Application of the finite element method to towed cable dynamics

This paper deals with towing an object through a fluid by means of a cable. For a slender, neutrally buoyant towbody, the planar configuration of the towed system is determined for steady motion and for time-dependent maneuvers of the towing vehicle. A formulation of the finite element method that applies to towed cable dynamics is presented including bending deformation and stretch of the elements, and nodal forces caused by acceleration, distributed weight, and hydrodynamic loading. Although based on established forms for fluid drag, the treatment and expressions for nodal hydrodynamic loading forces are new. The resultant system of equations for the unknown nodal displacements is solved by step-by-step integration in time using a scheme that eliminates troublesome longitudinal oscillations. Lumped and distributed systems are compared with respect to the treatment of mass and hydrodynamic loading and the effects of bending stiffness are illustrated.