Nonlinear dynamic response of mooring cables based on finite-strain theory

Abstract

This manuscript presents a formulation for mooring line dynamics using Tangential Differential Calculus (TDC) framework to handle geometric non-linearities in catenary and taut systems. Based on finite-strain theory, the model accounts for large deformations, self-weight, buoyancy, seabed interaction, and hydrodynamic drag. The study presents two solution procedures, GNL-FEM, a high-fidelity finite element model implemented in Julia, and GNL-ANA, a reduced-order semi-analytical model for efficient preliminary analysis.For GNL-FEM, mesh and element order convergence studies demonstrate optimal performance, followed by validation against MoorDyn for catenary lines. In cases involving swell waves, GNL-FEM is shown to minimise the spurious oscillations typically observed in lumped-mass models during slack-line events. A primary focus of this manuscript is the dynamic behaviour of taut mooring lines under harmonic transverse excitation. GNL-FEM results demonstrate progressive geometric hardening, as the system’s natural frequency increases with higher excitation amplitude. Furthermore, strain spectra exhibit distinct super-harmonics and sub-harmonics. GNL-ANA is shown to be accurate up to the second natural frequency, even under high pre-tension and excitation, providing a valuable tool for identifying energy hotspots and optimising material properties in synthetic lines. Overall, the framework provides a consistent and versatile basis for modelling complexities in mooring systems.