Nonlinear Dynamic Stability Analysis of Ground Effect Vehicles in Waves Using Poincaré–Lindstedt Perturbation Method

In this study, we present an analytical tool that can be used to predict the nonlinear dynamic response of ground effect vehicles (GEVs) advancing through sinusoidal head-sea waves. GEVs exhibit a unique instability phenomenon known as porpoising, which is an oscillatory motion along the heave and pitch axes that can cause serious structural damage. The heaving and pitching equations of motion are presented in the form of coupled, forced, and nonlinear Duffing-type equations with cubic nonlinearity. The analytical model developed in this study leverages the Poincaré–Lindstedt perturbation method to express the amplitude and frequency of motion in terms of all physical parameters. The accuracy and reliability of the proposed model were validated through computational fluid dynamics (CFD) simulations based on incompressible unsteady Reynolds-averaged Navier–Stokes (RANS) equations. The results show a strong agreement between the analytical tool and the CFD simulations, with minor discrepancies due to assumptions inherent in the 2D simulations, particularly the assumption that seawater only passes beneath the hull, resulting in increased buoyancy forces and reduced damping. This study offers a novel and practical method for predicting the dynamic stability of GEVs under realistic sea conditions, potentially enhancing safety and operational efficiency by mitigating the risks associated with porpoising.