Volterra (GZ)over-bar approach - a newmethod to accurately calculate the non-linear and time-varying roll restoring arm of ships in irregular longitudinal seas
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2017 Informa UK Limited, trading as Taylor & Francis Group. With several incidents of large amplitude roll motion of ships observed at sea over the past two decades, the dynamic stability of modern ship types has assumed significant importance. The move by the International Maritime Organization to develop a second generation level-2 criteria has resulted in considerable attention to the development of simplified analytical models for roll motion. Especially for the problem of parametric roll, there is still no analytical model which accurately captures the non-linear roll restoring stiffness taking into account the combined effect of incident waves and dynamic heave and pitch motions of the vessel. This paper extends our previous work to accurately capture both the linear and higher-order time-varying roll stiffness coefficients through an analytical model while taking into account incident waves and dynamic motion of the vessel. This approach called the Volterra (Formula presented.) method is compared against the existing simplified models and a non-linear time-domain simulation program to demonstrate better agreement of the proposed approach.
