On ship roll resonance frequency

The paper deals with the problem of modeling of rolling motion under a variety of excitation parameters. Special emphasis is put on the analysis and prediction of the frequency of the resonant mode of rolling, since it is often an essential issue in terms of motion of a ship related to her safety against capsizing or excessive amplitudes of roll. The research is performed for both free rolling and excited rolling and it is based on the one-degree-of-freedom equation. The conducted simulations were carried out paying special attention to the effects related to non-linear characteristics of stiffness represented by the GZ-curve and also the non-linearity of damping. A group of ships were considered in order to research and define the key factors governing rolling characteristics. The novel method for rolling period prediction was elaborated and tested revealing significant discrepancies between the results of the pending GM-based IMO-recommended method and the results of numerical simulations performed for a wide range of ships operational loading conditions. Since the research shows a drawback of the IMO formula for rolling period prediction a new formula is proposed instead.