti-gallopingtechnology was investigated, such as the mass block and interphase spacer devices. On thePort Credit test lines, the anti-galloping schemes were proposed and the optimized schemeswere got.
引文
[1]李黎，曹化锦，尹鹏等.防屈曲耗能支撑对大跨越输电塔风振控制研究.水电能源科学，2010(6)：121-124
[2]郭应龙，李国兴，龙传永.输电线路舞动.北京：中国电力出版社，2002
[3] Yang J, Stern F. A simple and efficient direct forcing immersed boundary frameworkfor fluid–structure interactions. Journal of Computational Physics,2012,231(15):5029-5061
[4]赵汝祥，胥婷，王德洲.输电线路舞动概况及故障分析.价值工程，2012(9)：18-19
[5]李黎，陈元坤，叶志雄等.架空输电线微风振动的室内模拟试验.华中科技大学学报(自然科学版)，2010(8)：99-102
[6]朱大林，马超，代生丽.输电线路多分裂导线次档距振荡分析.陕西电力，2012(11)：43-45
[7] Li L, Cao H, Ye K, et al. Simulation of Galloping and Wind-induced VibrationControl. Noise and Vibration Worldwide,2010,41(10):15-21
[8] Yang F, Yang J, Zhang Z. Unbalanced tension analysis for UHV transmission towersin heavy icing areas. Cold Regions Science and Technology,2012,70:132-140
[9]曹化锦，李黎，姜维等.输电塔-线体系舞动仿真及控制研究.振动与冲击，2011(12)：245-249
[10]夏正春.特高压输电线的覆冰舞动及脱冰跳跃研究：[博士学位论文].华中科技大学，2008
[11] Chabart O, Lilien J L. Galloping of electrical lines in wind tunnel facilities. Journal ofWind Engineering and Industrial Aerodynamics,1998,74–76:967-976
[12]谢运华.导线覆冰密度的研究.中国电力，1998(1)：46-51
[13]刘春城，刘佼.输电线路导线覆冰机理及雨凇覆冰模型.高电压技术，2011(1)：241-248
[14]巢亚锋，蒋兴良，毕茂强等.导线覆冰厚度的直径订正系数.高电压技术，2011(6)
[15]邹明华，邓洪洲.输电线路设计覆冰厚度统计模型取用.电网与清洁能源，2010(1)：40-44
[16] Weaver D S, Veljkovic I. Vortex shedding and galloping of open semi-circular andparabolic cylinders in cross-flow. Journal of Fluids and StructuresFluid-Structure andFlow-Acoustic Interactions involving Bluff Bodies,2005,21(1):65-74
[17] Alonso G, Meseguer J. A parametric study of the galloping stability oftwo-dimensional triangular cross-section bodies. Journal of Wind Engineering andIndustrial Aerodynamics,2006,94(4):241-253
[18] Gurung C B, Yamaguchi H, Yukino T. Identification and characterization ofgalloping of Tsuruga test line based on multi-channel modal analysis of field data.Journal of Wind Engineering and Industrial Aerodynamics,2003,91(7):903-924
[19] Van Dyke P, Laneville A. Galloping of a single conductor covered with a D-sectionon a high-voltage overhead test line. Journal of Wind Engineering and IndustrialAerodynamics5th International Colloquium on Bluff Body Aerodynamics andApplications,2008,96(6-7):1141-1151
[20] Alonso G, Meseguer J, Pérez-Grande I. Galloping stability of triangularcross-sectional bodies: A systematic approach. Journal of Wind Engineering andIndustrial AerodynamicsThe Fourth European and African Conference on WindEngineering,2007,95(9-11):928-940
[21] Alonso G, Valero E, Meseguer J. An analysis on the dependence on cross sectiongeometry of galloping stability of two-dimensional bodies having either biconvex orrhomboidal cross sections. European Journal of Mechanics-B/Fluids,2009,28(2):328-334
[22]顾明，马文勇，全涌等.两种典型覆冰导线气动力特性及稳定性分析.同济大学学报(自然科学版)，2009(10)：1328-1332
[23]马文勇，顾明，全涌等.准椭圆形覆冰导线气动力特性试验研究.同济大学学报(自然科学版)，2010(10)：1409-1413
[24]马文勇，顾明.扇形覆冰导线气动力特性及驰振不稳定性研究.振动与冲击，2012(11)：82-85
[25]刘小会.覆冰导线舞动非线性数值模拟方法及风洞模型试验：[博士学位论文].重庆大学，2011
[26]王昕.覆冰导线舞动风洞试验研究及输电塔线体系舞动模拟：[博士学位论文].浙江大学，2011
[27]楼文娟，王昕，许福友.覆冰导线气弹模型舞动风洞试验研究.土木工程学报，2011(11)：18-23
[28]王昕，楼文娟，沈国辉等.覆冰导线气动力特性风洞试验研究.空气动力学学报，2011(5)：573-579
[29]楼文娟，孙珍茂，许福友等.输电导线扰流防舞器气动力特性风洞试验研究.浙江大学学报(工学版)，2011(1)：93-98
[30]吕翼，楼文娟，孙珍茂等.覆冰三分裂导线气动力特性的数值模拟.浙江大学学报(工学版)，2010(1)：174-179
[31]吕翼.覆冰导线气动力特性的数值模拟研究：[硕士学位论文].浙江大学，2008
[32]展雪萍，于波，郭菁等.覆冰导线的空气动力参数数值模拟.武汉大学学报(工学版)，2012(1)：84-86
[33] Den Hartog J P. Transmission line vibration due to sleet. AIEE Trans,1932,51:67-71
[34] O N, G B P. Conductor Galloping Part I. Den Hartog Mechanism. IEEETransmission on Power Apparatus and Systems,1981,2(100):699-707
[35] Yu P, Desai Y M, Shah A H, et al. Three-degree-of-freedom model for galloping.Part I: Formulation. Journal of Engineering Mechanics,1993,119(12):2404-2425
[36]郭应龙，恽俐丽，鲍务均等.输电导线舞动研究.武汉水利电力大学学报，1995(5)：506-509
[37]黄涛.大跨越高压输电线路非线性舞动理论研究：[博士学位论文].华中科技大学，2007
[38] Yu P, Desai Y M, Popplewell N, et al. Three-degree-of-freedom model for galloping.Part II: Solutions. Journal of engineering mechanics,1993,119(12):2426-2448
[39] Cheng S, Larose G L, Savage M G, et al. Experimental study on the wind-inducedvibration of a dry inclined cable—Part I: Phenomena. Journal of Wind Engineeringand Industrial Aerodynamics,2008,96(12):2231-2253
[40] Piccardo G, Carassale L, Freda A. Critical conditions of galloping for inclined squarecylinders. Journal of Wind Engineering and Industrial AerodynamicsThe EleventhItalian National Conference on Wind Engineering, IN-VENTO-2010, Spoleto, Italy,June30th-July3rd2010,2011,99(6-7):748-756
[41] Matsumoto M, Yagi T, Hatsuda H, et al. Dry galloping characteristics and itsmechanism of inclined/yawed cables. Journal of Wind Engineering and IndustrialAerodynamics6th International Colloquium on Bluff Body Aerodynamics andApplications,2010,98(6-7):317-327
[42] Robertson I, Li L, Sherwin S J, et al. A numerical study of rotational and transversegalloping rectangular bodies. Journal of Fluids and Structures,2003,17(5):681-699
[43] Ming G. On wind–rain induced vibration of cables of cable-stayed bridges based onquasi-steady assumption. Journal of Wind Engineering and IndustrialAerodynamics12th International Conference on Wind Engineering,2009,97(7-8):381-391
[44] Ng Y T, Luo S C, Chew Y T. On using high-order polynomial curve fits in thequasi-steady theory for square-cylinder galloping. Journal of Fluids and Structures,2005,20(1):141-146
[45] Parkinson G V. The square prism as an aeroelastic nonlinear oscillator.QuarterlyJournalMechanicsandAppliedMathematics,1964,17:225-239
[46] Parkinson G V. On the aeroelastic instability of bluffcy linders. Journal of AppliedMechanics,1961,28:252-258
[47] Sisto F. Stall flutter in cascades. JournaloftheAeronauticalSciences,1953,20:598-604
[48] Novak M. Galloping oscillations of prismatic structures. ASCE Journal EngineeringMechanics Division,1972,98:27-46
[49] Novak M. Aeroelastic galloping of prismatic bodies. ASCE Journal EngineeringMechanics Division,1969,96:115-142
[50] Blevins R D, Iwan W D. The galloping response of a two-degree-of-freedom system.JournalofAppliedMathematics,1974,41:1113-1118
[51] Van Oudheusden B W. Aerodynamic stiffness and damping effects in the rotationalgalloping of arectangular cross-section. Journal of Fluids and Structures,2000,14:1119-1144
[52] Novak M, Tanaka H. Effect of turbulence on galloping instability. ASCE JournalEngineering Mechanics Division,1974,100:27-47
[53] Nakamura Y, Matsukawa T. Vortex excitation of rectangular cylinder with a longside normal to the flow. Journal of Fluid Mechanics,1987,180:171-191
[54] Hémon P, Santi F. ON THE AEROELASTIC BEHAVIOUR OF RECTANGULARCYLINDERS IN CROSS-FLOW. Journal of Fluids and Structures,2002,16(7):855-889
[55] Luo S C, Chew Y T, Ng Y T. Hysteresis phenomenon in the galloping oscillation of asquare cylinder. Journal of Fluids and Structures,2003,18(1):103-118
[56] Barrero-Gil A, Sanz-Andrés A, Alonso G. Hysteresis in transverse galloping: Therole of the inflection points. Journal of Fluids and Structures,2009,25(6):1007-1020
[57] Barrero-Gil A, Sanz-Andrés A, Roura M. Transverse galloping at low Reynoldsnumbers. Journal of Fluids and Structures,2009,25(7):1236-1242
[58] Alonso G, Sanz-Lobera A, Meseguer J. Hysteresis phenomena in transverse gallopingof triangular cross-section bodies. Journal of Fluids and Structures,2012,33:243-251
[59] Texier B, Zumbrun K. Galloping instability of viscous shock waves. Physica D:Nonlinear PhenomenaPerspectives in Fluid Dynamics,2008,237(10-12):1553-1601
[60] Vio G A, Dimitriadis G, Cooper J E. Bifurcation analysis and limit cycle oscillationamplitude prediction methods applied to the aeroelastic galloping problem. Journal ofFluids and Structures,2007,23(7):983-1011
[61] Luongo A, Piccardo G. Linear instability mechanisms for coupled translationalgalloping. Journal of Sound and Vibration,2005,288(4-5):1027-1047
[62]王昕，楼文娟，沈国辉.覆冰输电线路舞动气动阻尼识别.振动与冲击，2011(10)：160-164
[63] Davenport A G. Buffeting of suspension bridge by storm winds. In:Proceedings ofthe American Society of Civil Engineers,1962,88:233-268
[64] Gjelstrup H, Georgakis C T. A quasi-steady3degree-of-freedom model for thedetermination of the onset of bluff body galloping instability. Journal of Fluids andStructures,2011,27(7):1021-1034
[65] Martin W W, Currie I G, Naudascher E. Stream wise oscillations of cylinders. ASCEJournal of the Engineering Mechanics Division,1981,3(107):589-607
[66] Stoyanoff S. A unified approach for3D stability and time domain response analysiswith application of quasi-steady theory. Journal of Wind Engineering and IndustrialAerodynamics,2001,89(14–15):1591-1606
[67] Macdonald J H G, Larose G L. A unified approach to aerodynamic damping anddrag/lift instabilities, and its application to dry inclined cable galloping. Journal ofFluids and Structures,2006,22(2):229-252
[68] Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping—Part1: General formulation and solution for perfectly tuned system. Journal of WindEngineering and Industrial Aerodynamics,2008,96(3):291-307
[69] Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping—Part2: Analysis and prevention for arbitrary frequency ratio. Journal of WindEngineering and Industrial Aerodynamics,2008,96(3):308-326
[70] Cheng S, Irwin P A, Tanaka H. Experimental study on the wind-induced vibration ofa dry inclined cable—Part II: Proposed mechanisms. Journal of Wind Engineering andIndustrial Aerodynamics,2008,96(12):2254-2272
[71] Alonso G, Meseguer J, Sanz-Andrés A, et al. On the galloping instability oftwo-dimensional bodies having elliptical cross-sections. Journal of Wind Engineeringand Industrial Aerodynamics,2010,98(8-9):438-448
[72] Rienstra S W. Nonlinear free vibrations of coupled spans of overhead transmissionlines. Journal of engineering mathematics,2005,53(3):337-348
[73] Desai Y M, Yu P, Popplewell N, et al. Finite element modelling of transmission linegalloping. Computers&Structures,1995,57(3):407-420
[74] Desai Y M, Shah Y A H, Popplewell N. PERTURBATION-BASED FINITEELEMENT ANALYSES OF TRANSMISSION LINE GALLOPING. Journal ofSound and Vibration,1996,191(4):469-489
[75] Zhang Q, Popplewell N, Shah A H. GALLOPING OF BUNDLE CONDUCTOR.Journal of Sound and Vibration,2000,234(1):115-134
[76] Luongo A, Zulli D, Piccardo G. Analytical and numerical approaches to nonlineargalloping of internally resonant suspended cables. Journal of Sound andVibrationEUROMECH colloquium483, Geometrically non-linear vibrations ofstructures,2008,315(3):375-393
[77] Luongo A, Zulli D, Piccardo G. On the effect of twist angle on nonlinear galloping ofsuspended cables. Computers& StructuresComputational Structures Technology,2009,87(15-16):1003-1014
[78] Kaisara T, Ten Thije Boonkkamp I J H M. Galloping TransmissionLines:[Dissertation].2008
[79] Xinbo H, Guochang L, Baozhen T, et al. Power Line Galloping Acceleration SensorLocation Algorithm. Energy Procedia,2012,17, Part B:1109-1115
[80]周坤涛，郝淑英，刘君等.覆冰输电线结构及载荷对舞动的影响.振动与冲击，2012(1)：116-120
[81]谢增，刘吉轩，刘超群等.覆冰输电线路分裂导线舞动的建模与数值模拟.西安交通大学学报，2012(7)
[82]杨风利，杨靖波，付东杰等.输电线路导线舞动荷载分析.中国电机工程学报，2011(16)：102-107
[83]孙珍茂，楼文娟.覆冰输电导线舞动及防舞效果分析.振动与冲击，2010(5)：141-146
[84]孙珍茂，楼文娟.覆冰输电导线舞动非线性有限元分析.电网技术，2010(12)：214-218
[85]赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究：[博士学位论文].华中科技大学，2005
[86]王少华.输电线路覆冰导线舞动及其对塔线体系力学特性影响的研究：[博士学位论文].重庆大学，2008
[87]王昕，楼文娟.覆冰导线舞动数值解及影响因素分析.工程力学，2010(S1)：290-293
[88]马文勇，顾明.考虑摆动效应的覆冰导线两自由度驰振稳定性分析.工程力学，2012(1)：195-201
[89]马文勇，顾明，全涌等.覆冰导线任意方向驰振分析方法.同济大学学报(自然科学版)，2010(1)：130-134
[90]晏致涛，张海峰，李正良.基于增量谐波平衡法的覆冰输电线舞动分析.振动工程学报，2012(2)：161-166
[91]晏致涛，李正良，杨振华.基于结点6自由度的输电线舞动有限元分析.振动与冲击，2011(8)：112-117
[92]李文蕴，严波，刘小会.覆冰三分裂导线舞动的数值模拟方法.应用力学学报，2012(1)：9-14
[93] Li L, Jiang W, Cao H J. Galloping of Transmission Tower-Line System andAnti-Galloping Research. Applied Mechanics and Materials,2011,44:2666-2670
[94]曹化锦，李黎，陈元坤等.架空输电线的找形及舞动分析.华中科技大学学报(自然科学版)，2011(1)：102-105
[95]李黎，曹化锦，肖鹏等.输电线覆冰舞动的简化分析方法.工程力学，2011(S2)：152-156
[96]李黎，曹化锦，罗先国等.输电塔-线体系的舞动及风振控制.高电压技术，2011(5)：1253-1260
[97] Cao H, Li L, Chen Y, et al. Research on initial form-finding and galloping ofice-coated transmission conductors.In: ChengDu, China: IEEE Computer Society,2010:113-116
[98]何锃，赵高煜.分裂导线扭转舞动分析的动力学建模.工程力学，2001(2)：126-134
[99]何锃，李国兴.中山口大跨越导线舞动的分析计算.高电压技术，1997(4)：10-12
[100] Jianjun J, Hongxi W, Xiaodong C, et al. Neural Network Simulating the Tensility ofTransmission Line Ice Shedding. Energy Procedia,2012,17, Part B:1235-1241
[101]沈国辉，袁光辉，孙炳楠等.覆冰脱落对输电塔线体系的动力冲击作用研究.工程力学，2010(5)：210-217
[102]孙瑛，武岳，曹正罡.建筑风洞实验指南.北京：中国建筑工业出版社，2011
[103] J. F, W. F. Large eddy simulation of the flow past a circular cylinder at Re=3900.Journal of Wind Engineering and Industrial Aerodynamics,2002,90:1191-1206
[104]张凯，王瑞金，王刚. Flunet技术基础与应用实例（第二版）.北京：清华大学出版社，2010
[105] Ge Y J, Lin Z X, Cao F C, et al. Investigation and prevention of deck gallopingoscillation with computational and experimental techniques. Journal of WindEngineering and Industrial AerodynamicsFifth Asia-Pacific Conference on WindEngineering,2002,90(12-15):2087-2098
[106]王福军.计算流体动力学分析-CFD软件原理与应用.北京：清华大学出版社，2004
[107] Shimada K, Ishihara T. Predictability of unsteady two-dimensional k ε model onthe aerodynamic instabilities of some rectangular prisms. Journal of Fluids andStructures,2012,28:20-39
[108]王海期.非线性振动.北京：高等教育出版社，1992
[109] Allen J J, Smits A J. ENERGY HARVESTING EEL. Journal of Fluids andStructures,2001,15(3–4):629-640
[110] Tang L, Pa doussis M P, Jiang J. Cantilevered flexible plates in axial flow: Energytransfer and the concept of flutter-mill. Journal of Sound and Vibration,2009,326(1–2):263-276
[111] Zhu Q, Haase M, Wu C H. Modeling the capacity of a novel flow-energy harvester.Applied Mathematical Modelling,2009,33(5):2207-2217
[112] Barrero-Gil A, Alonso G, Sanz-Andres A. Energy harvesting from transversegalloping. Journal of Sound and Vibration,2010,329(14):2873-2883
[113] Chopra Anil K.著，译谢礼立.结构动力学：理论及其在地震工程中的应用：第2版.北京：高等教育出版社，2007
[114]龙晓鸿，李黎，胡亮.四渡河悬索桥抖振响应时域分析.工程力学，2010：113-117
[2]郭应龙，李国兴，龙传永.输电线路舞动.北京：中国电力出版社，2002
[3] Yang J, Stern F. A simple and efficient direct forcing immersed boundary frameworkfor fluid–structure interactions. Journal of Computational Physics,2012,231(15):5029-5061
[4]赵汝祥，胥婷，王德洲.输电线路舞动概况及故障分析.价值工程，2012(9)：18-19
[5]李黎，陈元坤，叶志雄等.架空输电线微风振动的室内模拟试验.华中科技大学学报(自然科学版)，2010(8)：99-102
[6]朱大林，马超，代生丽.输电线路多分裂导线次档距振荡分析.陕西电力，2012(11)：43-45
[7] Li L, Cao H, Ye K, et al. Simulation of Galloping and Wind-induced VibrationControl. Noise and Vibration Worldwide,2010,41(10):15-21
[8] Yang F, Yang J, Zhang Z. Unbalanced tension analysis for UHV transmission towersin heavy icing areas. Cold Regions Science and Technology,2012,70:132-140
[9]曹化锦，李黎，姜维等.输电塔-线体系舞动仿真及控制研究.振动与冲击，2011(12)：245-249
[10]夏正春.特高压输电线的覆冰舞动及脱冰跳跃研究：[博士学位论文].华中科技大学，2008
[11] Chabart O, Lilien J L. Galloping of electrical lines in wind tunnel facilities. Journal ofWind Engineering and Industrial Aerodynamics,1998,74–76:967-976
[12]谢运华.导线覆冰密度的研究.中国电力，1998(1)：46-51
[13]刘春城，刘佼.输电线路导线覆冰机理及雨凇覆冰模型.高电压技术，2011(1)：241-248
[14]巢亚锋，蒋兴良，毕茂强等.导线覆冰厚度的直径订正系数.高电压技术，2011(6)
[15]邹明华，邓洪洲.输电线路设计覆冰厚度统计模型取用.电网与清洁能源，2010(1)：40-44
[16] Weaver D S, Veljkovic I. Vortex shedding and galloping of open semi-circular andparabolic cylinders in cross-flow. Journal of Fluids and StructuresFluid-Structure andFlow-Acoustic Interactions involving Bluff Bodies,2005,21(1):65-74
[17] Alonso G, Meseguer J. A parametric study of the galloping stability oftwo-dimensional triangular cross-section bodies. Journal of Wind Engineering andIndustrial Aerodynamics,2006,94(4):241-253
[18] Gurung C B, Yamaguchi H, Yukino T. Identification and characterization ofgalloping of Tsuruga test line based on multi-channel modal analysis of field data.Journal of Wind Engineering and Industrial Aerodynamics,2003,91(7):903-924
[19] Van Dyke P, Laneville A. Galloping of a single conductor covered with a D-sectionon a high-voltage overhead test line. Journal of Wind Engineering and IndustrialAerodynamics5th International Colloquium on Bluff Body Aerodynamics andApplications,2008,96(6-7):1141-1151
[20] Alonso G, Meseguer J, Pérez-Grande I. Galloping stability of triangularcross-sectional bodies: A systematic approach. Journal of Wind Engineering andIndustrial AerodynamicsThe Fourth European and African Conference on WindEngineering,2007,95(9-11):928-940
[21] Alonso G, Valero E, Meseguer J. An analysis on the dependence on cross sectiongeometry of galloping stability of two-dimensional bodies having either biconvex orrhomboidal cross sections. European Journal of Mechanics-B/Fluids,2009,28(2):328-334
[22]顾明，马文勇，全涌等.两种典型覆冰导线气动力特性及稳定性分析.同济大学学报(自然科学版)，2009(10)：1328-1332
[23]马文勇，顾明，全涌等.准椭圆形覆冰导线气动力特性试验研究.同济大学学报(自然科学版)，2010(10)：1409-1413
[24]马文勇，顾明.扇形覆冰导线气动力特性及驰振不稳定性研究.振动与冲击，2012(11)：82-85
[25]刘小会.覆冰导线舞动非线性数值模拟方法及风洞模型试验：[博士学位论文].重庆大学，2011
[26]王昕.覆冰导线舞动风洞试验研究及输电塔线体系舞动模拟：[博士学位论文].浙江大学，2011
[27]楼文娟，王昕，许福友.覆冰导线气弹模型舞动风洞试验研究.土木工程学报，2011(11)：18-23
[28]王昕，楼文娟，沈国辉等.覆冰导线气动力特性风洞试验研究.空气动力学学报，2011(5)：573-579
[29]楼文娟，孙珍茂，许福友等.输电导线扰流防舞器气动力特性风洞试验研究.浙江大学学报(工学版)，2011(1)：93-98
[30]吕翼，楼文娟，孙珍茂等.覆冰三分裂导线气动力特性的数值模拟.浙江大学学报(工学版)，2010(1)：174-179
[31]吕翼.覆冰导线气动力特性的数值模拟研究：[硕士学位论文].浙江大学，2008
[32]展雪萍，于波，郭菁等.覆冰导线的空气动力参数数值模拟.武汉大学学报(工学版)，2012(1)：84-86
[33] Den Hartog J P. Transmission line vibration due to sleet. AIEE Trans,1932,51:67-71
[34] O N, G B P. Conductor Galloping Part I. Den Hartog Mechanism. IEEETransmission on Power Apparatus and Systems,1981,2(100):699-707
[35] Yu P, Desai Y M, Shah A H, et al. Three-degree-of-freedom model for galloping.Part I: Formulation. Journal of Engineering Mechanics,1993,119(12):2404-2425
[36]郭应龙，恽俐丽，鲍务均等.输电导线舞动研究.武汉水利电力大学学报，1995(5)：506-509
[37]黄涛.大跨越高压输电线路非线性舞动理论研究：[博士学位论文].华中科技大学，2007
[38] Yu P, Desai Y M, Popplewell N, et al. Three-degree-of-freedom model for galloping.Part II: Solutions. Journal of engineering mechanics,1993,119(12):2426-2448
[39] Cheng S, Larose G L, Savage M G, et al. Experimental study on the wind-inducedvibration of a dry inclined cable—Part I: Phenomena. Journal of Wind Engineeringand Industrial Aerodynamics,2008,96(12):2231-2253
[40] Piccardo G, Carassale L, Freda A. Critical conditions of galloping for inclined squarecylinders. Journal of Wind Engineering and Industrial AerodynamicsThe EleventhItalian National Conference on Wind Engineering, IN-VENTO-2010, Spoleto, Italy,June30th-July3rd2010,2011,99(6-7):748-756
[41] Matsumoto M, Yagi T, Hatsuda H, et al. Dry galloping characteristics and itsmechanism of inclined/yawed cables. Journal of Wind Engineering and IndustrialAerodynamics6th International Colloquium on Bluff Body Aerodynamics andApplications,2010,98(6-7):317-327
[42] Robertson I, Li L, Sherwin S J, et al. A numerical study of rotational and transversegalloping rectangular bodies. Journal of Fluids and Structures,2003,17(5):681-699
[43] Ming G. On wind–rain induced vibration of cables of cable-stayed bridges based onquasi-steady assumption. Journal of Wind Engineering and IndustrialAerodynamics12th International Conference on Wind Engineering,2009,97(7-8):381-391
[44] Ng Y T, Luo S C, Chew Y T. On using high-order polynomial curve fits in thequasi-steady theory for square-cylinder galloping. Journal of Fluids and Structures,2005,20(1):141-146
[45] Parkinson G V. The square prism as an aeroelastic nonlinear oscillator.QuarterlyJournalMechanicsandAppliedMathematics,1964,17:225-239
[46] Parkinson G V. On the aeroelastic instability of bluffcy linders. Journal of AppliedMechanics,1961,28:252-258
[47] Sisto F. Stall flutter in cascades. JournaloftheAeronauticalSciences,1953,20:598-604
[48] Novak M. Galloping oscillations of prismatic structures. ASCE Journal EngineeringMechanics Division,1972,98:27-46
[49] Novak M. Aeroelastic galloping of prismatic bodies. ASCE Journal EngineeringMechanics Division,1969,96:115-142
[50] Blevins R D, Iwan W D. The galloping response of a two-degree-of-freedom system.JournalofAppliedMathematics,1974,41:1113-1118
[51] Van Oudheusden B W. Aerodynamic stiffness and damping effects in the rotationalgalloping of arectangular cross-section. Journal of Fluids and Structures,2000,14:1119-1144
[52] Novak M, Tanaka H. Effect of turbulence on galloping instability. ASCE JournalEngineering Mechanics Division,1974,100:27-47
[53] Nakamura Y, Matsukawa T. Vortex excitation of rectangular cylinder with a longside normal to the flow. Journal of Fluid Mechanics,1987,180:171-191
[54] Hémon P, Santi F. ON THE AEROELASTIC BEHAVIOUR OF RECTANGULARCYLINDERS IN CROSS-FLOW. Journal of Fluids and Structures,2002,16(7):855-889
[55] Luo S C, Chew Y T, Ng Y T. Hysteresis phenomenon in the galloping oscillation of asquare cylinder. Journal of Fluids and Structures,2003,18(1):103-118
[56] Barrero-Gil A, Sanz-Andrés A, Alonso G. Hysteresis in transverse galloping: Therole of the inflection points. Journal of Fluids and Structures,2009,25(6):1007-1020
[57] Barrero-Gil A, Sanz-Andrés A, Roura M. Transverse galloping at low Reynoldsnumbers. Journal of Fluids and Structures,2009,25(7):1236-1242
[58] Alonso G, Sanz-Lobera A, Meseguer J. Hysteresis phenomena in transverse gallopingof triangular cross-section bodies. Journal of Fluids and Structures,2012,33:243-251
[59] Texier B, Zumbrun K. Galloping instability of viscous shock waves. Physica D:Nonlinear PhenomenaPerspectives in Fluid Dynamics,2008,237(10-12):1553-1601
[60] Vio G A, Dimitriadis G, Cooper J E. Bifurcation analysis and limit cycle oscillationamplitude prediction methods applied to the aeroelastic galloping problem. Journal ofFluids and Structures,2007,23(7):983-1011
[61] Luongo A, Piccardo G. Linear instability mechanisms for coupled translationalgalloping. Journal of Sound and Vibration,2005,288(4-5):1027-1047
[62]王昕，楼文娟，沈国辉.覆冰输电线路舞动气动阻尼识别.振动与冲击，2011(10)：160-164
[63] Davenport A G. Buffeting of suspension bridge by storm winds. In:Proceedings ofthe American Society of Civil Engineers,1962,88:233-268
[64] Gjelstrup H, Georgakis C T. A quasi-steady3degree-of-freedom model for thedetermination of the onset of bluff body galloping instability. Journal of Fluids andStructures,2011,27(7):1021-1034
[65] Martin W W, Currie I G, Naudascher E. Stream wise oscillations of cylinders. ASCEJournal of the Engineering Mechanics Division,1981,3(107):589-607
[66] Stoyanoff S. A unified approach for3D stability and time domain response analysiswith application of quasi-steady theory. Journal of Wind Engineering and IndustrialAerodynamics,2001,89(14–15):1591-1606
[67] Macdonald J H G, Larose G L. A unified approach to aerodynamic damping anddrag/lift instabilities, and its application to dry inclined cable galloping. Journal ofFluids and Structures,2006,22(2):229-252
[68] Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping—Part1: General formulation and solution for perfectly tuned system. Journal of WindEngineering and Industrial Aerodynamics,2008,96(3):291-307
[69] Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping—Part2: Analysis and prevention for arbitrary frequency ratio. Journal of WindEngineering and Industrial Aerodynamics,2008,96(3):308-326
[70] Cheng S, Irwin P A, Tanaka H. Experimental study on the wind-induced vibration ofa dry inclined cable—Part II: Proposed mechanisms. Journal of Wind Engineering andIndustrial Aerodynamics,2008,96(12):2254-2272
[71] Alonso G, Meseguer J, Sanz-Andrés A, et al. On the galloping instability oftwo-dimensional bodies having elliptical cross-sections. Journal of Wind Engineeringand Industrial Aerodynamics,2010,98(8-9):438-448
[72] Rienstra S W. Nonlinear free vibrations of coupled spans of overhead transmissionlines. Journal of engineering mathematics,2005,53(3):337-348
[73] Desai Y M, Yu P, Popplewell N, et al. Finite element modelling of transmission linegalloping. Computers&Structures,1995,57(3):407-420
[74] Desai Y M, Shah Y A H, Popplewell N. PERTURBATION-BASED FINITEELEMENT ANALYSES OF TRANSMISSION LINE GALLOPING. Journal ofSound and Vibration,1996,191(4):469-489
[75] Zhang Q, Popplewell N, Shah A H. GALLOPING OF BUNDLE CONDUCTOR.Journal of Sound and Vibration,2000,234(1):115-134
[76] Luongo A, Zulli D, Piccardo G. Analytical and numerical approaches to nonlineargalloping of internally resonant suspended cables. Journal of Sound andVibrationEUROMECH colloquium483, Geometrically non-linear vibrations ofstructures,2008,315(3):375-393
[77] Luongo A, Zulli D, Piccardo G. On the effect of twist angle on nonlinear galloping ofsuspended cables. Computers& StructuresComputational Structures Technology,2009,87(15-16):1003-1014
[78] Kaisara T, Ten Thije Boonkkamp I J H M. Galloping TransmissionLines:[Dissertation].2008
[79] Xinbo H, Guochang L, Baozhen T, et al. Power Line Galloping Acceleration SensorLocation Algorithm. Energy Procedia,2012,17, Part B:1109-1115
[80]周坤涛，郝淑英，刘君等.覆冰输电线结构及载荷对舞动的影响.振动与冲击，2012(1)：116-120
[81]谢增，刘吉轩，刘超群等.覆冰输电线路分裂导线舞动的建模与数值模拟.西安交通大学学报，2012(7)
[82]杨风利，杨靖波，付东杰等.输电线路导线舞动荷载分析.中国电机工程学报，2011(16)：102-107
[83]孙珍茂，楼文娟.覆冰输电导线舞动及防舞效果分析.振动与冲击，2010(5)：141-146
[84]孙珍茂，楼文娟.覆冰输电导线舞动非线性有限元分析.电网技术，2010(12)：214-218
[85]赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究：[博士学位论文].华中科技大学，2005
[86]王少华.输电线路覆冰导线舞动及其对塔线体系力学特性影响的研究：[博士学位论文].重庆大学，2008
[87]王昕，楼文娟.覆冰导线舞动数值解及影响因素分析.工程力学，2010(S1)：290-293
[88]马文勇，顾明.考虑摆动效应的覆冰导线两自由度驰振稳定性分析.工程力学，2012(1)：195-201
[89]马文勇，顾明，全涌等.覆冰导线任意方向驰振分析方法.同济大学学报(自然科学版)，2010(1)：130-134
[90]晏致涛，张海峰，李正良.基于增量谐波平衡法的覆冰输电线舞动分析.振动工程学报，2012(2)：161-166
[91]晏致涛，李正良，杨振华.基于结点6自由度的输电线舞动有限元分析.振动与冲击，2011(8)：112-117
[92]李文蕴，严波，刘小会.覆冰三分裂导线舞动的数值模拟方法.应用力学学报，2012(1)：9-14
[93] Li L, Jiang W, Cao H J. Galloping of Transmission Tower-Line System andAnti-Galloping Research. Applied Mechanics and Materials,2011,44:2666-2670
[94]曹化锦，李黎，陈元坤等.架空输电线的找形及舞动分析.华中科技大学学报(自然科学版)，2011(1)：102-105
[95]李黎，曹化锦，肖鹏等.输电线覆冰舞动的简化分析方法.工程力学，2011(S2)：152-156
[96]李黎，曹化锦，罗先国等.输电塔-线体系的舞动及风振控制.高电压技术，2011(5)：1253-1260
[97] Cao H, Li L, Chen Y, et al. Research on initial form-finding and galloping ofice-coated transmission conductors.In: ChengDu, China: IEEE Computer Society,2010:113-116
[98]何锃，赵高煜.分裂导线扭转舞动分析的动力学建模.工程力学，2001(2)：126-134
[99]何锃，李国兴.中山口大跨越导线舞动的分析计算.高电压技术，1997(4)：10-12
[100] Jianjun J, Hongxi W, Xiaodong C, et al. Neural Network Simulating the Tensility ofTransmission Line Ice Shedding. Energy Procedia,2012,17, Part B:1235-1241
[101]沈国辉，袁光辉，孙炳楠等.覆冰脱落对输电塔线体系的动力冲击作用研究.工程力学，2010(5)：210-217
[102]孙瑛，武岳，曹正罡.建筑风洞实验指南.北京：中国建筑工业出版社，2011
[103] J. F, W. F. Large eddy simulation of the flow past a circular cylinder at Re=3900.Journal of Wind Engineering and Industrial Aerodynamics,2002,90:1191-1206
[104]张凯，王瑞金，王刚. Flunet技术基础与应用实例（第二版）.北京：清华大学出版社，2010
[105] Ge Y J, Lin Z X, Cao F C, et al. Investigation and prevention of deck gallopingoscillation with computational and experimental techniques. Journal of WindEngineering and Industrial AerodynamicsFifth Asia-Pacific Conference on WindEngineering,2002,90(12-15):2087-2098
[106]王福军.计算流体动力学分析-CFD软件原理与应用.北京：清华大学出版社，2004
[107] Shimada K, Ishihara T. Predictability of unsteady two-dimensional k ε model onthe aerodynamic instabilities of some rectangular prisms. Journal of Fluids andStructures,2012,28:20-39
[108]王海期.非线性振动.北京：高等教育出版社，1992
[109] Allen J J, Smits A J. ENERGY HARVESTING EEL. Journal of Fluids andStructures,2001,15(3–4):629-640
[110] Tang L, Pa doussis M P, Jiang J. Cantilevered flexible plates in axial flow: Energytransfer and the concept of flutter-mill. Journal of Sound and Vibration,2009,326(1–2):263-276
[111] Zhu Q, Haase M, Wu C H. Modeling the capacity of a novel flow-energy harvester.Applied Mathematical Modelling,2009,33(5):2207-2217
[112] Barrero-Gil A, Alonso G, Sanz-Andres A. Energy harvesting from transversegalloping. Journal of Sound and Vibration,2010,329(14):2873-2883
[113] Chopra Anil K.著，译谢礼立.结构动力学：理论及其在地震工程中的应用：第2版.北京：高等教育出版社，2007
[114]龙晓鸿，李黎，胡亮.四渡河悬索桥抖振响应时域分析.工程力学，2010：113-117