Non-linear dynamics of a suspended travelling cable subject to transverse fluid excitation

Starting with the analysis of the fluid drag and lift on a suspended travelling cable subjected to transverse fluid excitation, the paper presents the expression of forces on the cable, and then a set of partial differential equations of in-plane and out-of-plane motions of the cable. In the case of small ratio of sag to span, the in-plane and out-of-plane modes of the first order dominate the motions of cable. Thus, the partial differential equations of cable are reduced to two ordinary differential equations of the second order by means of the Galerkin approach. Because the stiffness terms disappear in the ordinary differential equations when the cable is at equilibrium position, the co-ordinate transform proposed by Pilipchuk is used to describe the stretch and rotation of mid-span section of cable from the equilibrium position so that the transformed differential equations include linear stiffness terms. Afterwards, the differential equations are simplified by using the perturbation approach of two variables under the assumption that the Young's module of cable is not very small. As a result, the approximate cable dynamics yields a two-dimensional autonomous system and does not exhibit any chaotic motions. According to the approximated model, two equilibrium positions of cable are determined and their stability is analyzed. Finally, the influences of travelling velocity and cable density on the cable dynamics are discussed on the basis of numerical computations. The case studies show that the travelling velocity should be limited when a very light cable is laid under water in order to avoid harmful and dangerous swings.