Mathematical Modelling of Overhead Electric Power Line Wire Oscillations

This paper considers a mathematical model of an overhead electric power line wire, represented by a flexible tensile cable, expressed by a system of nonlinear partial differential equations. For its approximate solving, the Bubnov‒Galerkin method with the choice of small (linear) oscillation modes as the basis functions is used. Approximate analytical expressions for these modes, as well as the dependence of the eigenfrequencies on the cable tension are obtained. The method of approximate determination of multiple frequencies is described. The comparison of solutions obtained using the considered Galerkin approach and the finite difference method is carried out.