The roll motions are a key parameter on the design of FPSOs that operate in moderate and severe environmental conditions. To reduce the magnitude of roll motions, some techniques based on changing the vertical position of gravity center are used to put the roll natural period outside of the frequency range of the linear waves. However, recent model tests and also numerical calculations have shown that the vessel may still experience large roll motions which are considered to be induced by second-order wave loads. Further to the work in Rezende et al. (2007) to compute the roll response in frequency domain, new developments to perform simulations in time domain are presented here. In this new method, variations of second-order roll moments dependent on the roll and heave motions are taken into account consistently. It is shown that, unlike the horizontal loads, the quadratic transfer functions of the vertical loads depend on the instantaneous position of the vessel. The variation of the roll moment with the heave position of the vessel has been considered more important than the variation obtained only with the inclination of the vessel. Furthermore, numerical results of roll simulations are compared with model tests results and presented in the paper.

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