Effect of hull geometry on parametric resonances of spar in irregular waves

• Proposed a method of predicting the spar parametric resonance in irregular wave.
• The derived Hill equation for spar include non-harmonic excitation and random phase.
• The spar parameters sensitivity analysis on the instability can guide the design.
• Stability diagrams and contours map are given considering multifrequency excitations.

The parametric instabilities of spar platforms with different hull shapes are investigated in irregular waves. Parametric instability is a phenomenon that may cause excessive motion in offshore structures. It occurs when a system parameter varies with time, and the change meets certain conditions. For a spar platform, the parameter that causes parametric resonance is usually the metacentric height. In previous studies, the parametric instability of a spar was mainly analyzed in regular waves. However, real sea conditions are irregular. In addition, some accidents and experiments have shown that parametric resonance also occurs in irregular waves. This paper analyzes the parametric instability property of a spar platform being affected by multifrequency waves, which corresponds to realistic sea conditions. The stability is determined using both an analytic method and numerical simulation. The analytic investigation is carried out using Hill׳s equation. The heave amplitudes of the motion are simulated using the wave spectrum and response amplitude operator (RAO). Different hull shapes cause significant differences when analyzing the parametric instability due to irregular waves because of different RAOs. Stability diagrams containing the boundaries of the stability regions of different hull shapes are given based on the solution of Hill׳s equation. The numerical simulation can not only determine whether the spar is stable, but can also give the maximum pitch angle. The effects of the design parameters of a spar platform and the wave parameters are analyzed by giving the contours of the maximum pitch angle. The effects of time-varying displacement are also considered in this work. Stability diagrams and the contours of the maximum pitch angle are drawn to help with the prediction of the parametric instability. Some suggestions are also given to avoid the parametric pitch of a spar in design by selecting an appropriate design parameter and hull shape.