Asymptotic analysis of a translating cable arch

Abstract

The stability of a translating cable which stands in the shape of an arch between two supports is investigated. Asymptotic solutions for free in-plane and out-of-plane cable vibrations are derived under the assumption of small arch height. Without translation speed, the cable arch collapses under compressional loading. As translation speed is increased, however, the cable arch becomes tensioned and stable. A previous experiment confirms this prediction. The asymptotic solutions derived here show that the in-plane and out-of-plane vibration modes are stabilized in fundamentally different manners.