A New Approach for Melnikov Analysis of the Stability of a Ship with Water on Deck

• Incorporation of a linear-plus-quadratic damping term in the ship rolling equation preserves key dynamics of the physical system, as confirmed by model tests. • A new Melnikov-based method provides an upper bound on the domain of chaotic rolling motion (erratic rocking) under random excitation and response. • The proposed Melnikov criterion is verified using phase plane diagrams and Poincare maps. • This study is the first to systematically modify system parameters in the rolling equation for ship stability analysis.