Normal Vibrations Of Sagging Conductors Of Overhead Power Lines

The phenomenon of self-excitation of thermomechanical vibrations of current-carrying conductors, experimentally discovered by academician A.F. Ioffe, is of practical interest as a possible explanation of the phenomenon of galloping conductors of overhead power transmission lines (OHL) – low-frequency vibrations with frequencies of ~ 1 Hz and with amplitudes of the order of the static conductor sagging. To build the theoretical foundations of this phenomenon, as a special class of self-oscillating systems, it is necessary, first of all, a model of conductor vibrations in the OHL span. With regard to the most studied type of conductor vibrations, high-frequency aeolian vibration, excited by sign-alternating aerodynamic forces from the Karman vortex street, the classical model of a straight string is reasonably applied. However, to study low-frequency vibrations of the galloping type, it is necessary to take into account the effect of sagging of the conductor, the associated elastic tension and, in some cases, the nonlinear nature of the vibrations. The article presents two models for calculating the natural vibrations of sagging conductors (cables) within the framework of the technical theory of flexible threads, assuming the constancy of the tension force along the length. The first model describes linear oscillations of an elastic conductor in the sagging plane. For a system of equations with respect to the displacement components given in natural coordinates, an exact solution of the Sturm-Liouville problem with estimates of the frequency ranges arising is obtained. The second model describes nonlinear vibrations of an elastic conductor in the sagging plane and pendulum vibrations accompanied by an exit from it. The solution of the problem is based on the principle of possible displacements using the Ritz method. The structure of the frequency spectrum and the natural forms of transverse vibrations are studied. The developed models are intended for further investigation of thermomechanical vibrations of conductor and flexible cable systems.