The dynamics of translating cables

Abstract

The dynamics of a translating catenary are studied. The static and linearized dynamic governing equations are derived along the local tangential and normal directions and it is shown that in this form two simpler equations can be derived and solved asymptotically for both small and large sag cables, horizontal or inclined. For small sag cables the solutions of one of the asymptotic equations undergo fundamental changes for specific values of the elastic stiffness, inclination angle, sag-to-span ratio and speed of translation resulting in strong mode interactions. For horizontal cables this explains the phenomena of frequency coalescence and mode reversion [1], as well as the frequency crossover and modal changes of non-translating cables [2]. For inclined cables frequency coalescence never occurs, while mode reversion is partial and strongly dependent on the inclination angle. However, in all cases of mode interaction the dynamic tension is greatly amplified. For large sag cables the solution accounts for the significant tension and curvature variation. The solution reduces to previous results for non-translating cables horizontal [3, 4] or inclined [5].