In this paper, the stability of a ship with stabilizing tanks (U-tanks) in a longitudinal seaway is investigated. The effectiveness of properly adjusted tanks in beam sea is known. Their effect is to split the ordinary resonance peak in two other shifted in frequency. Its is possible to choose a value for the damping in the tanks so that the two peaks coalesce into one that is significantly reduced with respect to the situation without tanks. Here, we extend the analysis by taking into account the very dangerous parametric rolling in a longitudinal sea. To this end, the system of equations describing ship rolling, water motion in the tank and heave motion was considered. An approximate solution, obtained with the multiscale perturbation method allowed to obtain an expression for the threshold of parametric rolling. Preliminary results, relating to a typical application, indicate that the same damping optimisation of the tanks in beam sea, renders them effective also in longitudinal waves.
