覆冰导线舞动风洞试验研究及输电塔线体系舞动模拟
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摘要
舞动是输电单根导线或分裂导线在中低风速下呈现出的大幅度低频率的自激振动。近年来我国输电线路建设事业突飞猛进,电压等级和建设规模已跨进世界输电大国的行列,随着我国电网规模的发展和恶劣气象的频繁出现,电网发生舞动事故的频率和危害程度呈明显增加的趋势。深入开展导线舞动理论和防舞的研究,对保证我国输电安全具有十分重要的意义,本文将从覆冰导线气动力特性,覆冰导线气弹模型舞动风洞试验,单导线、分裂导线及输电塔线体系舞动数值仿真及相间间隔棒防舞研究等方面对输电导线舞动理论及防舞方法进行较为精细的深入研究和发展。本文工作主要包括以下几个方面：
1.2种覆冰形状单根导线及新月形覆冰分裂导线气动力特性风洞试验研究。针对厚覆冰特(超)高压输电导线,制作了新月形及D形两种典型覆冰断面导线节段模型,在风洞中利用测力天平获得单导线和分裂导线子导线在均匀流和均匀紊流中各风攻角下的气动力特性,研究了气动力系数对攻角的变化规律,以及风场中紊流、子导线干扰对试验结果的影响,根据Den Hartog理论分别计算了各种工况下覆冰导线可能发生舞动的风攻角范围。对于单根导线,结合以往试验结果,研究了两类覆冰冰型的气动力特征,得到了一些共性的规律。另外在风洞中对新月形覆冰导线在均匀流场和均匀紊流场下的表面风压分布进行了测量,进一步研究了其局部风压特性。
2.覆冰导线气弹模型的舞动风洞试验研究及气动阻尼识别。采用新月形和D形两种典型覆冰断面的导线节段模型,通过弹簧将节段模型与支架相连,利用弹簧和配重等架设了竖向／扭转频率比可调的覆冰单根或分裂导线气弹模型。在风洞中通过调整风攻角使覆冰导线节段模型舞动,获取了舞动响应时程；并采用与试验模型相对应的计算模型模拟得到相同工况下的舞动结果,验证了基于准定常假设的非线性舞动气动力模型,研究了通过静态气动力系数计算所得舞动响应与试验值之间的差异。利用Hilbert变换对舞动响应进行了气动阻尼识别,与理论值进行了比较,研究了其变化规律及各种因素的影响。
3.单根覆冰导线舞动的数值仿真。分别采用基于假定模态的舞动解析模型,以及通过三节点抛物线等参索单元模拟覆冰导线的有限元方法求解单根覆冰导线舞动响应,采用Newmark-β方法结合每个时间步内的Newton-Raphson迭代来求解导线舞动非线性动力方程,给出了导线舞动较为精确的时间积分解,对两种方法的求解结果进行了比较。并利用有限元方法对舞动进行了参数分析,研究了各种线路参数对舞动的影响。模拟了通过绝缘子悬挂的耐张-直线.耐张体系的三跨覆冰导线舞动响应,与单跨两端耐张覆冰导线舞动进行了对比,说明了绝缘子及令跨导线对舞动的影响。
4.覆冰分裂导线及输电塔线体系舞动响应的计算。利用有限元方法,用梁单元离散间隔棒,建立任意分裂覆冰导线有限元模型,通过模态分析研究了分裂导线动力特性及其影响因素,计算了四分裂覆冰导线在两种典型覆冰形状下的舞动响应。进一步建立了包含紧凑型直线输电塔架的耐张-直线-耐张三跨三相四分裂输电塔线体系有限元模型,计算了三相线路各跨在不同覆冰条件下的舞动响应,研究了覆冰导线舞动对绝缘子串及输电塔的作用特征,以及脉动风荷载分别作用于输电塔和导线时对舞动的影响。
5.相间间隔棒防舞研究。首先给出了各类相间间隔棒的物理模型及其有限元实现方法。针对500kV单回路竖向布置的三相四分裂导线,计算了其在安装不同数量、类型的相间间隔棒后子导线张拉力的增量。对安装有相间间隔棒的线路进行了动力特性分析。最后假定其中某相线路因覆冰产生舞动,比较了该相线路在安装了刚性及柔性两类相间间隔棒前后舞动响应的变化,得到了刚性和柔性相间间隔棒的受力状态,以及不同覆冰形状及风攻角下相间间隔棒的防舞效果。
Galloping is a low frequency and large amplitude vibration self-excited by single conductor or bundled conductors under mid/low wind velocity. In recent years, the construction of power transmission lines has witnessed great breakthroughs in China, both the voltage level and the construction scale are first-class around the world. However, with rapid development of the power system and frequent occurrence of extreme weather, the frequency and destruction level tend to increase obviously. Consequently, thorough investigation on conductor galloping theory and anti-galloping techniques is of considerable significance to the safety of power transmission lines. In this paper, delicate study including aerodynamic characteristics of iced conductors, galloping of aeroelastic iced conductor model in wind tunnel, numerical galloping simulation of single conductor, bundled conductors and transmission tower-line system as well as the anti-galloping effects of interphase spacer was carried out to obtain further development in conductor galloping theory and anti-galloping techniques. The paper is mainly focused on the following aspects:
1.Wind tunnel test study on aerodynamic characteristics of single conductor and bundled conductors with two typical ice-coating sections. As to ultra high voltage transmission conductors with thick ice-coating, truncated conductor models with crescent and D ice-coating sections were made, the aerodynamic coefficients of single conductor and bundled conductors in uniform flow and homogeneous turbulence flow under different attack angles were measured by force balance in wind tunnel. The variation of aerodynamic coefficients with attack angle has been investigated, and the influence of turbulence in the wind field and interference caused by sub-conductors also has been discussed. Based on Den Hartog theory, the ranges of attack angle in which galloping may occur to iced conductors under various cases were calculated respectively. As to single conductor, combined with former test results, the aerodynamic characteristics of the two ice-coating sections were studied and several general principles are received. Moreover, measurement has been conducted on the surface wind pressure distribution of the crescent iced conductor in two types of wind fields, thus further reflects local wind pressure attributes.
2.Wind tunnel study on galloping of aeroelastic iced conductor model and identification of its aerodynamic damping. Made in two typical ice-coating section forms(crescent section and D section), aeroelastic models of single conductor and bundled conductors were connected to brackets with springs. The ratio of vertical and rotational self-vibration frequency of the conductor models can be changed by varying spring stiffness, suspension position and additional weight. Galloping of aeroelastic models are excited and recorded respectively in the wind tunnel under appropriate wind speed and attack angles, futher, galloping responses in test were compared with numerical ones from FEM models based on quasi-steady assumption with static aerodynamic coefficients. Vertical and rotational aerodynamic damping in galloping were identified by Hilbert transform, impacts of various factors as wind speed, attack angle, ratio of vertical and rotational self-vibration frequency, iced profile and number of sub conductors on aerodynamic damping were discussed.
3. Numerical approach to galloping of single iced conductor. The response of single iced condutor galloping was simulated respectively by analytical model based on assumed-mode method and finite element model which iced conductor was modeled by a three-node, isoparametric cable element with parabolic shape function, a time marching algorithm using Newmarκ-βmethod in conjunction with Newton-Raphson iteration was utilized to integrate dynamic equilibrium equation involving geometric nonlinearities and nonlinear wind load, and results from two methods were compared. Factors influencing galloping were discussed in detailed by parametric analysis with FEM method. Galloping response of three-spans transmission was also derived and compared with response of single span, impacts of insulators and remote spans were discussed.
4. Galloping responses of bundled iced conductors and iced transmission tower-line system. The spacers are simulated by two-node beam elements, thus FEM model of bundled conductors with arbitrary number of sub conductors was established, modal analysis was employed to study dynamic property of four bundled conductors and factors impact on it, galloping of four bundled conductors with two types of ice-coating section were obtained. Futhermore, a three-phase four bundled transmission tower-line system with three spans was modeled, galloping responses of one or all phase were acquired when subjected to fluctuating wind load, dynamic loads on insulators and towers due to galloping conductors were determined, some useful conclusion for designing have been found.
5.Study on anti-galloping effect of interphase spacer. Firstly, physical models and their implements in finite element method of various interphase spacers were introduced. Then take a 500kV single-circuit three-phase four bundled transmission line with interphase spacer vertically installed for example, the tension increments in sub-conductors with different number and type of interphase spacers were calculated. Also, modal analysis of the transmission line with interphase spacers was conducted. In the end, suppose a certain phase gallops because of ice-coating, comparative analysis of galloping response before and after installing rigid and flexible interphase spacers were carried out.
1.2种覆冰形状单根导线及新月形覆冰分裂导线气动力特性风洞试验研究。针对厚覆冰特(超)高压输电导线,制作了新月形及D形两种典型覆冰断面导线节段模型,在风洞中利用测力天平获得单导线和分裂导线子导线在均匀流和均匀紊流中各风攻角下的气动力特性,研究了气动力系数对攻角的变化规律,以及风场中紊流、子导线干扰对试验结果的影响,根据Den Hartog理论分别计算了各种工况下覆冰导线可能发生舞动的风攻角范围。对于单根导线,结合以往试验结果,研究了两类覆冰冰型的气动力特征,得到了一些共性的规律。另外在风洞中对新月形覆冰导线在均匀流场和均匀紊流场下的表面风压分布进行了测量,进一步研究了其局部风压特性。
2.覆冰导线气弹模型的舞动风洞试验研究及气动阻尼识别。采用新月形和D形两种典型覆冰断面的导线节段模型,通过弹簧将节段模型与支架相连,利用弹簧和配重等架设了竖向／扭转频率比可调的覆冰单根或分裂导线气弹模型。在风洞中通过调整风攻角使覆冰导线节段模型舞动,获取了舞动响应时程；并采用与试验模型相对应的计算模型模拟得到相同工况下的舞动结果,验证了基于准定常假设的非线性舞动气动力模型,研究了通过静态气动力系数计算所得舞动响应与试验值之间的差异。利用Hilbert变换对舞动响应进行了气动阻尼识别,与理论值进行了比较,研究了其变化规律及各种因素的影响。
3.单根覆冰导线舞动的数值仿真。分别采用基于假定模态的舞动解析模型,以及通过三节点抛物线等参索单元模拟覆冰导线的有限元方法求解单根覆冰导线舞动响应,采用Newmark-β方法结合每个时间步内的Newton-Raphson迭代来求解导线舞动非线性动力方程,给出了导线舞动较为精确的时间积分解,对两种方法的求解结果进行了比较。并利用有限元方法对舞动进行了参数分析,研究了各种线路参数对舞动的影响。模拟了通过绝缘子悬挂的耐张-直线.耐张体系的三跨覆冰导线舞动响应,与单跨两端耐张覆冰导线舞动进行了对比,说明了绝缘子及令跨导线对舞动的影响。
4.覆冰分裂导线及输电塔线体系舞动响应的计算。利用有限元方法,用梁单元离散间隔棒,建立任意分裂覆冰导线有限元模型,通过模态分析研究了分裂导线动力特性及其影响因素,计算了四分裂覆冰导线在两种典型覆冰形状下的舞动响应。进一步建立了包含紧凑型直线输电塔架的耐张-直线-耐张三跨三相四分裂输电塔线体系有限元模型,计算了三相线路各跨在不同覆冰条件下的舞动响应,研究了覆冰导线舞动对绝缘子串及输电塔的作用特征,以及脉动风荷载分别作用于输电塔和导线时对舞动的影响。
5.相间间隔棒防舞研究。首先给出了各类相间间隔棒的物理模型及其有限元实现方法。针对500kV单回路竖向布置的三相四分裂导线,计算了其在安装不同数量、类型的相间间隔棒后子导线张拉力的增量。对安装有相间间隔棒的线路进行了动力特性分析。最后假定其中某相线路因覆冰产生舞动,比较了该相线路在安装了刚性及柔性两类相间间隔棒前后舞动响应的变化,得到了刚性和柔性相间间隔棒的受力状态,以及不同覆冰形状及风攻角下相间间隔棒的防舞效果。
Galloping is a low frequency and large amplitude vibration self-excited by single conductor or bundled conductors under mid/low wind velocity. In recent years, the construction of power transmission lines has witnessed great breakthroughs in China, both the voltage level and the construction scale are first-class around the world. However, with rapid development of the power system and frequent occurrence of extreme weather, the frequency and destruction level tend to increase obviously. Consequently, thorough investigation on conductor galloping theory and anti-galloping techniques is of considerable significance to the safety of power transmission lines. In this paper, delicate study including aerodynamic characteristics of iced conductors, galloping of aeroelastic iced conductor model in wind tunnel, numerical galloping simulation of single conductor, bundled conductors and transmission tower-line system as well as the anti-galloping effects of interphase spacer was carried out to obtain further development in conductor galloping theory and anti-galloping techniques. The paper is mainly focused on the following aspects:
1.Wind tunnel test study on aerodynamic characteristics of single conductor and bundled conductors with two typical ice-coating sections. As to ultra high voltage transmission conductors with thick ice-coating, truncated conductor models with crescent and D ice-coating sections were made, the aerodynamic coefficients of single conductor and bundled conductors in uniform flow and homogeneous turbulence flow under different attack angles were measured by force balance in wind tunnel. The variation of aerodynamic coefficients with attack angle has been investigated, and the influence of turbulence in the wind field and interference caused by sub-conductors also has been discussed. Based on Den Hartog theory, the ranges of attack angle in which galloping may occur to iced conductors under various cases were calculated respectively. As to single conductor, combined with former test results, the aerodynamic characteristics of the two ice-coating sections were studied and several general principles are received. Moreover, measurement has been conducted on the surface wind pressure distribution of the crescent iced conductor in two types of wind fields, thus further reflects local wind pressure attributes.
2.Wind tunnel study on galloping of aeroelastic iced conductor model and identification of its aerodynamic damping. Made in two typical ice-coating section forms(crescent section and D section), aeroelastic models of single conductor and bundled conductors were connected to brackets with springs. The ratio of vertical and rotational self-vibration frequency of the conductor models can be changed by varying spring stiffness, suspension position and additional weight. Galloping of aeroelastic models are excited and recorded respectively in the wind tunnel under appropriate wind speed and attack angles, futher, galloping responses in test were compared with numerical ones from FEM models based on quasi-steady assumption with static aerodynamic coefficients. Vertical and rotational aerodynamic damping in galloping were identified by Hilbert transform, impacts of various factors as wind speed, attack angle, ratio of vertical and rotational self-vibration frequency, iced profile and number of sub conductors on aerodynamic damping were discussed.
3. Numerical approach to galloping of single iced conductor. The response of single iced condutor galloping was simulated respectively by analytical model based on assumed-mode method and finite element model which iced conductor was modeled by a three-node, isoparametric cable element with parabolic shape function, a time marching algorithm using Newmarκ-βmethod in conjunction with Newton-Raphson iteration was utilized to integrate dynamic equilibrium equation involving geometric nonlinearities and nonlinear wind load, and results from two methods were compared. Factors influencing galloping were discussed in detailed by parametric analysis with FEM method. Galloping response of three-spans transmission was also derived and compared with response of single span, impacts of insulators and remote spans were discussed.
4. Galloping responses of bundled iced conductors and iced transmission tower-line system. The spacers are simulated by two-node beam elements, thus FEM model of bundled conductors with arbitrary number of sub conductors was established, modal analysis was employed to study dynamic property of four bundled conductors and factors impact on it, galloping of four bundled conductors with two types of ice-coating section were obtained. Futhermore, a three-phase four bundled transmission tower-line system with three spans was modeled, galloping responses of one or all phase were acquired when subjected to fluctuating wind load, dynamic loads on insulators and towers due to galloping conductors were determined, some useful conclusion for designing have been found.
5.Study on anti-galloping effect of interphase spacer. Firstly, physical models and their implements in finite element method of various interphase spacers were introduced. Then take a 500kV single-circuit three-phase four bundled transmission line with interphase spacer vertically installed for example, the tension increments in sub-conductors with different number and type of interphase spacers were calculated. Also, modal analysis of the transmission line with interphase spacers was conducted. In the end, suppose a certain phase gallops because of ice-coating, comparative analysis of galloping response before and after installing rigid and flexible interphase spacers were carried out.
引文
Angelo L, Daniele Z, Giuseppe P. A linear curved-beam model for the analysis of galloping in suspended cables[J]. Journal of Mechanics of Materials and Structures,2007,2(4):675-393
Angelo L. Daniele Z. Giuseppe P. Analytical and numerical approaches to nonlinear galloping of internaally resonant suspended cables[J]. Journal of Sound and Vibration,2008,315:375-393.
AIJ. AIJ recommendation for loads on buildings[S]. Architetural Institute of Japan,2004.
Baenziger M A. James W D. Wouters B, et al. Dynamic loads on transmission line structures due to galloping conductors[J]. IEEE Transactions on Power Delivery,1994,9(1):40-49.
Binder R C. Galloping of Conductors Can Be Suppressed[J]. Electric Light & Power,1962,40(9).
Bleivins R D. Flow-induced vibration.2nd Ed[M]. Van Nostrand Reinhold Co, New York,1990.
Braun A L. Awruch A M. Aerodynamic and aeroelastic analysis of bundled cable numerical simulation[J]. Journal of Sound and Vibration,2005,284:51-73.
Byun G S. Egbert R 1.2-degree-of-freedom analysis of power-line galloping by describing function methods[J]. Electric Power Systems Research,1991,21(3):187-193.
Chabart O, Lilien J L. Galloping of electrical lines in wind tunnel facilities[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,74:967-976.
Chadha J. A dynamic model investigation of conductor galloping[C]. IEEE Winter Power Meeting, 1974.
Chadha J, Jaster W. Ifluence of turbulence on the galloping instability of iced conductors[J]. IEEE Transactions on Power Apparatus and Systems,1975,94(5):1489-1499.
Chay M T, Albermani F, Hawes H. Wind load on transmission line structures simulated downbursts[C]. First World Congress on Asset Management, Gold Coast, Australia,2006.
Clough R W. Penzien J. Dynamics of structures[M]. Ncgraw-Hill. New York,1975.
Dempsey D, White H. Winds wreak havoc on lines[J]. Transmission and Distribution World,1996, 48(6):3-32.
Den Hartog J P. Transmission line vibration due to sleet[J]. AIEE Transactions,1932,51(4): 1074-1086.
Desai Y M, Popplewell N, Shah A H, et al., Geometric ninlinear static analysis of cable supported structures[J]. Computers & Structures,1988,29(6):1001-1009.
Desai Y M. Modelling of planar transmission line galloping[D]. University of Manitoba.1991.
Desai Y M, Yu P, Popplewell N, et al. Finite-element modeling of transimission-line galloping[J]. Computers & Structures,1995.57(3):407-420.
Desai Y M, Yu P. Shah A H. et al. Perturbation-based finite element analyses of transmission line galloping[J]. Journal of Sound and Vibration,1996,191(4):469-489.
Douglass D A. Roche J B. T2 wind motion resistant conductor[J]. IEEE Transactions on Power Apparatus and Systems,1985,104(10):2879-2887.
Edwards A T, Madeyski A. Progress report on the investigation of galloping of transmission line conductors[J]. AIEE Transactions,1956.75:666-686.
Edwards A T, Ko R G. Interphase spacers for controlling galloping of overhead conductors[C]. IEEE Symposium on Mechanical Oscillations of Overhead Transmission Lines, Vancouver, Australia, 1979.
EPRI. Transmission line reference book:wind-induced conductor motion[M]. Electrical Power Research Institute. Palo Alto, California,2008.
Fikke S M. Guidelines for field measurement of ice loadings on overhead power line conductors[R]. Cigre TB (Technical Brochure) 179. TF 22.06.01 August.
Gawronski K E. Non-linear galloping of bundle-conductor transmission lines[D].Clarkson College of technology,1977.
Gurung C B, Yamaguchi H, Yukino T. Identification and characterization of galloping of tsurugatest line based on multi-channel modal analysis of field data[J]. Journal of Wind Engineering & Industrial Aerodynamics,2003,91(7):903-924.
Halsan K A, Havard D G, Fikke S M, et al. Galloping studies at statnett using remote monitoring[C]. CIGRE SC22, WGll meeting, Graz, Austria,1998.
Havard D G. Pohlman J C. Five years'field trials of detuning pendulums for galloping control[J]. IEEE Transactions on Power Apparatus and Systems,1984,103(2):318-327.
Havard D G. Dynamic loads on transmission line structures during galloping[C]. The International Workshop on Atmospheric Icing of Structures, Brno, Czech Republic,2002.
Jing H, Yan B, Zhou S, et al. Parameter study on galloping of iced bundled conductors[C]. Power and Energy Engineering Conference (APPEEC), Chengdu, China,2010.
Hunt J C R, Richard D J W. Overhead line oscillations and the effect of aerodynamic dampers[J]. IEEE Transactions on Power Apparatus and Systems,1969,116(11):1869-1874.
Irvine H M. Cable structures[M]. MIT Press. Cambrige, Mass.1981.
Jamaleddine A, McClure G, Rousselet J, et al. Simulation of ice-shedding on electrical transmission lines using ADINA [J]. Computers and Structures.1993.47(4-5):523-536.
Jones K F. Coupled vertical and horizontal galloping[J]. Journal of Engineering Mechanics. 1992.118(1):92-107.
Kalman T, Farzaneh M, McClure G. Numerical analysis of the dynamic effects of shock-load-induced ice shedding on overhead ground wires [J]. Computers and Structures,2007. 85(7-8):375-384.
Kareem A. Gurley K. Damping in structure:its evaluation and treatment of uncertainly [J]. Journal of Wind Engineering & Industrial Aerodynamics,1996,59:131-157.
Keutgen R, Lilien J L. Benchmark cases for galloping with results obtained from wind tunnel facilities-validation of a finite element model [J]. IEEE Transactions on Power Delivery,2000,15(1): 367-374.
Kimura K, Fujino Y, Inoue M, et al. Unsteady aerodynamic force characteristics of ice-accreted four-conductor bundle transmission lines under large amplitude motion[J]. Journal of Structural Engineering,2000,46(2):1055-1062.
Lam K, Cheung W C, Phenomena of vortex shedding and flow interefrence of three cylinders in different equilateral arrangements[J]. Journal of Fluid Mechanics,1988,196:1-26.
Lee J C, Suppression of transmission line galloping by support compliance design[D]. Tulane University, New Orleans,1987.
Lilien J L, Dubois H, Overhead line vertical galloping on bundle configurations:stability criterions and amplitude prediction[M]. IEE Overhead Line Design and Construction:Theory and Practice (up to150kV),1988.
Lilien J L, Wang J, Chabart O, Pirotte P. Overhead transmission lines design, some mechanical aspects[C].ICPST'94 (International Conference on Power System Technology), Beijing, China, 1994.
Lilien J L, Vinogradov A, Full-scale tests of TDD antigalloping device (torsional damper and detuner)[J]. IEEE Transactions on Power Delivery,2002,17(2):638-643.
Marukawa H, Kato N, Fuji K, et al. Experimental evaluation of aerodynamic damping of tall buildings[J]. Journal of Wind Engineering & Industrial Aerodynamics,1996,59:177-190.
Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping[J]. Journal of Wind Engineering and Industrial Aerodynamics,2008,96(3):291-326.
Mathur R K. Shah A H, Trainor P G S, et al. Dynamics of a guyed transmission tower system[J]. IEEE Transactions on Power Delivery,1987, PWRD-2(3):908-916.
McConnell K G, Chang C N. A study of the axial-torsional coupling effect on a sagged trasmission Iine[J]. Experimental Mechanics.1986.26(4):324-329.
McDaniel W N. An analysis of galloping electric transmission lines[J]. AIEE Transactions,1960, 113(5):406-412.
Muhammad B W, Takashi I. Muhammad W S. Galloping response prediction of ice-accreted transmission lines[C]. The 4th International Conference on Advances in Wind and Structures(AWAS 08), Jeju, Korea,2008.
Nakamura Y. Galloping of bundled power line conductors[C]. Journal of Sound & Vibration,1980, 73(3):363-377.
Nigol O. Clarke G J. Conductor galloping and control based on torsional mechanism[C]. IEEE Power Engineering Society Winter Meeting, Paper No.C74016-2, New York,1974.
Nigol O, Clarke G J, Havard D G. Torsional stability of bundle conductors[J]. IEEE Transactions on Power Apparatus and Systems,1977,96(5):1666-1674.
Nigol O, Havard D G. Control of torsionally induced galloping with detuning pendulums[C]. IEEE PES Winter Meeting, Paper No A78125-7, New York,1978.
Nigol O. Buchan P G. Conductor galloping, part I:Den Hartog mechanism:part II:torsional mechanism[J]. IEEE Transactions on Power Apparatus and Systems,1981.100(2):699-720.
Otsuki A, Kajita O. Galloping phenomena of overhead transmission lines[[J]. Fujikura Technical Review,1975.7:33-46.
Ozaka A, Kagami J, Takeda K, et al. Observations of galloping on overhead transmission test lines with artificial snow accretion models[C].7th International Workshop on Atmospheric lcing of Structures, Chicoutimi, Canada:300-305.1996.
Parkinson G V Phenomena and modeling of flow-induced vibrations of bluff bodies[J]. Progress in Aerospace Sciences,1989,26(2):169-224.
Park K T, Kim S H, Park H S, et al. The determination of bridge displacement using measured acceleration[J]. Engineering Structures,2005.27(3):371-378.
Pon C J, Havard D G, Edwards A T. Performance of interphase spacers for galloping control[R]. Ontario Hydro Research Division Report No.82-216-K,1982.
Pon C J, Havard D G, Field trials of galloping control devices for bundle conductor lines[R]. Report on R & D Project 133 T 386, Canadian Electrical Association, Montreal,1994.
Price S J, Wake induced flutter of power transmission conductors[J]. Journal of Sound and Vibration, 1975,38(1):125-147.
Rawlins C B, Pohlman J C. On the state of galloping conductor technology[C].4th International Workshop on Atmospheric Icing of Structures, Paris, France,1988.
Richardson A S, Martuccelli J R, Price W S. An Investigation of Galloping Transmission Line Conductors[J]. IEEE Transactions Paper,1963,82:411-431.
Richardson A S. Dynamic analysis of lightly iced conductor galloping in two degrees of freedom[J]. IEE Proceedings C,1981,128(4):211-218.
Richardson A S. A study of galloping conductors on a 230kv transmission line[J]. Electric Power System Research,1991,21(1):43-55.
Savory E, Parke G, Zeinoddini M, et al. Modelling of tornado and microburst-induced wind loading and failure of a lattice transmission tower[J]. Engineering Structures,2001,23(4):365-375.
Schmidt J, Jurdens C, Design of interphase spacers with composite insulators and service experience[C]. CIGRE SC22-WG11 Task Force on Galloping, Rijeka, Yugoslavia,1989.
Shehata A Y, Damatty A A, Savory E. Finite element modeling of transmission line under downburst wind loading[J]. Finite Elements in Analysis and Design,2005,42(1):71-89.
Shimizu M, Ishihara T, Phuc P V. A wind tunnel study on quasi-steady and unsteady forces of ice accreted four bundled and single conductor transmission lines[J]. Denryoku Chuo Kenkyujo Abiko Kenkyujo Hokoku, U03044,2004.
Stumpf P. Investigation of aerodynamic stability for selected inclined cables and conductor cables[D]. University of Manitoba, Winnipeg, Canada,1990.
Tokoro S, Komatsu S, Nakasub M, et al. A study on wake-galloping employing full aeroelastic twin cable model[J]. Journal of Wind Engineering and Industrial Aerodynamics,2000,88:247-261.
Tornquist E L, Becker C, Galloping conductors and a method for studying them[J]. AIEE Transactions Paper,1947,66:1154-61.
Tsujimoto K, Iisaka H, Shimojima H, et al. Report on experimental observation of galloping behaviour in 8-bundled conductors[J]. IEEE Transactions on Power Apparatus and Systems,1983, 102(5):1193-1201.
Tunstall M, Koutselos L T. Further studies of the galloping instability & natural ice accretions on overhead line conductors[C].4th Int. Conf. on Atmospheric Icing of Structures. Paris, France,1988.
Tutar M, Oguz G. Large eddy simulation of wind flow around parallel buildings with varying configurations[J]. Fluid Dynamics Research,2002,31(5-6):289-315.
Van Dyke P, Laneville A. Galloping of a single conductor covered with a d-section on a high voltage overhead test line[C].5th International Colloquium on Bluff Body Aerodynamics and Applications, Ottawa, Canada, paper 377-380.2004.
Veletsos A S, Darbre G R. Dynamic stiffness of parabolic cables[J]. Earthquake Engineering and Structural Dynamics,1983,11(3):367-401.
Wang J W. Large vibrations of overhead electrical lines:a full 3-dof model for galloping studies[D]. Collection des Publications de la Faculte des Sciences Appliquees de l'Universite de Liege,1996, 151:1-227.
Wang J W, Lilien J L. A new theory for torsional stiffness of multi-span bundle overhead transmission Lines[J]. IEEE Transactions on Power Delivery,1998,13(4):1405～1411.
White W N. An analysis of the influence of support stiffness on transmission line galloping amplitudes[D]. Tulane University, New Orleans,1985.
Xiao X H, Wu J. Simulation and effects evaluation of anti-galloping devices for overhead transmission lines[C].4th IEEE Conference on Automation Science and Engineering Key Bridge Marriott, Washington DC, USA,2008
Yu P, Desai Y M, Shah A H, et al.3-degree-of-freedom model for galloping[J]. Journal of Engineering Mechanics-ASCE,1993,119(12):2404-2448.
Yu P, Popplewell N, Shah, A. H, Instability trends of inertially coupled galloping[J]. Journal of Sound and Vibration,1995,183(4):663-678.
Zdravkovich M M. Review of interefrence-iduced oscillations in flow past two circular cylinders in vairous arrangements[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,28(1-3): 183-200.
Zhang J H, Shi Y H, Liu G X, et al. Simulation of transmission line galloping using finite element method [C]. IEEE 2nd International Conference on Advances in Power System Control, Operation and Management, HongKong,1993.
Zhang Q, Popplewell N, Shah A H. Galloping of bundled conductor[J]. Journal of Sound and Vibration,2000,234(1):115-137.
蔡廷湘.输电线舞动新机理研究[J].中国电力,1998,31(10)：62-66.
陈晓明,邓洪洲,王肇民.大跨越输电线路舞动稳定性研究[J].工程力学,2004,21(1)：56-60.
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[J].同济大学学报,2009.37(10)：1328～1332.
郭应龙,李国兴,尤传永.输电线路舞动[M].中国电力出版社.北京,2002.
郭勇.大跨越输电塔线体系的风振响应及振动控制研究[D]浙江大学.杭州.2006.
何锃,钱天虹.覆冰三分裂导线扭控舞动的分析计算[J].华中科技大学学报,1998,26(10)：16-18.
何锃,赵高煜.分裂导线扭转舞动分析的动力学建模[J].工程力学.2001,18(2)：126-134.
胡杰,郭应龙,恽莉丽.三分裂输电导线舞动的有限元分析与计算[J].水利电力机械,1996.(4)：9-12.
胡松.大跨越输电线路的风振反应分析及振动控制研究[D].同济大学，上海.1999.
黄河.刘建军,李万平.覆冰导线气动力特性的数值模拟[J].工程力学,2003,增刊：201-204.
黄河,刘建军,李万平.覆冰导线绕流的数值模拟[J]于工程技术大学学报,2004,23(6)：767-769.
及荣军.330kV柔性相间复合绝缘间隔棒的研制[J].电网技术,2006,30(12)：112-115.
李万平，杨新祥,张立志.覆冰导线群的静气动力特性[J].空气动力学学报,1995,13(4)：427-435.
李万平.覆冰导线群的动气动力特性[J].空气动力学学报,2000,18(4)：413-419.
李万平,黄河,何锃.特大覆冰导线气动力特性测试[J].华中科技大学学报,2001,29(8)：84-86.
李文蕴.覆冰分裂导线舞动数值模拟方法研究[D].重庆大学,重庆,2009.
刘操兰.大跨越输电线路导线舞动研究[D].重庆大学,重庆,2009.
刘锡良，周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5)：81-84.
刘小会.架空高压输电线路风偏数值模拟研究[D].重庆大学,重庆,2007.
刘小会,严波,张宏雁,等.覆冰导线舞动非线性数值模拟方法[J].应力数学和力学.2009,30(4)：457-467.
刘振亚.国家电网公司输变电工程典型设计：500kV输电线路分册[M].中国电力出版社，北京,2007.
楼文娟,卢旦,杨毅,等.开孔建筑屋盖风振响应中的气动阻尼识别[J].空气动力学学报,2007,25(4)：419-424.
楼文娟,孙炳楠.风与结构的耦合作用及风振响应分析[J].工程力学,2000，17(5)：16-22.
楼文娟,孙珍茂,吕翼,等.扰流防舞器与气动力阻尼片的防舞效果[J].电网技术,2010,34(2)：200-204.
吕翼.覆冰导线气动力特性的数值模拟研究[D].浙江大学,杭州，2008
马进,丁斌,王勇.导线防舞动相间间隔棒铰链式联结金具的研制[J].华北电力技术,2010,(9)：1-4.
宁研.黄琦.张昌华，曹永兴.架空输电导线覆冰及舞动在线监测技术综述[J].四川电力技术.2009.32(6)：67-71.
孙炳楠.220千伏瓯江第三跨越直线高塔风洞试验报告[R].浙江大学.建筑工程学院,2004.
孙炳楠.220千伏舟山与大陆联网大跨越输电塔风洞试验报告[R].浙江大学，建筑工程学院，2006.
沈国辉.袁光辉,孙炳楠,楼文娟.覆冰脱落对输电塔线体系的动力冲击作用研究[J].工程力学,2010，27(5)：210-217.
孙珍茂.输电线路舞动分析及防舞技术研究[D].浙江大学,杭州.2010.
孙珍茂楼文娟.覆冰输电导线舞动及防舞效果分析[J].振动与冲击,2010,29(5)：141-146.
潘峰.孙炳楠,楼文娟.基于Hilbert Huang变换的大跨屋盖气动阻尼识别[J]浙江大学学报(工学版),2007,41(1)：65-70.
唐校友.线路舞动的低阻尼共振激发机理[J].东北电力大学学报，2006，26(1)：65-70.
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[D].重庆大学,重庆，2008.
王黎明,范钦珊,薛家麒.相间合成绝缘间隔棒后屈曲性态研究[J].清华大学学报(自然科学版),1996,36(6)：70-76.
王黎明,孙保强,张楚岩,等.750KV紧凑型线路相间间隔棒力学分析与计算[J].高压电技术,2009,35(10)：2551-2556.
王丽新,杨文兵,杨新华,等.输电线路舞动的有限元分析[J].华中科技大学学报(城市科学版)，2004.21(1)：76-80.
王昕,楼文娟,徐伟.雷暴冲击风对输电塔的作用特征.华中科技大学学报(城市科学版),2008,25(4)：10-14.
王昕，楼文娟,李宏男,等.雷暴冲击风作用下高耸输电塔风振响应[J].浙江大学学报(工学版).2009，43(8)：1520-1525.
干昕,楼文娟.导线舞动数值解及影响因素分析[J].工程力学.2010，增刊1：290-293.
王昕,楼文娟.多跨输电线路脱冰动力响应研究[J].工程力学,2011,28(1)：226-232.
王之宏.风荷载的模拟研究[J].建筑结构学报,1994,15(1)：44-52.
夏正春.特高压输电线的覆冰舞动及脱冰跳跃研究[D].华中科技大学,武汉,2008.
肖东坡.500kV输电线路风偏故障分析及对策[J].电网技术,2009,33(5)：99-102.
肖正直.晏致涛.李正良,等.八分裂输电导线结冰风洞试验及气动力特性试验[J].电网技术,2009(1)：90-94.
丁俊清.郭应龙,肖晓晖.输电导线舞动的计算机仿真[J].武汉大学学报，2002,35(1)：39-43.
苑吉河,蒋兴良.易辉,等.输电线路导线覆冰的国内外研究现状[J].高电压技术，2004，30(1)：6-9.
张相庭.结构风程[M].中国建筑工业出版社,北京.2006.
张禹芳.我国500kV输电线路风偏闪络分析[J].电网技术,2005，29(7)：65-67.
张子富,默增禄，何有兴,等.特高压直流直线塔断线荷载分析[J].电网技术,2010，34(5)：16-20.
赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究[D].华中科技大学,武汉,2005..
中华人民共和国国家标准.建筑结构荷载规范(2006)版GB50009-2001[S].中国建筑工业山版社,北京,2006.
周凌远,李乔.基于 UL 法的 CR 列式空间梁几何非线性分析[J].西南交通大学学报，2006,41(6)：690-695.
朱宽军,刘超群,任西春.架空输电线路舞动时导线动态张力分析[J].中国电力,2005,38(10)：40-44,
朱宽军,刘彬.架空输电线路分裂导线扭转刚度的计算[J].电网技术,2010，34(3)：210-214.
Angelo L. Daniele Z. Giuseppe P. Analytical and numerical approaches to nonlinear galloping of internaally resonant suspended cables[J]. Journal of Sound and Vibration,2008,315:375-393.
AIJ. AIJ recommendation for loads on buildings[S]. Architetural Institute of Japan,2004.
Baenziger M A. James W D. Wouters B, et al. Dynamic loads on transmission line structures due to galloping conductors[J]. IEEE Transactions on Power Delivery,1994,9(1):40-49.
Binder R C. Galloping of Conductors Can Be Suppressed[J]. Electric Light & Power,1962,40(9).
Bleivins R D. Flow-induced vibration.2nd Ed[M]. Van Nostrand Reinhold Co, New York,1990.
Braun A L. Awruch A M. Aerodynamic and aeroelastic analysis of bundled cable numerical simulation[J]. Journal of Sound and Vibration,2005,284:51-73.
Byun G S. Egbert R 1.2-degree-of-freedom analysis of power-line galloping by describing function methods[J]. Electric Power Systems Research,1991,21(3):187-193.
Chabart O, Lilien J L. Galloping of electrical lines in wind tunnel facilities[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,74:967-976.
Chadha J. A dynamic model investigation of conductor galloping[C]. IEEE Winter Power Meeting, 1974.
Chadha J, Jaster W. Ifluence of turbulence on the galloping instability of iced conductors[J]. IEEE Transactions on Power Apparatus and Systems,1975,94(5):1489-1499.
Chay M T, Albermani F, Hawes H. Wind load on transmission line structures simulated downbursts[C]. First World Congress on Asset Management, Gold Coast, Australia,2006.
Clough R W. Penzien J. Dynamics of structures[M]. Ncgraw-Hill. New York,1975.
Dempsey D, White H. Winds wreak havoc on lines[J]. Transmission and Distribution World,1996, 48(6):3-32.
Den Hartog J P. Transmission line vibration due to sleet[J]. AIEE Transactions,1932,51(4): 1074-1086.
Desai Y M, Popplewell N, Shah A H, et al., Geometric ninlinear static analysis of cable supported structures[J]. Computers & Structures,1988,29(6):1001-1009.
Desai Y M. Modelling of planar transmission line galloping[D]. University of Manitoba.1991.
Desai Y M, Yu P, Popplewell N, et al. Finite-element modeling of transimission-line galloping[J]. Computers & Structures,1995.57(3):407-420.
Desai Y M, Yu P. Shah A H. et al. Perturbation-based finite element analyses of transmission line galloping[J]. Journal of Sound and Vibration,1996,191(4):469-489.
Douglass D A. Roche J B. T2 wind motion resistant conductor[J]. IEEE Transactions on Power Apparatus and Systems,1985,104(10):2879-2887.
Edwards A T, Madeyski A. Progress report on the investigation of galloping of transmission line conductors[J]. AIEE Transactions,1956.75:666-686.
Edwards A T, Ko R G. Interphase spacers for controlling galloping of overhead conductors[C]. IEEE Symposium on Mechanical Oscillations of Overhead Transmission Lines, Vancouver, Australia, 1979.
EPRI. Transmission line reference book:wind-induced conductor motion[M]. Electrical Power Research Institute. Palo Alto, California,2008.
Fikke S M. Guidelines for field measurement of ice loadings on overhead power line conductors[R]. Cigre TB (Technical Brochure) 179. TF 22.06.01 August.
Gawronski K E. Non-linear galloping of bundle-conductor transmission lines[D].Clarkson College of technology,1977.
Gurung C B, Yamaguchi H, Yukino T. Identification and characterization of galloping of tsurugatest line based on multi-channel modal analysis of field data[J]. Journal of Wind Engineering & Industrial Aerodynamics,2003,91(7):903-924.
Halsan K A, Havard D G, Fikke S M, et al. Galloping studies at statnett using remote monitoring[C]. CIGRE SC22, WGll meeting, Graz, Austria,1998.
Havard D G. Pohlman J C. Five years'field trials of detuning pendulums for galloping control[J]. IEEE Transactions on Power Apparatus and Systems,1984,103(2):318-327.
Havard D G. Dynamic loads on transmission line structures during galloping[C]. The International Workshop on Atmospheric Icing of Structures, Brno, Czech Republic,2002.
Jing H, Yan B, Zhou S, et al. Parameter study on galloping of iced bundled conductors[C]. Power and Energy Engineering Conference (APPEEC), Chengdu, China,2010.
Hunt J C R, Richard D J W. Overhead line oscillations and the effect of aerodynamic dampers[J]. IEEE Transactions on Power Apparatus and Systems,1969,116(11):1869-1874.
Irvine H M. Cable structures[M]. MIT Press. Cambrige, Mass.1981.
Jamaleddine A, McClure G, Rousselet J, et al. Simulation of ice-shedding on electrical transmission lines using ADINA [J]. Computers and Structures.1993.47(4-5):523-536.
Jones K F. Coupled vertical and horizontal galloping[J]. Journal of Engineering Mechanics. 1992.118(1):92-107.
Kalman T, Farzaneh M, McClure G. Numerical analysis of the dynamic effects of shock-load-induced ice shedding on overhead ground wires [J]. Computers and Structures,2007. 85(7-8):375-384.
Kareem A. Gurley K. Damping in structure:its evaluation and treatment of uncertainly [J]. Journal of Wind Engineering & Industrial Aerodynamics,1996,59:131-157.
Keutgen R, Lilien J L. Benchmark cases for galloping with results obtained from wind tunnel facilities-validation of a finite element model [J]. IEEE Transactions on Power Delivery,2000,15(1): 367-374.
Kimura K, Fujino Y, Inoue M, et al. Unsteady aerodynamic force characteristics of ice-accreted four-conductor bundle transmission lines under large amplitude motion[J]. Journal of Structural Engineering,2000,46(2):1055-1062.
Lam K, Cheung W C, Phenomena of vortex shedding and flow interefrence of three cylinders in different equilateral arrangements[J]. Journal of Fluid Mechanics,1988,196:1-26.
Lee J C, Suppression of transmission line galloping by support compliance design[D]. Tulane University, New Orleans,1987.
Lilien J L, Dubois H, Overhead line vertical galloping on bundle configurations:stability criterions and amplitude prediction[M]. IEE Overhead Line Design and Construction:Theory and Practice (up to150kV),1988.
Lilien J L, Wang J, Chabart O, Pirotte P. Overhead transmission lines design, some mechanical aspects[C].ICPST'94 (International Conference on Power System Technology), Beijing, China, 1994.
Lilien J L, Vinogradov A, Full-scale tests of TDD antigalloping device (torsional damper and detuner)[J]. IEEE Transactions on Power Delivery,2002,17(2):638-643.
Marukawa H, Kato N, Fuji K, et al. Experimental evaluation of aerodynamic damping of tall buildings[J]. Journal of Wind Engineering & Industrial Aerodynamics,1996,59:177-190.
Macdonald J H G, Larose G L. Two-degree-of-freedom inclined cable galloping[J]. Journal of Wind Engineering and Industrial Aerodynamics,2008,96(3):291-326.
Mathur R K. Shah A H, Trainor P G S, et al. Dynamics of a guyed transmission tower system[J]. IEEE Transactions on Power Delivery,1987, PWRD-2(3):908-916.
McConnell K G, Chang C N. A study of the axial-torsional coupling effect on a sagged trasmission Iine[J]. Experimental Mechanics.1986.26(4):324-329.
McDaniel W N. An analysis of galloping electric transmission lines[J]. AIEE Transactions,1960, 113(5):406-412.
Muhammad B W, Takashi I. Muhammad W S. Galloping response prediction of ice-accreted transmission lines[C]. The 4th International Conference on Advances in Wind and Structures(AWAS 08), Jeju, Korea,2008.
Nakamura Y. Galloping of bundled power line conductors[C]. Journal of Sound & Vibration,1980, 73(3):363-377.
Nigol O. Clarke G J. Conductor galloping and control based on torsional mechanism[C]. IEEE Power Engineering Society Winter Meeting, Paper No.C74016-2, New York,1974.
Nigol O, Clarke G J, Havard D G. Torsional stability of bundle conductors[J]. IEEE Transactions on Power Apparatus and Systems,1977,96(5):1666-1674.
Nigol O, Havard D G. Control of torsionally induced galloping with detuning pendulums[C]. IEEE PES Winter Meeting, Paper No A78125-7, New York,1978.
Nigol O. Buchan P G. Conductor galloping, part I:Den Hartog mechanism:part II:torsional mechanism[J]. IEEE Transactions on Power Apparatus and Systems,1981.100(2):699-720.
Otsuki A, Kajita O. Galloping phenomena of overhead transmission lines[[J]. Fujikura Technical Review,1975.7:33-46.
Ozaka A, Kagami J, Takeda K, et al. Observations of galloping on overhead transmission test lines with artificial snow accretion models[C].7th International Workshop on Atmospheric lcing of Structures, Chicoutimi, Canada:300-305.1996.
Parkinson G V Phenomena and modeling of flow-induced vibrations of bluff bodies[J]. Progress in Aerospace Sciences,1989,26(2):169-224.
Park K T, Kim S H, Park H S, et al. The determination of bridge displacement using measured acceleration[J]. Engineering Structures,2005.27(3):371-378.
Pon C J, Havard D G, Edwards A T. Performance of interphase spacers for galloping control[R]. Ontario Hydro Research Division Report No.82-216-K,1982.
Pon C J, Havard D G, Field trials of galloping control devices for bundle conductor lines[R]. Report on R & D Project 133 T 386, Canadian Electrical Association, Montreal,1994.
Price S J, Wake induced flutter of power transmission conductors[J]. Journal of Sound and Vibration, 1975,38(1):125-147.
Rawlins C B, Pohlman J C. On the state of galloping conductor technology[C].4th International Workshop on Atmospheric Icing of Structures, Paris, France,1988.
Richardson A S, Martuccelli J R, Price W S. An Investigation of Galloping Transmission Line Conductors[J]. IEEE Transactions Paper,1963,82:411-431.
Richardson A S. Dynamic analysis of lightly iced conductor galloping in two degrees of freedom[J]. IEE Proceedings C,1981,128(4):211-218.
Richardson A S. A study of galloping conductors on a 230kv transmission line[J]. Electric Power System Research,1991,21(1):43-55.
Savory E, Parke G, Zeinoddini M, et al. Modelling of tornado and microburst-induced wind loading and failure of a lattice transmission tower[J]. Engineering Structures,2001,23(4):365-375.
Schmidt J, Jurdens C, Design of interphase spacers with composite insulators and service experience[C]. CIGRE SC22-WG11 Task Force on Galloping, Rijeka, Yugoslavia,1989.
Shehata A Y, Damatty A A, Savory E. Finite element modeling of transmission line under downburst wind loading[J]. Finite Elements in Analysis and Design,2005,42(1):71-89.
Shimizu M, Ishihara T, Phuc P V. A wind tunnel study on quasi-steady and unsteady forces of ice accreted four bundled and single conductor transmission lines[J]. Denryoku Chuo Kenkyujo Abiko Kenkyujo Hokoku, U03044,2004.
Stumpf P. Investigation of aerodynamic stability for selected inclined cables and conductor cables[D]. University of Manitoba, Winnipeg, Canada,1990.
Tokoro S, Komatsu S, Nakasub M, et al. A study on wake-galloping employing full aeroelastic twin cable model[J]. Journal of Wind Engineering and Industrial Aerodynamics,2000,88:247-261.
Tornquist E L, Becker C, Galloping conductors and a method for studying them[J]. AIEE Transactions Paper,1947,66:1154-61.
Tsujimoto K, Iisaka H, Shimojima H, et al. Report on experimental observation of galloping behaviour in 8-bundled conductors[J]. IEEE Transactions on Power Apparatus and Systems,1983, 102(5):1193-1201.
Tunstall M, Koutselos L T. Further studies of the galloping instability & natural ice accretions on overhead line conductors[C].4th Int. Conf. on Atmospheric Icing of Structures. Paris, France,1988.
Tutar M, Oguz G. Large eddy simulation of wind flow around parallel buildings with varying configurations[J]. Fluid Dynamics Research,2002,31(5-6):289-315.
Van Dyke P, Laneville A. Galloping of a single conductor covered with a d-section on a high voltage overhead test line[C].5th International Colloquium on Bluff Body Aerodynamics and Applications, Ottawa, Canada, paper 377-380.2004.
Veletsos A S, Darbre G R. Dynamic stiffness of parabolic cables[J]. Earthquake Engineering and Structural Dynamics,1983,11(3):367-401.
Wang J W. Large vibrations of overhead electrical lines:a full 3-dof model for galloping studies[D]. Collection des Publications de la Faculte des Sciences Appliquees de l'Universite de Liege,1996, 151:1-227.
Wang J W, Lilien J L. A new theory for torsional stiffness of multi-span bundle overhead transmission Lines[J]. IEEE Transactions on Power Delivery,1998,13(4):1405～1411.
White W N. An analysis of the influence of support stiffness on transmission line galloping amplitudes[D]. Tulane University, New Orleans,1985.
Xiao X H, Wu J. Simulation and effects evaluation of anti-galloping devices for overhead transmission lines[C].4th IEEE Conference on Automation Science and Engineering Key Bridge Marriott, Washington DC, USA,2008
Yu P, Desai Y M, Shah A H, et al.3-degree-of-freedom model for galloping[J]. Journal of Engineering Mechanics-ASCE,1993,119(12):2404-2448.
Yu P, Popplewell N, Shah, A. H, Instability trends of inertially coupled galloping[J]. Journal of Sound and Vibration,1995,183(4):663-678.
Zdravkovich M M. Review of interefrence-iduced oscillations in flow past two circular cylinders in vairous arrangements[J]. Journal of Wind Engineering and Industrial Aerodynamics,1998,28(1-3): 183-200.
Zhang J H, Shi Y H, Liu G X, et al. Simulation of transmission line galloping using finite element method [C]. IEEE 2nd International Conference on Advances in Power System Control, Operation and Management, HongKong,1993.
Zhang Q, Popplewell N, Shah A H. Galloping of bundled conductor[J]. Journal of Sound and Vibration,2000,234(1):115-137.
蔡廷湘.输电线舞动新机理研究[J].中国电力,1998,31(10)：62-66.
陈晓明,邓洪洲,王肇民.大跨越输电线路舞动稳定性研究[J].工程力学,2004,21(1)：56-60.
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[J].同济大学学报,2009.37(10)：1328～1332.
郭应龙,李国兴,尤传永.输电线路舞动[M].中国电力出版社.北京,2002.
郭勇.大跨越输电塔线体系的风振响应及振动控制研究[D]浙江大学.杭州.2006.
何锃,钱天虹.覆冰三分裂导线扭控舞动的分析计算[J].华中科技大学学报,1998,26(10)：16-18.
何锃,赵高煜.分裂导线扭转舞动分析的动力学建模[J].工程力学.2001,18(2)：126-134.
胡杰,郭应龙,恽莉丽.三分裂输电导线舞动的有限元分析与计算[J].水利电力机械,1996.(4)：9-12.
胡松.大跨越输电线路的风振反应分析及振动控制研究[D].同济大学，上海.1999.
黄河.刘建军,李万平.覆冰导线气动力特性的数值模拟[J].工程力学,2003,增刊：201-204.
黄河,刘建军,李万平.覆冰导线绕流的数值模拟[J]于工程技术大学学报,2004,23(6)：767-769.
及荣军.330kV柔性相间复合绝缘间隔棒的研制[J].电网技术,2006,30(12)：112-115.
李万平，杨新祥,张立志.覆冰导线群的静气动力特性[J].空气动力学学报,1995,13(4)：427-435.
李万平.覆冰导线群的动气动力特性[J].空气动力学学报,2000,18(4)：413-419.
李万平,黄河,何锃.特大覆冰导线气动力特性测试[J].华中科技大学学报,2001,29(8)：84-86.
李文蕴.覆冰分裂导线舞动数值模拟方法研究[D].重庆大学,重庆,2009.
刘操兰.大跨越输电线路导线舞动研究[D].重庆大学,重庆,2009.
刘锡良，周颖.风荷载的几种模拟方法[J].工业建筑,2005,35(5)：81-84.
刘小会.架空高压输电线路风偏数值模拟研究[D].重庆大学,重庆,2007.
刘小会,严波,张宏雁,等.覆冰导线舞动非线性数值模拟方法[J].应力数学和力学.2009,30(4)：457-467.
刘振亚.国家电网公司输变电工程典型设计：500kV输电线路分册[M].中国电力出版社，北京,2007.
楼文娟,卢旦,杨毅,等.开孔建筑屋盖风振响应中的气动阻尼识别[J].空气动力学学报,2007,25(4)：419-424.
楼文娟,孙炳楠.风与结构的耦合作用及风振响应分析[J].工程力学,2000，17(5)：16-22.
楼文娟,孙珍茂,吕翼,等.扰流防舞器与气动力阻尼片的防舞效果[J].电网技术,2010,34(2)：200-204.
吕翼.覆冰导线气动力特性的数值模拟研究[D].浙江大学,杭州，2008
马进,丁斌,王勇.导线防舞动相间间隔棒铰链式联结金具的研制[J].华北电力技术,2010,(9)：1-4.
宁研.黄琦.张昌华，曹永兴.架空输电导线覆冰及舞动在线监测技术综述[J].四川电力技术.2009.32(6)：67-71.
孙炳楠.220千伏瓯江第三跨越直线高塔风洞试验报告[R].浙江大学.建筑工程学院,2004.
孙炳楠.220千伏舟山与大陆联网大跨越输电塔风洞试验报告[R].浙江大学，建筑工程学院，2006.
沈国辉.袁光辉,孙炳楠,楼文娟.覆冰脱落对输电塔线体系的动力冲击作用研究[J].工程力学,2010，27(5)：210-217.
孙珍茂.输电线路舞动分析及防舞技术研究[D].浙江大学,杭州.2010.
孙珍茂楼文娟.覆冰输电导线舞动及防舞效果分析[J].振动与冲击,2010,29(5)：141-146.
潘峰.孙炳楠,楼文娟.基于Hilbert Huang变换的大跨屋盖气动阻尼识别[J]浙江大学学报(工学版),2007,41(1)：65-70.
唐校友.线路舞动的低阻尼共振激发机理[J].东北电力大学学报，2006，26(1)：65-70.
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[D].重庆大学,重庆，2008.
王黎明,范钦珊,薛家麒.相间合成绝缘间隔棒后屈曲性态研究[J].清华大学学报(自然科学版),1996,36(6)：70-76.
王黎明,孙保强,张楚岩,等.750KV紧凑型线路相间间隔棒力学分析与计算[J].高压电技术,2009,35(10)：2551-2556.
王丽新,杨文兵,杨新华,等.输电线路舞动的有限元分析[J].华中科技大学学报(城市科学版)，2004.21(1)：76-80.
王昕,楼文娟,徐伟.雷暴冲击风对输电塔的作用特征.华中科技大学学报(城市科学版),2008,25(4)：10-14.
王昕，楼文娟,李宏男,等.雷暴冲击风作用下高耸输电塔风振响应[J].浙江大学学报(工学版).2009，43(8)：1520-1525.
干昕,楼文娟.导线舞动数值解及影响因素分析[J].工程力学.2010，增刊1：290-293.
王昕,楼文娟.多跨输电线路脱冰动力响应研究[J].工程力学,2011,28(1)：226-232.
王之宏.风荷载的模拟研究[J].建筑结构学报,1994,15(1)：44-52.
夏正春.特高压输电线的覆冰舞动及脱冰跳跃研究[D].华中科技大学,武汉,2008.
肖东坡.500kV输电线路风偏故障分析及对策[J].电网技术,2009,33(5)：99-102.
肖正直.晏致涛.李正良,等.八分裂输电导线结冰风洞试验及气动力特性试验[J].电网技术,2009(1)：90-94.
丁俊清.郭应龙,肖晓晖.输电导线舞动的计算机仿真[J].武汉大学学报，2002,35(1)：39-43.
苑吉河,蒋兴良.易辉,等.输电线路导线覆冰的国内外研究现状[J].高电压技术，2004，30(1)：6-9.
张相庭.结构风程[M].中国建筑工业出版社,北京.2006.
张禹芳.我国500kV输电线路风偏闪络分析[J].电网技术,2005，29(7)：65-67.
张子富,默增禄，何有兴,等.特高压直流直线塔断线荷载分析[J].电网技术,2010，34(5)：16-20.
赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究[D].华中科技大学,武汉,2005..
中华人民共和国国家标准.建筑结构荷载规范(2006)版GB50009-2001[S].中国建筑工业山版社,北京,2006.
周凌远,李乔.基于 UL 法的 CR 列式空间梁几何非线性分析[J].西南交通大学学报，2006,41(6)：690-695.
朱宽军,刘超群,任西春.架空输电线路舞动时导线动态张力分析[J].中国电力,2005,38(10)：40-44,
朱宽军,刘彬.架空输电线路分裂导线扭转刚度的计算[J].电网技术,2010，34(3)：210-214.