Free floating objects, such as a self reacting wave energy converter (WEC), may experience a condition known as parametric resonance. In this situation, at least two degrees of freedom become coupled when the incident wave train has a frequency approximately twice the pitch or roll natural frequency. This can result in very large amplitude motion in pitch and/or roll. While classic linear theory has proven sufficient for describing small motions due to small amplitude waves, a point absorber WEC is often designed to operate in resonant conditions, and so exhibits significant non-linear responses. In this paper, a time-domain non-linear numerical model is presented for describing the dynamic stability of point absorbers. The pressure of the incident wave train is integrated over the instantaneous wetted surface to obtain the non-linear Froude-Krylov excitation force and the non-linear hydrostatic restoring forces, while first order diffraction-radiation forces are computed by a linear potential flow formulation. The model was applied to a scale model of a specific WEC design, the Wavebob. Comparison with limited data from scale model wave tank tests provided further confidence in the model.

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