MODELING THE POINT TRAJECTORY ON THE ELECTRIC TRANSMISSION WIRE UNDER THE CONDITIONS OF THE WINDS

Abstract

A model of a transmission line span under conditions of gusts of wind is considered. For this, a plane is chosen that is normal to the direction of flight (normal plane). On the plane, consider a point that is a trace of a power line wire. The paper provides a method of constructing the trajectory of a specified point under the condition that wind gusts affect the wire. A feature of research is the use for this of a mechanical analogue - a swinging spring (swinging spring). Those. a kind of pendulum that consists of a point load attached to a weightless spring. The second end of the spring is fixed motionless. We study the oscillations of a spring in a vertical plane, similar to a pendulum, provided that its wasp is straightforward. The feasibility of choosing such an analogue is explained by the need to study the dynamic system “wire in gusts of wind”, when nonlinearly coupled oscillatory components exchange energy with each other. Indeed, in the case of a point oscillation on the wire (in the normal plane), an energy exchange occurs between the transverse (horizontal) and longitudinal (vertical) oscillations of the point. This phenomenon can be investigated using the mathematical apparatus of a swinging spring, which illustrates the energy exchange between transverse (pendulum) and longitudinal (spring) vibrations.

In this case, the possibility of studying the state of resonance is of particular importance. For wires, resonance occurs when the frequency of horizontal vibrations is two times different from the frequency of vertical vibrations of a point on the wire (in the normal plane). A similar situation takes place for a swinging spring, where at resonance the frequency of longitudinal vibrations differs by half from the frequency of transverse vibrations. The studies are based on the main provisions of the Lagrange mechanics, with the help of which the trajectories of the point load of a swinging spring were described.

Keywords: trajectory of a point on the wire, Lagrange mechanics, generalized coordinates, load trajectory.