Parametric instability prediction in a top-tensioned riser in irregular waves

Abstract

The parametric instability of a top-tensioned riser (TTR) in irregular waves was predicted based on multi-frequency excitation. As the exploration of oil and gas moves into deeper water and the corresponding platforms encounter continuous wave loads, parametric resonance becomes an increasing challenge for TTR design. TTRs may suffer damage due to excessive stress or significant fatigue because of parametric resonance. Studies of the stability of long slender structures have been limited to regular waves, with an emphasis on explaining parametric resonance corresponding to simplified situations in which the related displacement or tension fluctuation is assumed to be an ideal harmonic signal. Waves are irregular in real sea conditions, therefore, the present study proposes a methodology to investigate the instability properties of TTRs in irregular waves. Hill's equation of a TTR system under multi-frequency excitation is derived based on linear-wave theory using a Pierson–Moskowitz wave spectrum. Analytic results are given for the stability limit of the related Hill's equation and they describe the stability of a TTR under irregular wave excitation. These new limits are compared to Mathieu-type stability limits. The stability diagram for Hill's equation with random phase modulation in multi-frequency excitation is obtained. To evaluate the proposed method, an example of the application of the stability diagram to TTR design is provided. Simulation results are compared under two types of wave excitation: single-frequency excitation and multi-frequency excitation, generated according to specific sea spectra. Parametric stability properties of a TTR system predicted by regular wave and irregular wave theory are different from each other. Although the transition curves both move to the upper zone of the parametric plane and the region of unstable zones shrink when the damping coefficient increases, the impact of damping is different. The results show that it is necessary to predict the parametric stability of TTR using irregular waves. Applying the stability diagram to a TTR in irregular waves shows that the introduction of extra damping to an unstable system can suppress the instability. In addition, the single-frequency excitation method predicts that the lower vibration mode is more likely to be excited, whereas the multi-frequency excitation method predicts that the higher vibration mode is more likely to fall into an unstable zone.