大跨越高压输电线路非线性舞动理论研究
|
摘要
高压输电线舞动会给电力设施造成巨大灾害,但是由于舞动的复杂性,人们对舞动机理还没有完全认识清楚,因此很难在实践中对症下药做好防治工作。为了保障电网的安全可靠运行,必须对输电线舞动现象进行更深入的研究。
本文在总结归纳前人研究的基础上,首要任务是尝试建立一套研究舞动理论的完整系统方法,各个章节都围绕此问题展开。
本文首先研究输电线的静力特性,这包括两个方面:输电线初始平衡构形分析和输电线静态响应分析。本文提出将索结构的找形方法用于确定输电线路的初始平衡形状,对精确有限单元法进行了补充和推广,使之适用于更复杂载荷情形和多跨输电线的找形分析。在确定了输电线的初始平衡构形和张力后,本文采用非线性有限单元法计算输电线在气动力作用下的静态响应,首先运用虚功原理推导出全Lagrange格式的非线性索单元的一般表达式,然后在此基础上给出一种具有转动自由度的五结点空间索单元的具体表达格式,该索单元不仅适用于分析一般索结构,而且适用于舞动的研究。本文还对用于输电线找形的有限元方法和用于输电线静态响应分析的有限元方法进行了比较。通过算例,证实了提出的单元和算法的正确性和可靠性。
本文深入研究了输电线舞动有限元模型。详细推导了三自由度舞动模型的位移关系,给出了舞动有限元方程的建立方法。对于建立的非线性舞动方程,首先分析传统时间积分算法无法对其求解的原因,然后在此基础上给出一种改进的时间积分算法,并对该算法的稳定性进行研究,得出了稳定性条件。除了改进算法,本文通过分析舞动有限元方程的特殊性,还提出将Runge-Kutta法用于该方程的求解,并给出了具体的求解步骤。由于用改进算法或Runge-Kutta法直接求解原方程计算量较大、且过程较复杂,因此本文在分析输电线舞动特点的基础上,采用振型叠加法将舞动方程转换到振型空间中求解。运用建立的有限元模型和给出的非线性舞动方程求解算法对某一实际输电线路进行了自由振动和舞动分析计算,计算结果与观测数据吻合较好。
本文深入研究了输电线舞动振子模型。给出了建立振子模型的一般方法,并统一采用无量纲方程表达振子模型。采用相对风速的精确表达式重新研究了单自由度舞动振子模型,给出了起舞的临界风速和舞动振幅的解析表达式,对舞动周期解的稳定性进行了分析,并对该模型与另两种简化模型进行了比较,指出采用单自由度振子模型分析输电线舞动时,系统阻尼不可忽略,而相对风速可以采用近似表达式而基本不影响求解精度。提出了一种新的考虑垂向振动和横向摆动耦合的二自由度振子模型,通过对该模型的分析得出结论,横向摆动对引起输电线舞动起重要作用,同时指出气动力系数格式中的常数项不仅影响输电线的静构形,也会对舞动产生影响。分别研究了垂向振动和轴向扭转耦合二自由度无偏心振子模型和偏心振子模型,得出了它们的解析解,并在此基础上研究舞动方程的非线性局部性态,同时用数值方法对解析解进行了验证。
对研究舞动的振子模型和有限元模型进行了比较,指出了各自的优缺点和适用范围。
本文首次对输电线舞动的全局性态进行了研究。采用普通胞映射法和Poincare型胞映射法分别对单自由度舞动振子模型和二自由度无偏心舞动振子模型进行了分析计算,验证了单自由度振子模型舞动周期解的全局稳定性,并对二自由度无偏心振子模型存在的多个稳定周期解(舞动)进行了识别、划分了各自的吸引域,还清晰的给出了该模型存在的一个奇怪吸引子。研究结果深化了对舞动机理的认识,并为输电线舞动的防治提供了理论依据。
Galloping of power transmission lines can lead to severe disruptions in the electrical power supply. But because of the complexity of the galloping, its mechanism hasn’t been understood clearly. So it’s difficult to prevent and cure the galloping in practice. In order to guarantee the safety and reliability of electrical network, the galloping phenomenon of power transmission lines must be studied seriously.
In this dissertation, the studies on nonlinear galloping theory for long conductors of power transmission lines are described. With the objective to develop a complete set of methods for galloping research, this project consists of a few tasks: static analysis of power transmission lines, galloping finite element modeling, development of galloping oscillator model and studies on global behaviors of nonlinear galloping.
The static analysis includes tow aspect: form-finding analysis and static response analysis. In this dissertation, the method for form-finding of cables is applied to compute the initial equilibrium state of power transmission lines. The exact element method is developed and expanded, so it can be used for analyzing more complex loading cases and for the form-finding analysis of multi-span power transmission lines. After determining the initial equilibrium state and tension of power transmission lines, a nonlinear finite element method is applied to compute the static response of power transmission lines under aerodynamic forces. The general expression of Lagrange nonlinear cable element is established firstly by using virtual work principle. And then occording to the properties of the iced cable, a 5-node cable element having rotational degree of freedom is derived. The difference between the exact element method and the nonlinear finite element method is also discussed in this thesis. The correctness and reliability of the element and the arithmetic proposed in this chapter are approved by several examples.
The displacement relationship of a three-degree-of-freedom model for galloping is derived and the general method for establishing galloping finite element model is provided. For the nonlinear galloping equations, the limitations of the traditional time integral scheme are given first. An improved time integral scheme is then introduced with fine details. The stability of the improved scheme is also studied and the stability condition is given. Except for the improved scheme, the Runge-Kutta method is also introduced to solve the galloping equations, and the detailed steps are given. The mode superposition method is used to overcome the difficulty brought by geometric nonlinear. The finite element model of an actual power transmission line is established. Using this model, the free oscillation analysis and galloping analysis of the power transmission line are performed. The results match well with the experimental findings.
Single-degree-of-freedom and two-degree-of-freedom oscillator models are studied. In this study, dimensionless form is used to express each oscillator model. The single-degree-of-freedom oscillator model is studied by using the exact expression of relative wind velocity. The analytical expressions of the critical wind velocity and the galloping amplitude are given and the stability of the periodic solution is also studied. By comparison the model proposed in this dissertation with other tow simplified models, conclusions can be drawn that the system damp can’t be ignored, but the relative wind velocity can be expressed by approximate formula. A new two-degree-of-freedom oscillator model that couples with the lateral and plunge vibrations is established. By analyzing this model, conclusions can be drawn that lateral vibration plays an important role in galloping and the constant items of aerodynamic coefficients not only affect the initial equilibrium of power transmission lines but also affect galloping. The non-eccentricity and eccentricity two-degree-of-freedom oscillator models are studied respectively and their analytical solutions are given. The local behaviors of nonlinear galloping equations are also studied. Moreover, a numerical solution is used for verifying the analytical solution.
By comparing the galloping finite element model and the galloping oscillator model, the advantages, the disadvantages and the scope of application for each model are found.
This study on the nonlinear global behavior of galloping equations is carried out for the first time. The single-degree-of-freedom and non-eccentricity two-degree-of-freedom oscillator models are studied respectively by using cell mapping method and the Poincare cell mapping method. The global stability of the periodic solution of single-degree-of-freedom oscillator model is verified. The stable periodic solutions of non-eccentricity oscillator model are recognized and their domains of attraction in a determined state space are presented. Moreover, a strange attractor of this model is given clearly. The results do not only deepen the understanding of galloping mechanism, but also provide a theoretical basis for preventing and curing power transmission line galloping.
本文在总结归纳前人研究的基础上,首要任务是尝试建立一套研究舞动理论的完整系统方法,各个章节都围绕此问题展开。
本文首先研究输电线的静力特性,这包括两个方面:输电线初始平衡构形分析和输电线静态响应分析。本文提出将索结构的找形方法用于确定输电线路的初始平衡形状,对精确有限单元法进行了补充和推广,使之适用于更复杂载荷情形和多跨输电线的找形分析。在确定了输电线的初始平衡构形和张力后,本文采用非线性有限单元法计算输电线在气动力作用下的静态响应,首先运用虚功原理推导出全Lagrange格式的非线性索单元的一般表达式,然后在此基础上给出一种具有转动自由度的五结点空间索单元的具体表达格式,该索单元不仅适用于分析一般索结构,而且适用于舞动的研究。本文还对用于输电线找形的有限元方法和用于输电线静态响应分析的有限元方法进行了比较。通过算例,证实了提出的单元和算法的正确性和可靠性。
本文深入研究了输电线舞动有限元模型。详细推导了三自由度舞动模型的位移关系,给出了舞动有限元方程的建立方法。对于建立的非线性舞动方程,首先分析传统时间积分算法无法对其求解的原因,然后在此基础上给出一种改进的时间积分算法,并对该算法的稳定性进行研究,得出了稳定性条件。除了改进算法,本文通过分析舞动有限元方程的特殊性,还提出将Runge-Kutta法用于该方程的求解,并给出了具体的求解步骤。由于用改进算法或Runge-Kutta法直接求解原方程计算量较大、且过程较复杂,因此本文在分析输电线舞动特点的基础上,采用振型叠加法将舞动方程转换到振型空间中求解。运用建立的有限元模型和给出的非线性舞动方程求解算法对某一实际输电线路进行了自由振动和舞动分析计算,计算结果与观测数据吻合较好。
本文深入研究了输电线舞动振子模型。给出了建立振子模型的一般方法,并统一采用无量纲方程表达振子模型。采用相对风速的精确表达式重新研究了单自由度舞动振子模型,给出了起舞的临界风速和舞动振幅的解析表达式,对舞动周期解的稳定性进行了分析,并对该模型与另两种简化模型进行了比较,指出采用单自由度振子模型分析输电线舞动时,系统阻尼不可忽略,而相对风速可以采用近似表达式而基本不影响求解精度。提出了一种新的考虑垂向振动和横向摆动耦合的二自由度振子模型,通过对该模型的分析得出结论,横向摆动对引起输电线舞动起重要作用,同时指出气动力系数格式中的常数项不仅影响输电线的静构形,也会对舞动产生影响。分别研究了垂向振动和轴向扭转耦合二自由度无偏心振子模型和偏心振子模型,得出了它们的解析解,并在此基础上研究舞动方程的非线性局部性态,同时用数值方法对解析解进行了验证。
对研究舞动的振子模型和有限元模型进行了比较,指出了各自的优缺点和适用范围。
本文首次对输电线舞动的全局性态进行了研究。采用普通胞映射法和Poincare型胞映射法分别对单自由度舞动振子模型和二自由度无偏心舞动振子模型进行了分析计算,验证了单自由度振子模型舞动周期解的全局稳定性,并对二自由度无偏心振子模型存在的多个稳定周期解(舞动)进行了识别、划分了各自的吸引域,还清晰的给出了该模型存在的一个奇怪吸引子。研究结果深化了对舞动机理的认识,并为输电线舞动的防治提供了理论依据。
Galloping of power transmission lines can lead to severe disruptions in the electrical power supply. But because of the complexity of the galloping, its mechanism hasn’t been understood clearly. So it’s difficult to prevent and cure the galloping in practice. In order to guarantee the safety and reliability of electrical network, the galloping phenomenon of power transmission lines must be studied seriously.
In this dissertation, the studies on nonlinear galloping theory for long conductors of power transmission lines are described. With the objective to develop a complete set of methods for galloping research, this project consists of a few tasks: static analysis of power transmission lines, galloping finite element modeling, development of galloping oscillator model and studies on global behaviors of nonlinear galloping.
The static analysis includes tow aspect: form-finding analysis and static response analysis. In this dissertation, the method for form-finding of cables is applied to compute the initial equilibrium state of power transmission lines. The exact element method is developed and expanded, so it can be used for analyzing more complex loading cases and for the form-finding analysis of multi-span power transmission lines. After determining the initial equilibrium state and tension of power transmission lines, a nonlinear finite element method is applied to compute the static response of power transmission lines under aerodynamic forces. The general expression of Lagrange nonlinear cable element is established firstly by using virtual work principle. And then occording to the properties of the iced cable, a 5-node cable element having rotational degree of freedom is derived. The difference between the exact element method and the nonlinear finite element method is also discussed in this thesis. The correctness and reliability of the element and the arithmetic proposed in this chapter are approved by several examples.
The displacement relationship of a three-degree-of-freedom model for galloping is derived and the general method for establishing galloping finite element model is provided. For the nonlinear galloping equations, the limitations of the traditional time integral scheme are given first. An improved time integral scheme is then introduced with fine details. The stability of the improved scheme is also studied and the stability condition is given. Except for the improved scheme, the Runge-Kutta method is also introduced to solve the galloping equations, and the detailed steps are given. The mode superposition method is used to overcome the difficulty brought by geometric nonlinear. The finite element model of an actual power transmission line is established. Using this model, the free oscillation analysis and galloping analysis of the power transmission line are performed. The results match well with the experimental findings.
Single-degree-of-freedom and two-degree-of-freedom oscillator models are studied. In this study, dimensionless form is used to express each oscillator model. The single-degree-of-freedom oscillator model is studied by using the exact expression of relative wind velocity. The analytical expressions of the critical wind velocity and the galloping amplitude are given and the stability of the periodic solution is also studied. By comparison the model proposed in this dissertation with other tow simplified models, conclusions can be drawn that the system damp can’t be ignored, but the relative wind velocity can be expressed by approximate formula. A new two-degree-of-freedom oscillator model that couples with the lateral and plunge vibrations is established. By analyzing this model, conclusions can be drawn that lateral vibration plays an important role in galloping and the constant items of aerodynamic coefficients not only affect the initial equilibrium of power transmission lines but also affect galloping. The non-eccentricity and eccentricity two-degree-of-freedom oscillator models are studied respectively and their analytical solutions are given. The local behaviors of nonlinear galloping equations are also studied. Moreover, a numerical solution is used for verifying the analytical solution.
By comparing the galloping finite element model and the galloping oscillator model, the advantages, the disadvantages and the scope of application for each model are found.
This study on the nonlinear global behavior of galloping equations is carried out for the first time. The single-degree-of-freedom and non-eccentricity two-degree-of-freedom oscillator models are studied respectively by using cell mapping method and the Poincare cell mapping method. The global stability of the periodic solution of single-degree-of-freedom oscillator model is verified. The stable periodic solutions of non-eccentricity oscillator model are recognized and their domains of attraction in a determined state space are presented. Moreover, a strange attractor of this model is given clearly. The results do not only deepen the understanding of galloping mechanism, but also provide a theoretical basis for preventing and curing power transmission line galloping.
引文
[1]陈晓明.大跨越输电线舞动及其控制研究.同济大学: [博士学位论文], 2002
[2]郭应龙,李国兴,尤传永.输电线路舞动.北京:中国电力出版社, 2003
[3]张兴旺.架空线路的振动分析及防振措施综述.南昌水专学报, 1994. 13(1): 51-55
[4]刘世新.导线舞动的起因分析与预防.东北电力技术, 1996(2): 36-38
[5]巫世晶,向农.神经网络在输电导线舞动监测诊断系统中的应用.华北电力技术, 1998(9): 1-4
[6]张忠河,王藏柱.舞动研究现状及发展趋势.电力情报, 1998(4): 6-8
[7]黄志明.我国超高压输电线路的建设和发展.中国电力, 1996, 29(12): 9-13
[8]黄志明.输电线路建设与展望.中国电力, 1999, 32(10): 34-37
[9]中岛立生.输电技术的发展现状和展望.国际电力, 1998(3): 38-44
[10] A. S. Richardson. Dynamic Analysis of Lightly Iced Conductor Galloping in 2 Degrees of Freedom. IEE Proceedings-c Generation Transmission and Distribution, 1981, 128(4): 211-218
[11]黄经亚.电力线路导线舞动与防护.湖北省电力工业局(资料), 1993
[12]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, 28(5): 506-509
[13]刘延柱,陈立群.非线性振动.北京:高等教育出版社, 2001
[14] M. I. Kazakevich, A. G. Vasilenko. Closed Analytical Solution for Galloping Aeroelastic Self-oscillations. Journal of Wind Engineering and industrial Aerodynamics, 1996, 65(1-3): 353-360
[15] O. Nigol, P. G. Buchan. Conductor Galloping. 1. Den Hartog Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2): 699-707
[16] O. Nigol, P. G. Buchan. Conductor Galloping. 2. Torsional Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2): 708-720
[17] P. Yu, Y. M. Desai, A. H. Shah et al. 3-degree-of-freedom Model for Galloping. 1. Formulation. Journal of Engineering Mechanics-ASCE, 1993, 119(12): 2404-2425
[18] P. Yu, Y. M. Desai, N. Popplewell et al. 3-degree-of-freedom Model for Galloping. 2. Solutions. Journal of Engineering Mechanics-ASCE, 1993, 119(12): 2426-2448
[19] Y. M. Desai, P. Yu, N. Popplewell et al. Finite-element Modeling of Transmission-line Galloping. Computers & Structures, 1995, 57(3): 407-420
[20] Y. M. Desai, P. Yu, A. H. Shah et al. Perturbation-based Finite Element Analyses of Transmission Line Galloping. Journal of Sound and Vibration, 1996, 191(4): 469-489
[21] Q. Zhang, N. Popplewell, A. H. Shah. Galloping of Bundle Conductor. Journal of Sound and Vibration, 2000, 234(1): 115-134
[22] W. N. McDaniel. An analysis of galloping electric transmission line. Trans. IEEE Power Appl. Sys., Aug. 1960: 406-414
[23] K. F. Jones. Coupled vertical and horizontal galloping. J. Engrg. Mech., ASCE, 118(1): 92-107
[24] R. D. Blevins, W. D. Iwan. The Galloping Response of a 2-degree-of-freedom system. Journal of Applied Mechanics-ASME, 1974, 41: 1113-1118
[25] Y. M. Desai, A. H. Shah, N. Popplewell. Galloping Analysis for 2-degree-of-freedom Oscillator. Journal of Engineering Mechanics-ASCE, 1990, 116(12): 2583-2602
[26] P. Yu, A. H. Shah, N. Popplewell. Inertially Coupled Galloping of Iced Conductors. Journal of Applied Mechanics-transactions of the ASME, 1992, 59(1): 140-145
[27] G. S. Byun, R. I. Egbert. 2-degree-of-freedom Analysis of Power-line Galloping by Describing Function Methods. Electric Power Systems Research, 1991, 21(3): 187-193
[28] T. I. Haaker, Van der Burgh Ahp. Rotational Galloping of Two Coupled Oscillators. Meccanica, 1998, 33(3): 219-227
[29] T. I. Haaker, B. W. Vanoudheusden. One-degree-of-freedom Rotational Galloping Under strong Wind Conditions. International Journal of Non-linear Mechanics, 1997, 32(5): 803-814
[30] P. McComber, A. Paradis. A Cable Galloping Model for Thin Ice Accretions. Atmospheric Research, 1998, 46(1998): 13-25
[31]赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究.华中科技大学: [博士学位论文], 2005
[32]何锃,赵高煜,李上明.大跨越分裂导线的静力求解.中国电机工程学报, 2001, 21(11): 34-37
[33]何锃,黄伟,赵高煜.基于一种新单元的分裂导线静力响应有限元求解.高电压技术, 2002, 28(1): 1-4
[34]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, 18(2): 126-134
[35]何锃,赵高煜.安装防振锤的分裂导线自由振动的有限元计算.工程力学, 2003, 20(1): 101-105
[36]赵高煜,何锃.安装失谐摆的大跨越分裂导线自由振动计算.中国电机工程学报, 2003, 23(2): 63-66
[37] Zhao Gaoyu, He Zeng. Modes Computation and Analysis for Long Multi-span Bundle Conductors of Power Transmission Lines with Galloping Control Devices. Acta Mechanica Solida Sinica, 2002, 15(4): 350-357
[38]王丽新,杨文兵,杨新华等.输电线路舞动的有限元分析.华中科技大学学报(城市科学版), 2004, 21(1): 76-80
[39]杨新华,王丽新,王乘等.考虑多种影响因素的导线舞动三维有限元分析.动力学与控制学报, 2004, 2(4): 84-89
[40]刘文杰.架空输电导线舞动动态仿真与扰流防舞器的研究.武汉大学: [硕士学位论文], 2005
[41]蔡廷湘.输电线舞动新机理研究.中国电力, 1998, 31(10): 62-66
[42]范钦珊,官飞,赵坤民等.覆冰导线舞动的机理分析及动态模拟.清华大学学报(自然科学版), 1995, 35(2): 34-40
[43]徐中年.大气湍流对输电线舞动的影响.中国电力, 1995(11): 50-53
[44]李万平,杨新祥,张立志.覆冰导线群的静气动力特性.空气动力学报, 1995, 13(4): 427-434
[45]李万平.覆冰导线群的动态气动力特性.空气动力学报, 2000, 18(4): 413-420
[46]李万平,黄河,何锃.特大覆冰导线气动力特性测试.华中科技大学学报, 2001, 29(8): 84-86
[47]李国兴,杨肇成,李奠川等.中山口大跨越舞动的防治与研究.中国电力, 1995(5): 56-61
[48]何锃,李国兴.中山口大跨越导线舞动的分析计算. High Voltage Engineering, 1997, 23(4): 12-14
[49]王海期,罗晋华,黄飞等.中山口大跨越分裂导线固有参数测量和防舞机理分析.超高压输变电运行技术,湖北省电力工业局超高压输变电局编, 1990
[50]何锃,罗晋华,王海期.中山口大跨越覆冰导线舞动分析、计算报告.武汉:华中理工大学力学系, 1994
[51]高压架空输电线路舞动建模及计算机仿真.华北电力大学: [硕士学位论文], 2003
[52]黄经亚.架空送电线路导线舞动的分析研究.中国电力, 1995(2): 21-26
[53]丁明,戴仁昶,洪梅等.影响输电网可靠性的气候条件模拟.电力系统自动化, 1997, 21(1): 18-20
[54] M. A. Baenziger, W. D. James, B. Wouters et al. Dynamic Loads on Transmission-line Structures Due to Galloping Conductors. IEEE Transactions on Power Delivery, 1994, 9(1): 40-47
[55] H. B. White, M. A. Baenziger, W. D. James et al. Dynamic Loads on Transmission-line Structures Due to Galloping Conductors– Discussion. IEEE Transactions on Power Delivery, 1994, 9(1): 48-49
[56] K. C. S. Kwok, W. H. Melbourne. Freestream Turbulence Effects on Galloping. Journal of the Engineering Mechanics Division-ASCE, 1980, 106(2): 273-288
[57] M. Yamaoka, J. Hasegawa. Fundamental Characteristics of Overhead Transmission Line Galloping Determined by Simulating Calculation Using Equivalent Single-conductor Method. Electrical Engineering in Japan, 1995, 115(7): 11-28
[58]邵德民,张维,何珍珍等.利用灰色聚类分析方法进行安徽省导线舞动气象区划.中国电力, 1996, 29(7): 39-42
[59]谭晓,明安特.重冰区500kV大跨越导线选取.电力建设, 2000(5): 16-18
[60]李军.湖南电网三相短路融冰利弊分析.湖南电力, 1998(4): 20-24
[61]蒋兴良,张丽华.输电线路除冰防冰技术综述.高电压技术, 1997, 23(1):73-76
[62]吴盛麟.对我国输电线路工作的几点建议.电网技术, 1994, 18(2): 49-53
[63]龙小乐,鲍务均,郭应龙等.输电导线覆冰研究.武汉水利电力大学学报, 1996, 29(5): 102-107
[64] R. Keutgen, J. L. Lilien. A New Damper to Solve Galloping on Bundled Lines. Theoretical Background, Laboratory and Field Results. IEEE Transactions on Power Delivery, 1998, 13(1): 260-265
[65] O. Nigol, D. G. Havard. Control of Torsionally Induced Conductor Galloping With Detuning Pendulums. IEEE Transactions on Power Apparatus and Systems, 1978, 97(4): 1008-1008
[66] D. G. Havard. Detuning for Controlling Galloping of Single Conductor Transmission-lines. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 12-13
[67] D. G. Havard. Detuning Pendulums for Controlling Galloping of Bundle Conductor Transmission-lines. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 13-13
[68] D. G. Havard, J. C. Pohlman. Field Trials of Detuning Pendulums for Controlling Galloping of Single and Bundle Conductors. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 12-12
[69]樊社新.间隔棒对舞动的影响.电力建设, 1997(8): 16-17
[70]恽俐丽,郭应龙,王建坤.扰流器防舞机理的理论研究.武汉水利电力大学学报, 1996, 29(1): 38-43
[71]王黎明,范钦珊,薛家麒等.相间合成绝缘间隔棒大挠度屈曲研究及应用.清华大学学报(自然科学版), 1997, 37(1): 9-12
[72] M. D. Rowbottom, J. G. Allnutt. Mechanical Dampers for the Control of Full Span Galloping Oscillations. IEE Proceedings-c Generation Transmission and Distribution, 1982, 129(3): 123-135
[73] M. D. Rowbottom. The Optimization of Mechanical Dampers to Control Self-excited Galloping Oscillations. Journal of Sound and Vibration, 1981, 75(4): 559-576
[74] Y. M. Desai, A. H. Shah, N. Popplewell. Galloping Analysis for 2-degree- of-freedom Oscillator. Journal of Engineering Mechanics-ASCE, 1990, 116(12): 2583-2602
[75] M. D. Rowbottom. Effect of an Added Mass on the Galloping of an Overhead Line. Journal of Sound and Vibration, 1979, 63(2): 310-313
[76] A. S. Richardson, S. A. Fox. A Practical Approach to the Prevention of Galloping in Figure-8 cables. IEEE Transactions on Power Apparatus and Systems, 1980, 99(2): 823-828
[77] S. K. Biswas, H. Riaz, N. U. Ahmed. Modal Dynamics and Stabilizer Design for Galloping Transmission-lines. Electric Power Systems Research, 1987, 12(3): 175-182
[78] H. Wang, A. R. Elcrat, R. I. Egbert. Modeling and Boundary Control of Conductor Galloping. Journal of Sound and Vibration, 1993, 161(2): 301-315
[79]段树乔.悬挂重锤的悬垂式绝缘子串的振动.中国电力, 1998, 31(2): 25-27
[80]周敬宣,付问君,李艳萍. 500kV大跨越输电线路护线金具的抗磨试验与设计改型.中国电力, 1997, 30(6): 41-43
[81]王黎明,薛家麒,阙维国. 220kV紧凑型线路间隔棒位置及防摆性能的研究.中国电力, 1997, 30(2): 34-37
[82]能源部东北电力设计院.电力工程高压送电线路设计手册[M].北京:水利电力出版社, 1991
[83]袁驷,程大业,叶康生.索结构找形分析的精确单元法.建筑结构学报, 2005, 26(2): 46-51
[84]沈世钊,徐崇宝,赵臣,悬索结构设计.北京:中国建筑工业出版社, 1997
[85]唐建民,何署廷.悬索结构非线性有限元分析.河海大学学报, 1998, 26(6): 45-49
[86] Y. M. Desai, N. Popplewell, A. H. Shah et al, Geometric Nonlinear Static Analysis of Cable Supported Structures, Computers and Structures, 1988; 29(6): 1001-1009
[87] Tang Jianmin, Shen Zuyan, Qian Ruojun. A nonlinear finite element method with five-node curved element for analysis of cable structures. Proceedings of the IASS International Symposium, Italy: Milano, 1995, 2: 929-93
[88] H. Max Irvine. Cable Structures. The MIT Press, Cambridge, Massachusetts, and London, England, 1983
[89]向阳,沈世钊.悬索结构的初始形状确定分析.哈尔滨建筑大学学报, 1997, 30(3): 29-33
[90] H. K. Schek. The Force Densities Method for Form-finding and Computation of General Nets. Computer Methods in Applied Mechanics Engineering, 1974, 3(1): 115-134
[91] M. R. Barnes. Form-finding and Analysis of Prestressed Nets and Membranes. Computers and Structures, 1988, 30(3): 685-695
[92]王勖成.有限单元法.北京:清华大学出版社, 2003
[93] K. E. Gawronski. Nonlinear Galloping of Bundle-conductor Transmission Lines. Ph. D. Thesis, Clarkson College of Technology, 1977
[94]关治,陆金甫.数值分析基础.北京:高等教育出版社, 1998
[95]钟万勰.结构动力方程的精细时程积分法.大连理工大学学报, 1994, 34(2): 131-136
[96] A. T. Edwars, A. Madeyski. Progress Report on the Investigation of Galloping of Transmission Line Conductors. AIEE Trans. Distrib. Winter Meeting, New York, 1956
[97] J. W. Wang, J. L. Lilien. A New Theory for Torsional Stiffness of Multi-span Bundle Overhead Transmission Lines. IEEE Transactions on Power Delivery, 1998, 13(4): 1405-1411
[98]赵跃宇,王连华,刘伟长等.悬索非线性动力学中的直接法与离散法.力学学报, 2005, 37(3): 329-338
[99]刘秉正,彭建华.非线性动力学.北京:高等教育出版社, 2004
[100] Wind-induced Conductor Motion. Transmission line reference book, EPRI, California, 1979
[101] C. S. Hsu. Cell-to-Cell Mapping. Method of Global Analysis for Nonlinear System. New York: Springer-Verlag, 1987
[102] C. S. Hsu. Global Analysis by Cell Mapping. International Journal of Bifurcation and Chaos, 1992, 2(4): 727-771
[103]刘信安,王宗笠,蒋启华等.胞映射基本理论与算法实现.计算机与应用化学, 2000, 17(5): 427-435
[104]朱因远,周纪卿.非线性振动和运动稳定性.西安:西安交通大学出版社, 1992
[105] J. Levitas, T. Weller, J. Singer. Poincare-like Simple Cell Mapping for Nonlinear Dynamic Systems. Journal of Sound and Vibration, 1994, 176(10): 641-662
[106]龚璞林,徐建学.用广义胞映射研究参数不确定的所吸引子共存系统.应用数学和力学, 1998, 19(12): 1087-1094
[107]刘恒,虞烈,谢友柏等. Poincare型胞映射分析方法及其应用.力学学报, 1999, 31(1): 91-99
[108]刘梦君,沈允文,董海军.基于插值与点映射相结合的全局分析方法.应用力学学报, 2004, 21(1): 26-29
[2]郭应龙,李国兴,尤传永.输电线路舞动.北京:中国电力出版社, 2003
[3]张兴旺.架空线路的振动分析及防振措施综述.南昌水专学报, 1994. 13(1): 51-55
[4]刘世新.导线舞动的起因分析与预防.东北电力技术, 1996(2): 36-38
[5]巫世晶,向农.神经网络在输电导线舞动监测诊断系统中的应用.华北电力技术, 1998(9): 1-4
[6]张忠河,王藏柱.舞动研究现状及发展趋势.电力情报, 1998(4): 6-8
[7]黄志明.我国超高压输电线路的建设和发展.中国电力, 1996, 29(12): 9-13
[8]黄志明.输电线路建设与展望.中国电力, 1999, 32(10): 34-37
[9]中岛立生.输电技术的发展现状和展望.国际电力, 1998(3): 38-44
[10] A. S. Richardson. Dynamic Analysis of Lightly Iced Conductor Galloping in 2 Degrees of Freedom. IEE Proceedings-c Generation Transmission and Distribution, 1981, 128(4): 211-218
[11]黄经亚.电力线路导线舞动与防护.湖北省电力工业局(资料), 1993
[12]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, 28(5): 506-509
[13]刘延柱,陈立群.非线性振动.北京:高等教育出版社, 2001
[14] M. I. Kazakevich, A. G. Vasilenko. Closed Analytical Solution for Galloping Aeroelastic Self-oscillations. Journal of Wind Engineering and industrial Aerodynamics, 1996, 65(1-3): 353-360
[15] O. Nigol, P. G. Buchan. Conductor Galloping. 1. Den Hartog Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2): 699-707
[16] O. Nigol, P. G. Buchan. Conductor Galloping. 2. Torsional Mechanism. IEEE Transactions on Power Apparatus and Systems, 1981, 100(2): 708-720
[17] P. Yu, Y. M. Desai, A. H. Shah et al. 3-degree-of-freedom Model for Galloping. 1. Formulation. Journal of Engineering Mechanics-ASCE, 1993, 119(12): 2404-2425
[18] P. Yu, Y. M. Desai, N. Popplewell et al. 3-degree-of-freedom Model for Galloping. 2. Solutions. Journal of Engineering Mechanics-ASCE, 1993, 119(12): 2426-2448
[19] Y. M. Desai, P. Yu, N. Popplewell et al. Finite-element Modeling of Transmission-line Galloping. Computers & Structures, 1995, 57(3): 407-420
[20] Y. M. Desai, P. Yu, A. H. Shah et al. Perturbation-based Finite Element Analyses of Transmission Line Galloping. Journal of Sound and Vibration, 1996, 191(4): 469-489
[21] Q. Zhang, N. Popplewell, A. H. Shah. Galloping of Bundle Conductor. Journal of Sound and Vibration, 2000, 234(1): 115-134
[22] W. N. McDaniel. An analysis of galloping electric transmission line. Trans. IEEE Power Appl. Sys., Aug. 1960: 406-414
[23] K. F. Jones. Coupled vertical and horizontal galloping. J. Engrg. Mech., ASCE, 118(1): 92-107
[24] R. D. Blevins, W. D. Iwan. The Galloping Response of a 2-degree-of-freedom system. Journal of Applied Mechanics-ASME, 1974, 41: 1113-1118
[25] Y. M. Desai, A. H. Shah, N. Popplewell. Galloping Analysis for 2-degree-of-freedom Oscillator. Journal of Engineering Mechanics-ASCE, 1990, 116(12): 2583-2602
[26] P. Yu, A. H. Shah, N. Popplewell. Inertially Coupled Galloping of Iced Conductors. Journal of Applied Mechanics-transactions of the ASME, 1992, 59(1): 140-145
[27] G. S. Byun, R. I. Egbert. 2-degree-of-freedom Analysis of Power-line Galloping by Describing Function Methods. Electric Power Systems Research, 1991, 21(3): 187-193
[28] T. I. Haaker, Van der Burgh Ahp. Rotational Galloping of Two Coupled Oscillators. Meccanica, 1998, 33(3): 219-227
[29] T. I. Haaker, B. W. Vanoudheusden. One-degree-of-freedom Rotational Galloping Under strong Wind Conditions. International Journal of Non-linear Mechanics, 1997, 32(5): 803-814
[30] P. McComber, A. Paradis. A Cable Galloping Model for Thin Ice Accretions. Atmospheric Research, 1998, 46(1998): 13-25
[31]赵高煜.大跨越高压输电线路分裂导线覆冰舞动的研究.华中科技大学: [博士学位论文], 2005
[32]何锃,赵高煜,李上明.大跨越分裂导线的静力求解.中国电机工程学报, 2001, 21(11): 34-37
[33]何锃,黄伟,赵高煜.基于一种新单元的分裂导线静力响应有限元求解.高电压技术, 2002, 28(1): 1-4
[34]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, 18(2): 126-134
[35]何锃,赵高煜.安装防振锤的分裂导线自由振动的有限元计算.工程力学, 2003, 20(1): 101-105
[36]赵高煜,何锃.安装失谐摆的大跨越分裂导线自由振动计算.中国电机工程学报, 2003, 23(2): 63-66
[37] Zhao Gaoyu, He Zeng. Modes Computation and Analysis for Long Multi-span Bundle Conductors of Power Transmission Lines with Galloping Control Devices. Acta Mechanica Solida Sinica, 2002, 15(4): 350-357
[38]王丽新,杨文兵,杨新华等.输电线路舞动的有限元分析.华中科技大学学报(城市科学版), 2004, 21(1): 76-80
[39]杨新华,王丽新,王乘等.考虑多种影响因素的导线舞动三维有限元分析.动力学与控制学报, 2004, 2(4): 84-89
[40]刘文杰.架空输电导线舞动动态仿真与扰流防舞器的研究.武汉大学: [硕士学位论文], 2005
[41]蔡廷湘.输电线舞动新机理研究.中国电力, 1998, 31(10): 62-66
[42]范钦珊,官飞,赵坤民等.覆冰导线舞动的机理分析及动态模拟.清华大学学报(自然科学版), 1995, 35(2): 34-40
[43]徐中年.大气湍流对输电线舞动的影响.中国电力, 1995(11): 50-53
[44]李万平,杨新祥,张立志.覆冰导线群的静气动力特性.空气动力学报, 1995, 13(4): 427-434
[45]李万平.覆冰导线群的动态气动力特性.空气动力学报, 2000, 18(4): 413-420
[46]李万平,黄河,何锃.特大覆冰导线气动力特性测试.华中科技大学学报, 2001, 29(8): 84-86
[47]李国兴,杨肇成,李奠川等.中山口大跨越舞动的防治与研究.中国电力, 1995(5): 56-61
[48]何锃,李国兴.中山口大跨越导线舞动的分析计算. High Voltage Engineering, 1997, 23(4): 12-14
[49]王海期,罗晋华,黄飞等.中山口大跨越分裂导线固有参数测量和防舞机理分析.超高压输变电运行技术,湖北省电力工业局超高压输变电局编, 1990
[50]何锃,罗晋华,王海期.中山口大跨越覆冰导线舞动分析、计算报告.武汉:华中理工大学力学系, 1994
[51]高压架空输电线路舞动建模及计算机仿真.华北电力大学: [硕士学位论文], 2003
[52]黄经亚.架空送电线路导线舞动的分析研究.中国电力, 1995(2): 21-26
[53]丁明,戴仁昶,洪梅等.影响输电网可靠性的气候条件模拟.电力系统自动化, 1997, 21(1): 18-20
[54] M. A. Baenziger, W. D. James, B. Wouters et al. Dynamic Loads on Transmission-line Structures Due to Galloping Conductors. IEEE Transactions on Power Delivery, 1994, 9(1): 40-47
[55] H. B. White, M. A. Baenziger, W. D. James et al. Dynamic Loads on Transmission-line Structures Due to Galloping Conductors– Discussion. IEEE Transactions on Power Delivery, 1994, 9(1): 48-49
[56] K. C. S. Kwok, W. H. Melbourne. Freestream Turbulence Effects on Galloping. Journal of the Engineering Mechanics Division-ASCE, 1980, 106(2): 273-288
[57] M. Yamaoka, J. Hasegawa. Fundamental Characteristics of Overhead Transmission Line Galloping Determined by Simulating Calculation Using Equivalent Single-conductor Method. Electrical Engineering in Japan, 1995, 115(7): 11-28
[58]邵德民,张维,何珍珍等.利用灰色聚类分析方法进行安徽省导线舞动气象区划.中国电力, 1996, 29(7): 39-42
[59]谭晓,明安特.重冰区500kV大跨越导线选取.电力建设, 2000(5): 16-18
[60]李军.湖南电网三相短路融冰利弊分析.湖南电力, 1998(4): 20-24
[61]蒋兴良,张丽华.输电线路除冰防冰技术综述.高电压技术, 1997, 23(1):73-76
[62]吴盛麟.对我国输电线路工作的几点建议.电网技术, 1994, 18(2): 49-53
[63]龙小乐,鲍务均,郭应龙等.输电导线覆冰研究.武汉水利电力大学学报, 1996, 29(5): 102-107
[64] R. Keutgen, J. L. Lilien. A New Damper to Solve Galloping on Bundled Lines. Theoretical Background, Laboratory and Field Results. IEEE Transactions on Power Delivery, 1998, 13(1): 260-265
[65] O. Nigol, D. G. Havard. Control of Torsionally Induced Conductor Galloping With Detuning Pendulums. IEEE Transactions on Power Apparatus and Systems, 1978, 97(4): 1008-1008
[66] D. G. Havard. Detuning for Controlling Galloping of Single Conductor Transmission-lines. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 12-13
[67] D. G. Havard. Detuning Pendulums for Controlling Galloping of Bundle Conductor Transmission-lines. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 13-13
[68] D. G. Havard, J. C. Pohlman. Field Trials of Detuning Pendulums for Controlling Galloping of Single and Bundle Conductors. IEEE Transactions on Power Apparatus and Systems, 1980, 99(1): 12-12
[69]樊社新.间隔棒对舞动的影响.电力建设, 1997(8): 16-17
[70]恽俐丽,郭应龙,王建坤.扰流器防舞机理的理论研究.武汉水利电力大学学报, 1996, 29(1): 38-43
[71]王黎明,范钦珊,薛家麒等.相间合成绝缘间隔棒大挠度屈曲研究及应用.清华大学学报(自然科学版), 1997, 37(1): 9-12
[72] M. D. Rowbottom, J. G. Allnutt. Mechanical Dampers for the Control of Full Span Galloping Oscillations. IEE Proceedings-c Generation Transmission and Distribution, 1982, 129(3): 123-135
[73] M. D. Rowbottom. The Optimization of Mechanical Dampers to Control Self-excited Galloping Oscillations. Journal of Sound and Vibration, 1981, 75(4): 559-576
[74] Y. M. Desai, A. H. Shah, N. Popplewell. Galloping Analysis for 2-degree- of-freedom Oscillator. Journal of Engineering Mechanics-ASCE, 1990, 116(12): 2583-2602
[75] M. D. Rowbottom. Effect of an Added Mass on the Galloping of an Overhead Line. Journal of Sound and Vibration, 1979, 63(2): 310-313
[76] A. S. Richardson, S. A. Fox. A Practical Approach to the Prevention of Galloping in Figure-8 cables. IEEE Transactions on Power Apparatus and Systems, 1980, 99(2): 823-828
[77] S. K. Biswas, H. Riaz, N. U. Ahmed. Modal Dynamics and Stabilizer Design for Galloping Transmission-lines. Electric Power Systems Research, 1987, 12(3): 175-182
[78] H. Wang, A. R. Elcrat, R. I. Egbert. Modeling and Boundary Control of Conductor Galloping. Journal of Sound and Vibration, 1993, 161(2): 301-315
[79]段树乔.悬挂重锤的悬垂式绝缘子串的振动.中国电力, 1998, 31(2): 25-27
[80]周敬宣,付问君,李艳萍. 500kV大跨越输电线路护线金具的抗磨试验与设计改型.中国电力, 1997, 30(6): 41-43
[81]王黎明,薛家麒,阙维国. 220kV紧凑型线路间隔棒位置及防摆性能的研究.中国电力, 1997, 30(2): 34-37
[82]能源部东北电力设计院.电力工程高压送电线路设计手册[M].北京:水利电力出版社, 1991
[83]袁驷,程大业,叶康生.索结构找形分析的精确单元法.建筑结构学报, 2005, 26(2): 46-51
[84]沈世钊,徐崇宝,赵臣,悬索结构设计.北京:中国建筑工业出版社, 1997
[85]唐建民,何署廷.悬索结构非线性有限元分析.河海大学学报, 1998, 26(6): 45-49
[86] Y. M. Desai, N. Popplewell, A. H. Shah et al, Geometric Nonlinear Static Analysis of Cable Supported Structures, Computers and Structures, 1988; 29(6): 1001-1009
[87] Tang Jianmin, Shen Zuyan, Qian Ruojun. A nonlinear finite element method with five-node curved element for analysis of cable structures. Proceedings of the IASS International Symposium, Italy: Milano, 1995, 2: 929-93
[88] H. Max Irvine. Cable Structures. The MIT Press, Cambridge, Massachusetts, and London, England, 1983
[89]向阳,沈世钊.悬索结构的初始形状确定分析.哈尔滨建筑大学学报, 1997, 30(3): 29-33
[90] H. K. Schek. The Force Densities Method for Form-finding and Computation of General Nets. Computer Methods in Applied Mechanics Engineering, 1974, 3(1): 115-134
[91] M. R. Barnes. Form-finding and Analysis of Prestressed Nets and Membranes. Computers and Structures, 1988, 30(3): 685-695
[92]王勖成.有限单元法.北京:清华大学出版社, 2003
[93] K. E. Gawronski. Nonlinear Galloping of Bundle-conductor Transmission Lines. Ph. D. Thesis, Clarkson College of Technology, 1977
[94]关治,陆金甫.数值分析基础.北京:高等教育出版社, 1998
[95]钟万勰.结构动力方程的精细时程积分法.大连理工大学学报, 1994, 34(2): 131-136
[96] A. T. Edwars, A. Madeyski. Progress Report on the Investigation of Galloping of Transmission Line Conductors. AIEE Trans. Distrib. Winter Meeting, New York, 1956
[97] J. W. Wang, J. L. Lilien. A New Theory for Torsional Stiffness of Multi-span Bundle Overhead Transmission Lines. IEEE Transactions on Power Delivery, 1998, 13(4): 1405-1411
[98]赵跃宇,王连华,刘伟长等.悬索非线性动力学中的直接法与离散法.力学学报, 2005, 37(3): 329-338
[99]刘秉正,彭建华.非线性动力学.北京:高等教育出版社, 2004
[100] Wind-induced Conductor Motion. Transmission line reference book, EPRI, California, 1979
[101] C. S. Hsu. Cell-to-Cell Mapping. Method of Global Analysis for Nonlinear System. New York: Springer-Verlag, 1987
[102] C. S. Hsu. Global Analysis by Cell Mapping. International Journal of Bifurcation and Chaos, 1992, 2(4): 727-771
[103]刘信安,王宗笠,蒋启华等.胞映射基本理论与算法实现.计算机与应用化学, 2000, 17(5): 427-435
[104]朱因远,周纪卿.非线性振动和运动稳定性.西安:西安交通大学出版社, 1992
[105] J. Levitas, T. Weller, J. Singer. Poincare-like Simple Cell Mapping for Nonlinear Dynamic Systems. Journal of Sound and Vibration, 1994, 176(10): 641-662
[106]龚璞林,徐建学.用广义胞映射研究参数不确定的所吸引子共存系统.应用数学和力学, 1998, 19(12): 1087-1094
[107]刘恒,虞烈,谢友柏等. Poincare型胞映射分析方法及其应用.力学学报, 1999, 31(1): 91-99
[108]刘梦君,沈允文,董海军.基于插值与点映射相结合的全局分析方法.应用力学学报, 2004, 21(1): 26-29