Unstable resonant heave and pitch motions of a floating deep draft platform, under the action of a regular wave with the frequency equal to the sum of the heave and pitch natural frequencies, can be developed by nonlinear instability (Liu, Yan & Yung 2010). The instability is associated with difference-frequency interactions between the body motion and the ambient wave. In this work, we study the effect of the nonlinear instability upon floating platforms with relatively shallow drafts whose wave damping at heave/pitch natural frequencies may not be small. Direct time-domain numerical simulations of wave-structure interactions, which can take into account different levels of nonlinearity effects, are applied to understand the characteristics of the unstable coupled heave/pitch (or heave/roll) resonant motion and its dependence on the key physical factors. In particular, it is found that such a nonlinear instability at other wave conditions involving sum-frequency interactions between the body motion and the ambient wave can also occur. For practical applications, long-time nonlinear simulations with irregular waves are also performed. The results show that depending on the sea conditions and damping in the system, the unstable resonant motion associated with the nonlinear instability can be significant for platforms with shallow drafts.

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