Parametric Resonance Analyses for Spar Platform in Irregular Waves

The parametric instability of a spar platform in irregular waves is analyzed. Parametric resonance is a phenomenon that may occur when a mechanical system parameter varies over time. When it occurs, a spar platform will have excessive pitch motion and may capsize. Therefore, avoiding parametric resonance is an important design requirement. The traditional methodology includes only a prediction of the Mathieu stability with harmonic excitation in regular waves. However, real sea conditions are irregular, and it has been observed that parametric resonance also occurs in non-harmonic excitations. Thus, it is imperative to predict the parametric resonance of a spar platform in irregular waves. A Hill equation is derived in this work, which can be used to analyze the parametric resonance under multi-frequency excitations. The derived Hill equation for predicting the instability of a spar can include non-harmonic excitation and random phases. The stability charts for multi-frequency excitation in irregular waves are given and compared with that for single frequency excitation in regular waves. Simulations of the pitch dynamic responses are carried out to check the stability. Three-dimensional stability charts with various damping coefficients for irregular waves are also investigated. The results show that the stability property in irregular waves has notable differences compared with that in case of regular waves. In addition, using the Hill equation to obtain the stability chart is an effective method to predict the parametric instability of spar platforms. Moreover, some suggestions for designing spar platforms to avoid parametric resonance are presented, such as increasing the damping coefficient, using an appropriate RAO and increasing the metacentric height.

Ince-Strutt Stability Charts for Ship Parametric Roll Resonance in Irregular Waves

Ince-Strutt stability chart of ship parametric roll resonance in irregular waves is conducted and utilized for the exploration of the parametric roll resonance in irregular waves. Ship parametric roll resonance will lead to large amplitude roll motion and even wreck. Firstly, the equation describing the parametric roll resonance in irregular waves is derived according to Grim’s effective theory and the corresponding Ince-Strutt stability charts are obtained. Secondly, the differences of stability charts for the parametric roll resonance in irregular and regular waves are compared. Thirdly, wave phases and peak periods are taken into consideration to obtain a more realistic sea condition. The influence of random wave phases should be taken into consideration when the analyzed points are located near the instability boundary. Stability charts for different wave peak periods are various. Stability charts are helpful for the parameter determination in design stage to better adapt to sailing condition. Last, ship variables are analyzed according to stability charts by a statistical approach. The increase of the metacentric height will help improve ship stability.