Asymptotics for a System of Nonlinearly Coupled Wave Equations with an Application to the Galloping Oscillations of Overhead Transmission Lines

摘要

An asymptotic theory for a class of initial-boundary value problems for systems of weakly, nonlinearly coupled wave equations is presented. The theory implies the well-posedness of the problem in the classical sense and the validity of formal approximations on long time-scales. As an application of the theory an initial-boundary value problem for a system of weakly, nonlinearly coupled wave equations is studied using a two-timescale perturbation method. From an aeroelastic analysis it is shown that this problem may be regarded as a model describing the galloping oscillations of overhead transmission lines in the vertical and in the horizontal direction.