More and more vessels for offshore engineering applications have a roll period beyond 20 seconds in order to avoid the wave frequency excitations on the roll motion. That is particularly true for the latest drilling vessels. However, this will lead to an unexpected second-order roll motion of the ships. This paper will present a new methodology to evaluate the second-order roll motions of the ships in random seas. The higher-order boundary element method (HOBEM) has been utilized to generate the second order difference-frequency roll excitations on the ships and the second-order ship roll motions were predicted by a frequency-domain method. A series of model tests have been conducted and the test results have a good agreement with the numerical predictions. Therefore, this new method has been verified and validated.

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