大跨越导线动张力计算和模型实验
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摘要
为正确认识塔线耦合力等效应理论基础的导线线端动张力,保障线路安全运行的工程需要,在考虑导线初始垂度和抗拉刚度情况下,建立了导线自由振动的非线性微分方程,用连续化超越函数解法,将导线自由振动曲线形式分为正对称和反对称两类模态分别进行模态分析,得出导线动张力成分仅由在平面内对称模态振动引起。将导线不平衡合力对各阶正对称模态幅值求导后为零,联立后求解,即可得到各阶正对称模态幅值,使叠加后的正对称模态与导线实际振动更逼近。将导线在平面正对称基本振型参数规一化后,推导出了导线线端动张力的近似计算公式。对某实际工程的近似公式计算结果与气动弹性模型实验数据对比分析的一致结论说明了动张力近似公式计算结果准确,导线振动过程中线内动张力与初始张力数量级相同。因此,可得出这样结论,导线在实际振动过程中,线端张力变化很大,尤其导线产生低频大振幅舞动时,应慎重考虑由此引起的导线首先失效隐患。
Considering the original sag and tensile stiffness of the transmission line system,the nonlinear differential equation of the line's free libration is deduced.The line's in-plane free vibration curve shape of two types modes is composed,i.e.the symmetrical mode and the antisymmetric mode,which are gotten by the continuous transcendental equation method,and the model analysis is processed respectively.At the same time,the dynamic tension of the line's end is only produced by the symmetrical in-plane mode.Assumed that the first-order derivative of the imbalance resultant force along the whole line with respect to the limiting value of each symmetrical in-plane vibration mode was zero,the simultaneous equations are formed,then the limiting values are deduced by the equations.The technique insures that the mode superposition was very approached the line's actual libration.Then the simplified formula of line's dynamic tension is constructed,which is gotten by the normalized parameters of the line's symmetrical modal shape when it vibrates freely in plane.At last,the contrast analysis is carried out between the results about one actual works by the proposed method and the data of aero elastic model experiment.The conclusion illuminates that the proposed method is accurate,and the order of magnitude of the line's dynamic tension is the same as the original tension.So the markedly change of tension of the true vibration line should be taken into account,especially the galloping line,otherwise it would induce the latent disaster of the lead firstly.
Considering the original sag and tensile stiffness of the transmission line system,the nonlinear differential equation of the line's free libration is deduced.The line's in-plane free vibration curve shape of two types modes is composed,i.e.the symmetrical mode and the antisymmetric mode,which are gotten by the continuous transcendental equation method,and the model analysis is processed respectively.At the same time,the dynamic tension of the line's end is only produced by the symmetrical in-plane mode.Assumed that the first-order derivative of the imbalance resultant force along the whole line with respect to the limiting value of each symmetrical in-plane vibration mode was zero,the simultaneous equations are formed,then the limiting values are deduced by the equations.The technique insures that the mode superposition was very approached the line's actual libration.Then the simplified formula of line's dynamic tension is constructed,which is gotten by the normalized parameters of the line's symmetrical modal shape when it vibrates freely in plane.At last,the contrast analysis is carried out between the results about one actual works by the proposed method and the data of aero elastic model experiment.The conclusion illuminates that the proposed method is accurate,and the order of magnitude of the line's dynamic tension is the same as the original tension.So the markedly change of tension of the true vibration line should be taken into account,especially the galloping line,otherwise it would induce the latent disaster of the lead firstly.
引文
[1]Liang Shuoguo,Wang Lizheng,Ma Zhenxin.An analysis of wind induced responses dashengguan electrical transmission to-wen-line systemacross the yangtze river[C]∥Wind Engineering into the21st Century,Proceedings of the10th International Conference on Wind Engineering.Copenhagen,Denmark:Pub-lished by Balkema,1999.
[2]梁枢果.输电塔-线体系的气弹模型风洞试验与动力特性、风振响应分析[R].上海:同济大学土木工程防灾国家重点实验室研究报告,2002.
[3]李宏男,王前信.大跨越输电塔体系的动力特性[J].土木工程学报,1997,30(5):28-36.LI Hong-nan,WANG Qian-xin.Dynamic characteristics of long-span transmission lines and their supporting towers[J].China Civil Engineering Journal,1997,30(5):28-36.
[4]Irivine H M,Caughey T K.The linear theory of free vibrations of a suspended cable[C]∥Proceedings of the Royal Society,Se-ries A,Mathematical Physical and Engineering Sciences.Lon-don,England:Published by the Royal Society,1974:299-315.
[5]Irivine H Max.Cable structure[M].Cambridge:The Massa-chusetts Institute of Technology Press,1981.
[6]Luongo A,Rega G,Vestroni F.Planar nonlinear free vibration of an elastic cable[J].Journal of Nonlinear Mechanics,1984,19(1):39-52.
[7]王珂晟,唐国金.架空电线在悬链状态下的非线性振动响应分析[J].振动与冲击,2003,22(2):69-72.WANG Ke-sheng,TANG Guo-jin.Response analysis of nonlin-ear vibration of overhead power line under suspension chain state[J].Journal of Vibration and Shock,2003,22(2):69-72.
[8]梁枢果,朱继华,王力争.大跨越输电塔线体系动力特性分析[J].地震工程与工程振动,2003,23(6):63-69.LI ANG Shu-guo,ZHU Ji-hua,WANG Li-zheng.Analysis of dynamic characters of electrical transmission tower-line system with a big span[J].Earthquake Engineering and Engineering Vibration,2003,23(6):63-69.
[9]郭应龙,李国兴,尤传永.输电线路舞动[M].北京:电力工业出版社,2002.
[10]王少华,蒋兴良,孙才新.输电线路导线舞动的国内外研究现状[J].高电压技术,2005,31(10):11-14.WANG Shao-hua,JI ANG Xing-liang,SUN Cai-xin.Study status of conductor galloping on transmission line[J].High Voltage Engineering,2005,31(10):11-14.
[11]王茂成,吕永丽,邹洪英,等.10kV绝缘导线雷击断线机理分析和防治措施[J].高电压技术,2007,33(1):102-105.WANG Mao-cheng,L Yong-li,ZOU Hong-ying,et al.A-nalysis of lightning-caused break mechanism of10kVinsula-tion-covered conductors and its countermeasures[J].High Voltage Engineering,2007,33(1):102-105.
[12]高电压技术编辑部.风对导线和铁塔的作用力[J].高电压技术,1979,5(3):89-90.
[13]何锃,李国兴.中山口大跨越导线舞动的分析计算[J].高电压技术,1997,23(4):12-14.HE Zeng,LI Guo-xing.Analysis galloping of Zhongshankou large span overheadline[J].High Voltage Engineering,1997,23(4):12-14.
[14]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[J].高电压技术,2002,28(1):1-5.HE Zeng,HUANG Wei,ZHAO Gao-yu.Static response of long span bundled conductor power line[J].High Voltage En-gineering,2002,28(1):1-5.
[15]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.ZHU Kuan-jun,LI U Chao-qun,REN Xi-chun.Analysis ondynamic tension of conductor under transmission line galloping[J].China Electric Power,2005,38(10):40-44.
[16]韩银全,梁枢果.输电塔线体系完全气弹模型设计[C]∥第十三界全国结构风工程学术会议论文集(上册).大连,中国:中H国A土N木Yi工n-程qu学an会,2007:260-265.
[2]梁枢果.输电塔-线体系的气弹模型风洞试验与动力特性、风振响应分析[R].上海:同济大学土木工程防灾国家重点实验室研究报告,2002.
[3]李宏男,王前信.大跨越输电塔体系的动力特性[J].土木工程学报,1997,30(5):28-36.LI Hong-nan,WANG Qian-xin.Dynamic characteristics of long-span transmission lines and their supporting towers[J].China Civil Engineering Journal,1997,30(5):28-36.
[4]Irivine H M,Caughey T K.The linear theory of free vibrations of a suspended cable[C]∥Proceedings of the Royal Society,Se-ries A,Mathematical Physical and Engineering Sciences.Lon-don,England:Published by the Royal Society,1974:299-315.
[5]Irivine H Max.Cable structure[M].Cambridge:The Massa-chusetts Institute of Technology Press,1981.
[6]Luongo A,Rega G,Vestroni F.Planar nonlinear free vibration of an elastic cable[J].Journal of Nonlinear Mechanics,1984,19(1):39-52.
[7]王珂晟,唐国金.架空电线在悬链状态下的非线性振动响应分析[J].振动与冲击,2003,22(2):69-72.WANG Ke-sheng,TANG Guo-jin.Response analysis of nonlin-ear vibration of overhead power line under suspension chain state[J].Journal of Vibration and Shock,2003,22(2):69-72.
[8]梁枢果,朱继华,王力争.大跨越输电塔线体系动力特性分析[J].地震工程与工程振动,2003,23(6):63-69.LI ANG Shu-guo,ZHU Ji-hua,WANG Li-zheng.Analysis of dynamic characters of electrical transmission tower-line system with a big span[J].Earthquake Engineering and Engineering Vibration,2003,23(6):63-69.
[9]郭应龙,李国兴,尤传永.输电线路舞动[M].北京:电力工业出版社,2002.
[10]王少华,蒋兴良,孙才新.输电线路导线舞动的国内外研究现状[J].高电压技术,2005,31(10):11-14.WANG Shao-hua,JI ANG Xing-liang,SUN Cai-xin.Study status of conductor galloping on transmission line[J].High Voltage Engineering,2005,31(10):11-14.
[11]王茂成,吕永丽,邹洪英,等.10kV绝缘导线雷击断线机理分析和防治措施[J].高电压技术,2007,33(1):102-105.WANG Mao-cheng,L Yong-li,ZOU Hong-ying,et al.A-nalysis of lightning-caused break mechanism of10kVinsula-tion-covered conductors and its countermeasures[J].High Voltage Engineering,2007,33(1):102-105.
[12]高电压技术编辑部.风对导线和铁塔的作用力[J].高电压技术,1979,5(3):89-90.
[13]何锃,李国兴.中山口大跨越导线舞动的分析计算[J].高电压技术,1997,23(4):12-14.HE Zeng,LI Guo-xing.Analysis galloping of Zhongshankou large span overheadline[J].High Voltage Engineering,1997,23(4):12-14.
[14]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[J].高电压技术,2002,28(1):1-5.HE Zeng,HUANG Wei,ZHAO Gao-yu.Static response of long span bundled conductor power line[J].High Voltage En-gineering,2002,28(1):1-5.
[15]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.ZHU Kuan-jun,LI U Chao-qun,REN Xi-chun.Analysis ondynamic tension of conductor under transmission line galloping[J].China Electric Power,2005,38(10):40-44.
[16]韩银全,梁枢果.输电塔线体系完全气弹模型设计[C]∥第十三界全国结构风工程学术会议论文集(上册).大连,中国:中H国A土N木Yi工n-程qu学an会,2007:260-265.
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