Spatial vibrations of power transmission conductors with ice deposits

The problem of free spatial vibrations of an overhead power line wire with an asymmetric mass distribution over a cross-section caused by ice deposits on its surface, which give the cross-section an asymmetric shape, is considered. As a result, an eccentricity is formed between the centers of torsional stiffness and mass in the cross section and a dynamic connection of vertical, torsional and “pendulum” vibrations occurs with the output of the wire from the sagging plane. The wire is modeled by a flexible heavy elastic rod that resists only stretching and torsion. The case of a weakly sagging wire is investigated, when the tension and curvature of its centerline can be considered constant within the span. It is also believed that the elasticity of the ice casing is small compared to the elasticity of the wire. The mathematical model is constructed taking into account the interaction of longitudinal, torsional and transverse waves polarized in the vertical and horizontal planes. The relations of the phase velocities of all types of waves are analyzed and a group of particular subsystems determining partial oscillations is identified. The partial and natural frequencies and waveforms of the wire are studied. Analytical solutions to the problem of determining the spectrum of natural frequencies and forms of spatial vibrations are obtained. The effect of the ice casing on the vibration spectrum of the wire is studied. The dependence of the wave number of torsional vibrations on the frequency has been found, which is determined not only by the elastic-inertial, but also by the gravitational factor, which is strongly manifested for wires in long spans, especially those prone to Aeolian vibration (galloping). This circumstance is essential for the analysis of the Aeolian vibration phenomenon from the positions linking the occurrence of dancing by the convergence of the frequencies of torsional and transverse modes during the icing of the wire. It has been shown that the ratio of these frequencies, which cause an auto-oscillatory process, turns out to be significantly more complex.