摘要
输电导线的舞动研究是一项国际上十分重视并广泛研究的重要课题，既有重要的学术价值，又有非常重大的社会经济意义。由于其学科涉及面较宽，影响因素复杂且随机因素较多，研究工作涉及到理论研究、计算机仿真、空气动力学参数试验、模拟试验和现场实施，因而耗资巨大，研究周期较长。至今为止，尽管研究者众多，历时多年，重要成果仍然很少，学术专著至今罕见。本文通过试验得出了关于覆冰分裂输电导线的动力学参数，建立了关于输电导线单自由度滞后非线性模型和考虑到耦合振动的两自由度的非线性模型，并对此进行了非线性动力学分析（分岔和混沌）。具体获得的主要研究成果（创新点）如下：
覆冰分裂输电导线空气动力学参数的确定。首次通过试验，得到了关于覆冰分裂输电导线的动力学参数（升力系数，阻力系数和扭转系数）。在本文研究之前，从现有文献和资料来看，关于覆冰单根导线的试验仅有国外的尼格尔等人完成的覆冰单根导线的空气动力参数试验和国内的中山口舞动治理工程空气动力试验两个。有关分裂输电导线的试验在本文之前没有见到。
覆冰分裂导线的滞后非线性无量纲单自由度系统模型的建立。建立了关于覆冰分裂输电导线的单自由度无量纲滞后非线性数学模型。本文基于试验数据，在建立单自由度无量纲滞后模型的基础之上，对系统进行非线性分析，建立了分岔参数和物理参数之间的对应关系，并利用奇异性理论得到了系统的转迁集和分岔图。最后得到了开折参数对于系统的相互影响关系。
考虑到耦合因素的覆冰导线两自由度无量纲系统模型的建立。覆冰输电导线由于其质量上存在着偏心和风功角的变化，会同时产生惯性力耦合和空气动力学耦合，分裂导线亦是如此。本文在试验数据的基础上，建立了两自由度的非线性模型并在此技术之上进行了非线性分岔和混沌分析，得到了覆冰分裂输电导线系统的最简规范形。进一步得到了系统的普适开折参数和原系统参数之间的关系。讨论了系统的余唯2分岔，揭示了个参数对覆冰分裂输电导线系统动力学行为的影响。
强非线性系统和弱非线性系统的判据式的确立。基于所建立的两自由度非线性数学模型，从理论上证明了覆冰分裂输电导线系统在铅垂方向上的振动隶属于强非线性振动系统，而在扭转方向上的振动隶属于弱非线性系统。
The galloping of the iced transmission line is an international research topic. Manyresearchers have paid more attention to this problem which not only has importantacademic value, but also has great social and economic significance. The topic involvesmany filed and there are many complex factors in the proceeding of study, such as thatdesign theory study, computer simulation, aerodynamics parameter identification,analog simulation and file trials. So it is expensive and has a long study period.Although there are so many researchers in the world until now, the achievement aboutthe galloping is still very little and the academic monographs are hard to be funded. Inour study, the air dynamics parameters are firstly obtained through the wind tunnel testof Tianjin University. Then a new one-degree-of-freedom hysteretic nonlinear modeland a two-degree-of-freedom nonlinear model are constructed. And then base on theexperiment data, the analysis of nonlinear dynamics (bifurcation and chaos) isinvestigated via numerical simulation. The main achievements (creative ideas) are asfollows:
The aerodynamics parameters of the quad iced bundle conductors are identified:the aerodynamics parameters (lift coefficient, drag coefficient and torsional coefficient)are firstly be obtained through the wind tunnel in the world. According the existingliterature, there are only two tests about the single conductor: one is aerodynamicparameters experiment by O. Nigol in Canada, and another is anti-gallopingaerodynamic experiment in Zhongshan export. But before our experiment, we can findany experiment about the quad iced bundle conductor.
A new one-degree-of-freedom hysteretic nonlinear model is constructed about thequad iced bundle conductors: In our study, consider the structure characteristic of theconductor, we give a non-dimensional hysteretic nonlinear model. The bifurcationequation is obtained by applying the undetermined fundamental frequency method ofthe complex normal form. The sensitivity parameters and its range of values areobtained to analyze and to control the galloping the quad iced bundle conductor.
A new two-degree-of-freedom nonlinear model is constructed about the quad icedbundle conductors: Due to that the quality of the eccentric conductor and wind attachangle are changed, there are both inertial force coupled and aerodynamics force coupled, so a new model is developed to consider this coupled force. By applying centermanifold and invertible linear transformation, the co-dimension-2bifurcation isanalyzed. The relationships of parameters between this system and the original systemare obtained to analyze and to control the galloping of the quad iced bundle conductor.The Lyapunov exponent and the Lyapunov dimension are investigated via numericalsimulation to present a rigorous proof of existence of chaos.
A new criterion formula is established to distinguish which system (strongnonlinear system or weekly nonlinear system) the quad iced bundle conductors isbelong to. Based on the two-degree-of-freedom nonlinear model and the criterionformula, we find that the vibration in the vertical direction is strong nonlinear vibrationand in the torsional direction is weakly nonlinear vibration.
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