GALLOPING BEHAVIORS OF SECTOR-SHAPE ICED EIGHT BUNDLE CONDUCTORS1)

考虑到重冰区的特高压输电线路更容易形成接近扇形的覆冰,结合风洞实验及数值模拟方法研究了扇形覆冰八分裂导线的舞动特征。通过扇形覆冰八分裂输电线的节段模型风洞实验,获得各覆冰子导线随风攻角变化的气动参数。在ABAQUS软件中建立单档扇形覆冰八分裂输电线路的有限元模型,通过程序UEL输入各覆冰子导线的气动参数,根据数值模拟结果可获得舞动轨迹及振幅等舞动特征,最后讨论了风速、档距和初始风攻角对八分裂导线舞动特征的影响。     

WIND TUNNEL TEST AND STABILITY STUDY OF ICED QUAD BUNDLE CONDUCTOR1)

通过覆冰四分裂导线与单导线风洞试验,得到了4种不同工况下的空气动力系数,接着采用等效替代法得到关于四分裂导线中心轴的等效气动力系数,再将该系数与相同条件下进行风洞试验所得的单导线气动力系数作对比。结合Den Hartog横向驰振机理与Nigol扭转稳定机理,分析了等效后覆冰四分裂导线的稳定区与不稳定区,并将其与单导线的稳定区与不稳区作对比,分析了两者的失稳。本文所得结论能对覆冰导线舞动研究与仿舞技术研究有一定的参考价值。     

考虑温度效应的覆冰导线动力学建模及舞动特征研究

针对以往研究忽略了温度效应对覆冰导线舞动特性的影响,本文推导了考虑温度效应影响的覆冰导线舞动控制方程.基于悬链法、热应力理论推导了覆冰导线的偏微分舞动方程,接着通过Galerkin法将该偏微分方程转化为常微分方程.建立气动载荷模型,将气动力引入到舞动方程中,随后采用多尺度求得了覆冰导线的位移响应,最后进行了参数分析、算...     

覆冰四分裂导线动态气动系数风洞试验

覆冰导线舞动是由这些导线的气动不稳定性引起的。由于导线动态空气动力特性不同于静态气动系数,本文针对新月形冰形制作了覆冰四分裂导线模型,通过风洞试验动态测试的装置设定可测量不同扭转频率下的空气动力系数。风洞试验得到了不同扭转运动频率、风速和覆冰厚度等关键工况下新月形覆冰四分裂导线的动态空气动力系数。风洞试验结果显示,动态气动系数与静态气动系数存在显著差异。不同于静态气动系数,动态气动系数曲线是环形的,多种参数对气动系数影响明显。结果表明,风洞试验结果为覆冰分裂导线运动研究及其防治技术提供了必要的数据。     

不同自由度下覆冰四分裂导线舞动特征分析

基于哈密顿变分准则，推导了单档导线的振动控制方程，通过建立的气动荷载模型得到考虑气动荷载影响的覆冰导线舞动控制方程．进行风洞试验并得到覆冰四分裂导线的三分力气动系数，利用泰勒定律将气动系数在攻角α = 0处展开，得到了气动系数的三次拟合曲线．采用摄动法求解了二自由度下覆冰导线的位移响应，接着采用数值法求解了三自由度下覆冰导线的位移响应．最后，通过具体的数值算例分析了两者位移响应的区别．算例分析表明：二自由度下覆冰导线的位移响应与三自由度下覆冰导线的位移响应存在一定的区别，三自由度下覆冰导线的舞动更符合导线真实状态下的舞动，其结果更具有参考价值．     

覆冰三分裂导线舞动的数值模拟方法

以覆冰三分裂导线为研究对象,提出了一种模拟覆冰分裂导线舞动的数值方法。用Hamilton变分原理建立系统的动力学平衡方程,利用罚函数法引入子导线上间隔棒连接点的运动约束条件;采用Newmark法进行时间积分、Newton-Raphson法迭代求解非线性方程。通过数值算例验证了方法的正确性。在该方法的应用中由于尾流影响而导致迎风侧子导线和背风侧子导线所受空气动力载荷不同,数值模拟结果反映了这一因素对各子导线舞动轨迹的影响。此方法为分裂导线舞动的深入研究提供了一种有效途径。     

一种新的覆冰导线舞动非线性有限元分析方法

本文基于Hamilton原理,建立了耦合三个平动自由度和一个扭转自由度以及偏心覆冰作用下导线的非线性舞动方程,提出了一种新的覆冰导线舞动分析非线性有限元模型,将相邻跨导线和绝缘子等效为线性弹簧单元,同时考虑覆冰导线非线性气动力和大幅舞动的几何非线性,采用Newmark-β时间积分结合修正的Newton-Raphson非线性迭代求解舞动有限元方程。本文数值解与D形覆冰导线舞动实测值无论在振幅还是频率方面均吻合得非常好,证明了本文新提出的导线舞动有限元模型的准确性。本文研究还表明：舞动是一种以上下运动为主的低频振动,通常发生在一阶上下自振频率附近,其振幅和频率由输电线路的物理参数和风载荷唯一确定,与初始运动状态无关。     

Self-Excited Wind-Induced Vibrations and Limit Cycles in Bundled Conductors

Abstract. Wake-induced oscillations on bundled conductors of overhead transmission lines are investigated. These oscillations are due to the leeward conductor lying in the wake of the windward one. We consider a twin horizontal bundle of overhead lines. First of all, the critical wind velocity (bifurcation point) of incipient flutter is identified [3, 4]. A nonlinear analysis is adopted to investigate the post-bifurcational behaviour of the oscillations. Using, if necessary a reduction to the center manifold, and an additional normal form transformation we obtain amplitude equations which can be analyzed qualitatively with regard to the unfolding parameters.Sommario: Vengono studiate le oscillazioni indotte dal distacco di scia in fasci di conduttori di linee di trasmissione sospese. Queste oscillazioni sono presenti nel conduttore sottovento che giace nella scia del conduttore sopravvento. In particolare viene considerato il caso di una coppia di conduttori disposti orizzontalmente. Prima di tutto, viene identificata la velocità critica del vento (punto di biforcazione) dovuta al flutter incipiente [3, 4]. Viene utilizzata un'analisi non lineare al fine di valutare il comportamento post-biforcativo delle oscillazioni. Usando, se necessario, una riduzione alla varietà centrale e un'addizionale applicazione del metodo della forma normale, si ottengono equazioni nelle ampiezze che possono essere analizzate in modo qualitativo con riferimento ai parametri essenziali.     

Modes computation and analysis for long multi-span bundle conductors of power transmission lines with galloping control devices

A new type of element which is suitable for solving the modes of the galloping long multi-span bundle conductor structures is presented. The element is composed of all sub-conductor segments between two spacers. Based on the linearized governing differential equations of the conductors, the mass matrix and stiffness matrix of the element in consideration of the constrained relations imposed on the conductors by spacers are derived. The dynamic characteristics of the galloping control devices can be directly added to the element. The modes for an actual power line structure are computed by using the element formula and FEM procedures, where seven cases of different galloping control device allocations are considered. Compared with the measured data, the method is shown to be reliable and effective. Analysis and discussions of the computational results are given. Some hints that are helpful to further investigation of galloping are also obtained.     

Experimental investigation of wind-induced vibrations of main cables for suspension bridges in construction phases

The main cables of suspension bridges show a changing cross-sectional shape with the evolution of construction phases, and they may suffer from severe wind-induced vibrations at certain conditions. The primary objective of this research was to examine the aerodynamic performance of the main cable in construction phases and to develop appropriate countermeasures to eliminate the potential wind-induced vibrations. Two cross-sections with different shapes of a main cable were chosen, and a series of wind tunnel tests were performed in a reduced wind velocity range of 32–366 using elastically mounted sectional models. Galloping occurred for the two cross-sections under certain wind incidence angles when a critical velocity was reached. No obvious hysteresis phenomenon of galloping was observed in the tests. The steady amplitude of galloping increased linearly with wind velocity and the increasing rate almost kept constant for different structural damping ratios. The aerodynamic nonlinearity, rather than the structural damping nonlinearity, is the main source leading to the limited amplitude oscillation. An empirical expression of galloping amplitudes for the two cross-sections was derived based on the test data. Meanwhile, the critical wind velocity was studied in a Scruton (Sc) number range of 108–4196 (as varied by changing the initial structural damping ratio between 0.093% and 3.62%). Results showed that the Den Hartog criterion was applicable to forecast the possibility of galloping, but not able to estimate the critical wind velocity for the main cable. Linear fitting method can be used to predict the critical velocity based on the experimental data. Finally, three vibration mitigation measures were studied, and a combination of structural and aerodynamic measures was recommended for galloping mitigation of main cables.     

连续档覆冰导线舞动数值模拟及参数分析简

本文对仅有一档满足舞动条件的连续档输电线路的振动进行了详细地研究. 利用ABAQUS 通用软件建立考虑绝缘子串连续档覆冰输电线的精细有限元模型,通过用户自定义单元UEL 施加空气动力载荷,获得考虑几何非线性的连续档覆冰导线大幅振动的时域解. 根据数值结果研究了连续档输电导线档距及档数变化对连续档内不同档输电线舞动的影响规律,所得结果对连续档覆冰导线舞动和防舞技术的研究具有一定的参考价值.     

Experimental and theoretical investigation of galloping of transversely inclined slender prisms

Galloping is characterized by large and periodical oscillations which may lead to collapse of slender structures. This study is the first attempt of a comprehensive experimental and theoretical investigation of galloping of transversely inclined prisms. A modified quasi-steady model is proposed with a constant term to estimate the galloping of a transversely inclined prism, which is later experimentally investigated by conducting a static Synchronous Multi-Pressure Sensing System (SMPSS) test and an aeroelastic test in a boundary layer wind tunnel. The galloping responses of the prisms were measured in the aeroelastic test, while the aerodynamic force coefficients were determined from the SMPSS test. These experimental results were subsequently utilized to validate the quasi-steady model. Based on the proposed model, the galloping responses of the prisms were predicted and compared with the experimental results. The experimentally measured and theoretically predicted galloping responses are discussed with respect to aerodynamic damping ratios, onset galloping wind speeds, distributed pressure coefficients, point pressure spectra and vortex shedding frequencies. Interesting findings are summarized.     

VORTEX-EXCITED VIBRATIONS IN BUNDLED CONDUCTORS: A MATHEMATICAL MODEL

Wind-excited vibrations generated by vortex shedding are very common in high-voltage overhead transmission lines. Although such vibrations are barely perceptible due to their low amplitudes (less than a conductor diameter), they are, however, extremely important since they may lead to conductor fatigue. Mathematical models are therefore necessary for the computation of these vibrations, in order to evaluate the risk of potential damage to the line as well as for studying the efficiency of damping measures. For single conductor lines, the so-called energy-balance method gives good results in estimating the vibration amplitudes. However, the problem becomes more involved for bundled conductors with spacer dampers, commonly used in high-power transmission in many countries, and a modified form of the energy-balance method is presented here. Singular perturbation methods are employed, along with the energetically equivalent standing wave amplitudes obtained from the modified energy-balance methods, to determine the bending strains at critical points. This gives an estimate for the maximum strain levels in a conductor, which can be very useful in the design of transmission lines and for the optimization of the corresponding damping devices.     

气动力⁃安培力⁃谐波激励作用下载流导线的非线性振动特征

研究了气动力-安培力-受迫激励联合作用下载流新月形覆冰导线的振动特征,在传统只考虑安培力的载 流导线振动方程中引入了气动力和受迫激励项,使得模型更加符合实际工程．首先建立了载流新月形覆冰输电 导线模型,接着推导了载流覆冰导线模型的振动方程,利用Galerkin方法将该振动方程转变为有限维度的常微 分方程,采用多尺度法进行摄动求解,求得幅-频响应函数,并对比分析主共振情况下考虑气动力与不考虑气 动力时载流、间距、风速、张力、激励幅值对振动幅值的影响．研究结果表明：考虑气动力的振动幅值较未考 虑气动力时小．各线路参数对导线的幅值都有一定程度的影响,并且使系统表现出明显的软弹簧特征和复杂的 动力学行为．本文研究成果能为实际工程提供一定参考价值     

基于3自由度的新月形覆冰输电线舞动稳定性研究

针对覆冰输电线舞动问题提出了一种基于非对称空气动力系数矩阵的临界风速计算方法．基于拟静态理论得到覆冰输电线的气动载荷，该气动载荷考虑了横向运动以及扭转运动对相对风攻角的影响，最后建立等效的3自由度覆冰输电线舞动模型．在初始风攻角处对气动载荷进行泰勒展开，得到非对称的线性空气动力系数矩阵．结合3自由度振动方程以及非对称空气动力系数矩阵，采用Rourh-Hurwitz准则计算覆冰输电线舞动发生的临界风速．通过风洞实验测得新月型覆冰单导线的空气动力系数，根据本文提出的理论分析了竖向振动频率、面外振动频率以及扭转振动频率对临界风速的影响，最后与DenHartog理论得到的临界风速进行了对比．本文研究成果对于指导覆冰输电线路防舞设计具有理论意义．     

Incident flow effects on the performance of piezoelectric energy harvesters from galloping vibrations

In this paper, we investigate experimentally the concept of energy harvesting from galloping oscillations with a focus on wake and turbulence effects. The harvester is composed of a unimorph piezoelectric cantilever beam with a square cross-section tip mass. In one case, the harvester is placed in the wake of another galloping harvester with the objective of determining the wake effects on the response of the harvester. In the second case, meshes were placed upstream of the harvester with the objective of investigating the effects of upstream turbulence on the response of the harvester. The results show that both wake effects and upstream turbulence significantly affect the response of the harvester. Depending on the spacing between the two squares and the opening size of the mesh, wake and upstream turbulence can positively enhance the level of the harvested power.     

A model to predict the coupled axial torsion properties of ACSR electrical conductors

The modeling of ACSR (aluminum-conductor steel-reinforced) electrical conductors for dynamic analysis requires some knowledge of the mechanical properties of the conductor. It was found both experimentally and theoretically, using a simple strength of materials approach, that the axial-torsional behavior of ACSR conductors is highly coupled; i.e., axial motion causes torsional motion and vice versa. Although wind-induced oscillation of ACSR power lines has been observed for years, the importance of axial-torsional coupling has not been generally recognized, nor studied. A simplified mathematical model correlated well with experimental measurements for this type of coupled mechanical behavior. It is hoped that being able to control the amount of coupling through cable design may lead to better control of wind-induced oscillations.     

Control of cross-flow-induced vibrations of square cylinders using linear and nonlinear delayed feedbacks

We investigate the effectiveness of linear and nonlinear time-delay feedback controls to suppress high amplitude oscillations of an elastically mounted square cylinder undergoing galloping oscillations. A representative model that couples the transverse displacement and the aerodynamic force is used. The quasi-steady approximation is used to model the galloping force. A linear analysis is performed to investigate the effect of linear time-delay controls on the onset speed of galloping and natural frequencies. It is demonstrated that a linear time-delay control can be used to delay the onset speed of galloping. The normal form of the Hopf bifurcation is then derived to characterize the type of the instability (supercritical or subcritical) and to determine the effects of the linear and nonlinear time-delay parameters on their outputs near the bifurcation. The results show that the nonlinear time-delay control can be efficiently implemented to significantly reduce the galloping amplitude and suppress any dangerous behavior by converting any subcritical Hopf bifurcation into a supercritical one.     

On the quasi-steady analysis of one-degree-of-freedom galloping with combined translational and rotational effects

Galloping is the low-frequency, self-excited oscillation of an elastic structure in a wind field. Its analysis is commonly based on a quasi-steady aerodynamic analysis, in which the instantaneous wind forces are derived from force data obtained in static wind tunnel tests. For the galloping of a rigid prismatic beam the validity of the quasi-steady assumption is critically assessed for the case that rotational effects must be included in the aerodynamics. An oscillator structure with one (torsional) degree of freedom is proposed which allows a reliable modelling. Its effective motion can be considered as being composed of a translation with a coupled rotation of the cross section, and can be regarded as a natural extension of pure translational galloping. The analysis reveals that the resulting aerodynamic damping is determined by the sectional aerodynamic normal force coefficient alone. An aerodynamic damping coefficient is defined that can be expressed uniquely in terms of an aerodynamic amplitude, allowing a normalization of the galloping curve. This result can be used to analyze both purely translational and combined galloping, which are found to differ only by the way the structural amplitude (displacement) is related to the aerodynamic amplitude. An interesting result is that for large wind speeds rotational galloping displays an aerodynamic limit, in contrast to translation galloping where the limit-cycle amplitude increases linearly with wind speed. Results obtained from wind tunnel experiments confirm the major findings of the analysis.     

温度效应对覆冰导线舞动特征的影响研究

以某耐张段单跨导线作为研究对象,基于哈密顿原理和增量热场理论,建立了考虑温度效应的覆冰导线非线性舞动模型并推导出其舞动方程。分别使用近似模态和复杂模态得到离散后的面内-面外耦合的有限维度舞动方程,接着采用多尺度法得到该方程的近似解。数值算例研究表明,温度对频率的影响与Irvine参数有关,对张力的影响与初始张力的范围有关,而且降温会增大导线舞动幅值;采用精确模态计算得到的舞动幅值显著小于使用近似模态计算得到的幅值。