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 travel ling 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 fir st order dominate the motions of cable. Thus, the partial differential equa tions of cable are reduced to two ordinary differential equations of the se cond order by means of the Galerkin approach. Because the stiffness terms d isappear in the ordinary differential equations when the cable is at equili brium position, the co-ordinate transform proposed by Pilipchuk is used to describe the stretch and rotation of mid-span section of cable from the equ ilibrium position so that the transformed differential equations include li near stiffness terms. Afterwards, the differential equations are simplified by using the perturbation approach of two variables under the assumption t hat the Young's module of cable is not very small. As a result, the approxi mate cable dynamics yields a two-dimensional autonomous system and does not exhibit any chaotic motions. According to the approximated model. two equi librium positions of cable are determined and their stability is analyzed. Finally, the influences of travelling velocity and cable density on the cab le dynamics are discussed on the basis of numerical computations. The case studies show that the travelling velocity should be limited when a very lig ht cable is laid under water in order to avoid harmful and dangerous swings . (C) 2001 Academic Press.