DYNAMIC CONFIGURATIONS OF A TRAVELING CABLE SUBJECT TO TRANSVERSE FLUID EXCITATION
行进绳索在横向流体激励下的运动

Suspended cables are extensively used in various fields of engineering, especially in marine engineering. A great number of studies have shown that the dynamics of a suspended cable often exhibits complex nonlinear behavior. When an underwater cable is being laid, it is traveling at certain velocity in water. This makes the cable dynamics much more complicated than that of a suspended cable in air. To the authors' knowledge, the dynamics of a traveling cable subject to fluid excitation is still an open problem. However, it is essential to understand and predict the dynamics of the traveling cables in water in their design phase. Starting with the analysis of the fluid drag on a traveling cable subject to transverse fluid excitation, this paper presents the expression of fluid force applied on the cable and then the dynamic equations 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 of cable dominate the motion of cable. Thus, the dynamic equations of cable are reduced to two ordinary differential equations by means of the Galerkin approach. Because the stiffness terms disappear in the differential equations when the cable is at equilibrium position, the coordinate transform proposed by Pilipchuk is used to describe the stretching and rotation of the 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 variable parameters. As a result, the approximate cable dynamics yields a two- dimensional autonomous system and does not exhibit any chaotic motions. Finally, the influences of the traveling velocity of cable and the gravity on the cable dynamics are numerically analyzed.