An Asymptotic Theory for a Class of Initial-Boundary Value Problems for Weakly Nonlinear Wave Equations with an Application to a Model of the Galloping Oscillations of Overhead Transmission Lines

The aim of this paper is to contribute to the foundation of the asymptotic methods for initial-boundary value problems and initial value problems for weakly nonlinear hyperbolic partial differential equations of order two. In this paper an asymptotic theory for a class of initial-boundary value problems for weakly nonlinear 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 timescales. As an application of the theory, an initial-boundary value problem for a Rayleigh wave equation is studied in detail using a two-timescale perturbation method. From an aeroelastic analysis, it is shown that this initial-boundary value problem may be regarded as a model describing the growth of wind-induced oscillations of overhead transmission lines.