To accurately simulate the motion of slack marine cables, it is necessary to capture the effects of the cable’s bending and torsional stiffness. In this paper, a computationally efficient and novel third-order finite element is presented that provides a representation of both the bending and torsional effects and accelerates the convergence of the model at relatively large element sizes. Using a weighted residual approach, the discretized motion equations for the new cubic element are developed. Applying inter-element constraint equations, we demonstrate how an assembly of these novel elemental equations can be significantly reduced to prevent the growth of the system equations normallly associated with such higher order elements and allow for faster evaluation of the cable dynamics in either taut or low-tension situations.

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Tethered marine systems experience large tensile loads in their tether when operating in rough seas. Heave compensation systems can be used to reduce these loads and increase the safe operating sea states. In this work, a discrete representation of a passive heave compensator is developed and added to a finite-element model of a deep-sea ROV system to investigate the performance of ship-mounted and cage-mounted compensation systems. Numerical simulations are performed for operating depths ranging from 3280–16,400 ft (1000–5000 m) and a range of compensator stiffnesses. Both ship and cage-mounted systems reduced the natural frequencies, rms cage motion and rms tension, and extended the operating sea state of the ROV. During extreme seas, the cage-mounted compensator effectively eliminated all snap loads. However, the compensator’s characteristics must be carefully chosen because a poorly designed compensator can exacerbate operational problems. [S0892-7219(00)00903-1]