Non-Linear Free Vibrations of Coupled Spans of Suspended Cables

Summary

The problem of free in-plane nonlinear nearly harmonic vibrations of elastic suspended cables is investigated, with particular emphasis on the configuration of multiple spans, coupled via suspension strings, which is relevant in the context of overhead transmission lines. A systematic asymptotic theory is developed, for a suitable set of small parameters based on a shallow geometry and the presence of only transversal waves. The finally obtained reduced set of equations is solved by a variant of the Lindstedt-Poincaré technique. The (non-trivial) solutions for multiple spans appear to be gravity waves, considerably different from the elasto-gravity waves in the symmetric single span configuration (which is included for reference). An internal resonance is discovered giving a new explanation to the practically observed asymmetry of the vertical displacement. Application of the theory to describe the reaction force induced to a suspension string is indicated.