COUPLED NONLINEAR HEAVE–PITCH MOTION MODEL FORMULATION AND HYDRODYNAMIC CHARACTERIZATION

In this study, Coupled Nonlinear Heave–Pitch Motion Model Formulation and Hydrodynamic Characterization was carried out to investigate the interaction between vertical displacement and angular rotation of a ship under irregular wave conditions. Excessive heave and pitch motions can affect vessel stability, structural safety, cargo operations, and seakeeping performance. The research focused on developing a coupled nonlinear mathematical model for a Series 60 ship hull using frequency-dependent added mass, radiation damping, hydrostatic restoring forces, nonlinear restoring terms, and wave excitation forces. Unlike studies focusing mainly on linear motion prediction or individual response characteristics, this study incorporates cubic nonlinear restoring terms and hydrodynamic coefficients obtained from ANSYS AQWA for comparison. The Pierson–Moskowitz spectrum was adopted to represent irregular waves with a significant wave height of 7.45 m and a zero-crossing period of 10 s. The AQWA results recorded peak heave and pitch response amplitude operators (RAOs) of 1.019 m/m and 2.380°/m, respectively, under 180° head seas. Heave added mass decreased from 23.4 × 10⁶ kg at 0.3 rad/s to 7.36 × 10⁶ kg at 1.4 rad/s, representing a 68.5% reduction. Heave radiation damping peaked at 7.24 × 10⁵ Ns/m at 0.8 rad/s. At 3 m heave displacement, nonlinear restoring force increased by 19.4% above the linear value, while pitch restoring moment increased by 6.6% at 0.30 rad. These results demonstrate that nonlinear effects become more significant at larger motion amplitudes. The developed model contributes a mathematical basis for ship-motion assessment and supports improved seakeeping analysis. Further time-domain simulation and validation against AQWA response predictions are recommended to establish model accuracy under severe sea conditions.