Nonlinear free vibrations of coupled spans of overhead transmission lines

Abstract

The weakly nonlinear, freely vibrating motion of a system of coupled spans of suspended overhead transmission lines is studied. It is shown that the natural vibration is the gravity mode, of which the unsteady tension component vanishes in the first harmonic. The problem was born out of a study of the phenomenon of galloping, which is a high amplitude periodic oscillation of overhead transmission lines due to steady cross wind. Particular attention is given to an intermodal resonance, which may be interesting for galloping control.

Calculating in-plane frequencies of multispan cables using the Exterior-Matrix Method

“…If the mass per unit length is 1 kg/m, AE = 2.156 × 10 7 N, and the sag is 10 m, we find that the length of a semi-span is [9], but we can emulate this situation simply by setting m T = m N = k N = 0. The isolators can be made to be virtually inelastic by letting k T = 2, 500, 000 N/m.…”

“…If we break the tension into X -and Y -components, we find that the equations of motion for an elastic catenary are given by [9] and [6] to be ∂ ∂γ…”

“…In [9], the isolators were assumed to be inelastic, so that the point where the cables joined would always be a certain distance from the fixed point on the top of the isolator. Also, the tensions in the direction normal to the isolator were assumed to be the same.…”

“…In this section we will work out the eigenfrequencies for the examples given in [6] and [9]. One of the examples considered in [9] is a 2-span section represented in Fig.…”

“…In [9] these type of vibrations are called gravity waves because the tension does not change in leading order, so that gravity is the main restoring force.…”