Volterra GZ Approach - A New Method to Accurately Calculate the Non-linear and Time-varying Roll Restoring Arm of Ships in Irregular Longitudinal Seas
Abhilash Somayajula and Jeffrey Falzarano
With the several incidents of large amplitude roll motion of ships observed at sea over the past two decades, 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 a 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 nonlinear 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 (Somayajula and Falzarano 2017) 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 GZ method is compared against the existing simplified models and a nonlinear time domain simulation program to demonstrate better agreement of the proposed approach.
Keywords: Volterra GZ; Parametric roll; Analytical roll model; Nonlinear roll restoring arm; Single degree of freedom model; Grim effective wave; SIMDYN; Nonlinear time domain simulation;