基于几何强非线性覆冰分裂导线模型动力学行为研究

发布时间：2018-09-09 15:48

【摘要】：在覆冰状态下，输电导线会承受自重、冰载、风压及由大幅舞动所产生的动载荷的综合作用。导线在该作用影响下所引起的内部张力一旦达到或超过设计载荷，便会很容易出现导线断裂、杆塔倒塌等严重灾害。频繁出现的覆冰导线舞动使电力系统面临更加严重的威胁，因此，国内外的学者们正致力于解决这一工程实际问题。目前，关于覆冰导线舞动的理论模型基本都是建立在单自由度或多自由度耦合的集中参数模型基础上；基于非线性动力系统理论开展的导线舞动研究也十分有限。针对这些问题，本文的研究主要从以下几个方面展开： (1)为了充分体现导线所具有的垂度和柔性，本课题依据弹性力学和气动弹性理论，建立了覆冰四分裂导线垂直、水平及扭转振动耦合的三维连续体动力学偏微分方程。采用模态假设，运用Galerkin离散法将其转化为常微分方程，分析了结构参数对各阶模态线性固有频率的影响。应用数值模拟研究了不同档距覆冰四分裂导线在不同风速下的振动特性，所得模拟结果与非线性有限元模型动力分析结果基本一致。 (2).本课题确定了在不同跨度的工况下，具有几何强非线性特性的导线垂直振动水平张力的范围。以具有典型强非线性振动特性的覆冰导线振动系统为基础，通过研究各种因素对舞动的影响，揭示了覆冰导线舞动的内在机理，发现了舞动导线系统中丰富的非线性动力学现象，发展了现有的舞动机理。研究结果表明由输电线的柔性和大振幅所造成的几何强非线性特性在不同档距内普遍存在。 (3).根据规范形理论，应用适用于强非线性振动系统的待定固有频率法并借助于符号运算语言Mathematica编制的通用程序计算了系统的规范形，得到导线在前3阶模态坐标下垂直振动的振幅和振动频率。分析结果表明各阶模态振幅均随风速均增加而增大，1阶模态振动频率偏离固有频率随振幅增加而减小，2、3阶模态振动频率偏离固有频率随振幅增加而增大，各阶模态振动频率随幅值的变化规律与动力学方程中二次或三次非线性项有关。 (4).以初始攻角作为分岔参数，分析了系统的动力学稳定性。应用程序计算了垂直与扭转振动耦合系统的中心流形，，得到在极坐标下前9阶Hopf分岔A规范形。确定了使系统动力失稳并致舞动的初始攻角等参数范围值，研究结果表明初始攻角是控制舞动发生及舞动幅值的主要结构因素。该研究为工程实际中导线防舞、减轻甚至消除舞动带来的危害提供了理论依据。
[Abstract]:Under the condition of icing, the transmission line will bear the combined effects of self weight, ice load, wind pressure and dynamic load caused by large galloping. Once the internal tension caused by the action of wire reaches or exceeds the design load, it is easy to cause serious disasters such as wire fracture, tower collapse and so on. The frequent ice conductor galloping makes the power system face more serious threat. Therefore, scholars at home and abroad are devoting themselves to solve the practical problem of this project. At present, the theoretical models of icing conductor galloping are based on the single degree of freedom (DOF) or multi-degree-of-freedom (DOF) coupling model, and the research on conductor galloping based on nonlinear dynamic system theory is also very limited. In order to fully reflect the sag and flexibility of conductors, this thesis is based on the theory of elasticity and Aeroelasticity. A partial differential equation of three-dimensional continuum dynamics with vertical, horizontal and torsional vibration coupling is established. The modal assumption and Galerkin discretization method are used to transform it into ordinary differential equations, and the influence of structural parameters on the natural frequencies of various modes is analyzed. Numerical simulation is used to study the vibration characteristics of ice-coated four-splitting conductors with different spacing at different wind speeds. The simulated results are in good agreement with the dynamic analysis results of nonlinear finite element model. (2) In this paper, the range of horizontal tension of vertical vibration of conductors with strong geometric nonlinearity under different span conditions is determined. Based on the ice-covered wire vibration system with typical strong nonlinear vibration characteristics, the internal mechanism of the ice conductor galloping is revealed by studying the influence of various factors on the galloping. The abundant nonlinear dynamic phenomena in the galloping conductor system are found, and the existing galloping mechanism is developed. The results show that the strong geometric nonlinearity caused by the flexibility and large amplitude of transmission lines exists in different spacing. (3). According to the normal form theory, the undetermined natural frequency method suitable for strong nonlinear vibration system and the general program of symbolic operation language Mathematica are used to calculate the normal form of the system. The amplitude and frequency of the vertical vibration of the conductor in the first three modal coordinates are obtained. The results show that the amplitude of each mode increases with the increase of wind speed, and the frequency deviation from the natural frequency of the first-order modal vibration decreases with the increase of the amplitude, and the deviation frequency of the third-order mode vibration frequency increases with the increase of the amplitude. The variation of vibration frequency with amplitude is related to the quadratic or cubic nonlinear terms in the dynamic equation. (4). The dynamic stability of the system is analyzed with the initial angle of attack as the bifurcation parameter. The central manifold of the coupled system of vertical and torsional vibration is calculated by the program, and the A-normal form of the first nine Hopf bifurcation is obtained in polar coordinates. The range of parameters such as the initial angle of attack which causes the dynamic instability and galloping of the system is determined. The results show that the initial angle of attack is the main structural factor controlling the occurrence and amplitude of the galloping. The research provides a theoretical basis for the engineering practice to prevent wire from dancing and to reduce or even eliminate the harm caused by galloping.
【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TM75;O322

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