Mathieu instability of a spar platform with mooring and risers
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Mathieu instability for a spar platform arises when there is a harmonic variation in the pitch restoring coefficients caused by large heave motion and the period of the heave motion is half of the pitch natural period. The pitch restoring coefficient can be represented by a function of the displaced volume and the metacentric height of spar hull. Due to heave motion, the displaced volume and the metacentric height of the spar platform change in time and this heave/pitch coupling can be represented by Mathieu's equation. The objective of this study is to evaluate damping effects and hull/mooring/riser coupled effects on the principal instability. In the simulation, the heave/pitch coupling of the spar platform is considered using the modified Mathieu equation. The wave elevation effect on Mathieu instability is also investigated. The Mathieu instability of a practical spar platform is carefully checked by a series of systematic simulations and comparisons of many different scenarios. When heave resonance occurs at the heave natural period equal to half of the pitch natural period, Mathieu instability, a kind of lock-in phenomenon, actually arises to increase the pitch motion significantly. The available damping is found to be important in suppressing the instability. The results also show that the additional pitch restoring force from buoyancy-cans plays an important role in the spar Mathieu instability. 2004 Published by Elsevier Ltd.