A computationally efficient analytical modeling approach for parametric oscillations in floating bodies

Parametric resonance in floating bodies is a complex nonlinear dynamic problem with significant implications for offshore engineering, renewable energy systems and naval architecture. To address the computational challenges inherent in modelling such phenomena, this paper presents an analytical model that incorporates position dependence into the hydrodynamic coefficients for the wave excitation force, enabling conventional analytic hydrodynamic models to be augmented and recast into a form akin to the Mathieu equation. Originally conceived for analysing heave-only oscillations, this research extends the model’s applicability to include the pitch, thereby broadening its utility in understanding the nonlinear dynamics of marine structures. The effectiveness of the model in capturing parametric resonance is evaluated by comparing it with the results from a high-fidelity, computationally expensive, model with nonlinear Froude–Krylov forces. The proposed model boasts a speed advantage of over 10000 times compared to the model with nonlinear Froude–Krylov forces, while also offering the considerable benefit of facilitating analytical investigation methods. The capacity of the model to be generalised appears promising, as the extension to a 2-DoFs system demonstrates favourable outcomes. • A heave-only oscillation model of floating bodies was extended to include pitch. • The model includes position-dependent wave excitation forces. • A model with nonlinear Froude–Krylov forces was used as a benchmark for comparison. • Our model shows parametric resonance in the expected wave amplitude–frequency region. • Our model runs 1000 faster than the benchmark.