Nonlinear frequency-domain analysis of motion suppression for moored vessels using hydraulic auxiliary mooring systems

Hydraulic auxiliary mooring (HAM) systems, as an advanced mooring technology, enhance harbor operational safety and efficiency by suppressing vessel motions. Despite their practical implementations worldwide, publicly available research literature on the motion suppression mechanisms and performance of HAM systems remains notably limited. This paper proposes a comprehensive analytical framework to investigate HAM system characteristics in single-degree-of-freedom mooring configurations. A physical simulation model based on vessel hydrodynamics and hydraulic principles is developed to analyze the quasi-static characteristics of the HAM restoring forces and serve as a validation benchmark. To efficiently and accurately obtain the frequency-domain response, the HAM restoring force is identified as a Jenkins friction damper and modeled using a first-order harmonic balance approximation, thereby establishing a novel nonlinear frequency-domain (NLFD) model that incorporates coupling stiffness—a factor commonly neglected in hydraulic power-take-off (PTO) models. Cross-validation against the physical simulation results confirms the accuracy of the NLFD model. Parametric studies identify optimal mechanical parameters and reveal that the HAM system achieves motion suppression through the synergy of variable equivalent stiffness and frictional energy dissipation, with significant effects observed at low frequencies. The findings provide practical guidance for the engineering application of HAM systems and are expected to provide a feasible solution for the frequency-domain analysis and performance optimization of hydraulic PTO systems in marine engineering applications.