Dynamical analysis of transmission line cables. Part 1—linear theory

Barbieri, Renato; Barbieri, Nilson; Júnior, Oswaldo Honorato de Souza

doi:10.1016/s0888-3270(02)00217-0

Cited by 51 publications

(20 citation statements)

References 7 publications

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“…Third, the magnitude of the damping factors lies in the range of 10 −3 -10 −1 for the first five modes. The curves shown in Figure 1 reproduce qualitatively those three behaviors verified experimentally by Barbieri et al [32].…”

Section: Damped-free Vibrations Of the Conductorsupporting

confidence: 84%

“…However, here, as a first approximation, the equivalent viscous damping coefficient is assumed as a constant. Barbieri et al [32] have performed experimental tests on a laboratory span with samples of the conductor Ibis for three different lengths: 13.385, 32.300 and 65.355 m. Those authors have plotted the measured damping factors as a function of the mode number for the three conductor lengths analyzed. From the plots shown in [32], three important conclusions may be drawn.…”

Section: Damped-free Vibrations Of the Conductormentioning

confidence: 99%

“…The curves shown in Figure 6 are computed with N T = 100 and for T = 10 700 N, = 0.8127 kg/m L = 32.3 m and x s = 9.7 m. The conductor parameters were chosen in an attempt to compare the analytical results obtained here with the numerical ones provided by Barbieri et al [32]. Unfortunately, those authors provide neither the driving point (the parameter x s in the present model) nor the coordinate x, which makes it difficult for the direct comparison with their results.…”

mentioning

confidence: 99%

“…Unfortunately, those authors provide neither the driving point (the parameter x s in the present model) nor the coordinate x, which makes it difficult for the direct comparison with their results. The values adopted for the parameters x s and x were chosen on a trial-and-error basis so as to reproduce the qualitative behavior verified numerically by Barbieri et al [32].…”

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confidence: 99%

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On the application of generalized integral transform technique to wind‐induced vibrations on overhead conductors

Matt

2008

Numerical Meth Engineering

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The aim of the present paper is to describe the application of the generalized integral transform technique (GITT) for the theoretical analysis of wind-induced vibrations on overhead conductors. In the mathematical model adopted, the complicated helicoidal geometry of the conductor is simplified by treating it as a homogeneous taut string simple supported at both ends. Solving the governing partial differential equation through the GITT approach, one derives purely analytical or analytical-numerical solutions for the conductor transverse displacement as a function of both position and time. In order to highlight the potential and flexibility of the GITT approach to account for realistic features of the phenomenon, three particular cases of practical interest are analyzed in detail, for which benchmark results are provided: (i) the damped-free vibrations of the conductor; (ii) the harmonic-forced vibrations of the conductor without and with Stockbridge dampers; and (iii) the forced vibrations of the conductor under a non-linear wind excitation. The current results may be combined with previous analytical predictions to compute the conductor amplitudes and bending strains at critical locations. Although this work is focused on a taut string model for the conductor, the approach described herein may be easily extendable to the beam model.The aerodynamic lift forces arising from the periodic shedding of vortices in the wake of the conductor are responsible for its subsequent vibrations in a direction transverse to the wind flow.Aeolian vibrations on transmission line conductors arise due to wind speeds in the range of 1-10 m/s. Based on the typical values for conductor diameters (15-30 mm) and on the values of the dynamic viscosity and specific mass of the standard air, a simple calculation reveals that such vibrations arise in wind flows with Reynolds number in the range of 10 3 -10 4 . For subsonic flows in this range of Reynolds number, also called sub-critical range [4], it is well known that the vortexshedding phenomenon has a well-defined frequency, commonly referred to as shedding frequency [4,5]. Experimental observations indicate that the shedding frequency, f s , is directly proportional to the wind speed normal to the conductor, U , and inversely proportional to the conductor diameter, D; the proportionality constant being the Strouhal number, St. It is also well known that the Strouhal number is a function of both the geometry and the Reynolds number for low Mach number flows [6]; for example, for smooth circular cylinders St ≈ 0.2 such that the shedding frequency may be computed as f s = 0.2U/D. Typical conductors of high voltage transmission lines are composed of wires helically wrapped around a central core. Although transmission line conductors are not geometrically identical to smooth circular cylinders, experimental measurements in the field have revealed that the Strouhal number for the formers lies in the range of 0.185-0.22 (see, for example, [1,7,8]). Under operational conditions, overhead condu...

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Section: Damped-free Vibrations Of the Conductorsupporting

confidence: 84%

Section: Damped-free Vibrations Of the Conductormentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On the application of generalized integral transform technique to wind‐induced vibrations on overhead conductors

Matt

2008

Numerical Meth Engineering

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“…Recently, several researchers have theoretically investigated the galloping mechanism, and mathematical models have been presented to simulate the dynamical behavior of transmission [6][7][8][9]. Other authors have attempted to establish equations of motion to describe the observed three-dimensional galloping behavior on iced transmission lines [10,11].…”

Section: Introductionmentioning

confidence: 99%

Full-Scale Reconstruction for Transmission Line Galloping Curves Based on Attitudes Sensors

Yang

et al. 2018

Mathematical Problems in Engineering

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Caused by strong winds or nonuniform icing, conductor galloping is one of the major hazards that should be monitored in a timely fashion. In this paper, we proposed a new full-scale reconstruction method for transmission line curves based on the attitude sensors that uses only the tangential information and arc-length constraint. Meanwhile, a comparatively low-complexity algorithm is presented: (1) quaternion rotation to generate the tangent vectors; (2) a modified B-spline global interpolation to evaluate the curvature information; and (3) a linear mapping method to correct reconstruction curves. Moreover, sensors placement method is put forward according to the galloping features. Finally, both simulation and experimental results demonstrate that the proposed method can accurately reconstruct the galloping curves in a relatively short time, which fulfills the requirement of the real-time galloping monitoring system.

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