A Comparative Assessment of Simplified Models for Simulating Parametric Roll
Abhilash Somayajula and Jeffrey Falzarano
The motion of a ship or an offshore platform at sea is governed by a coupled set of nonlinear differential equations. In general, analytical solutions for such systems do not exist and recourse is taken to time domain simulations to obtain numerical solutions. Each simulation is time consuming and captures only a single realization of the many possible responses. In a design spiral when the concept design of a ship/platform is being iteratively changed, simulating multiple realizations for each interim design is impractical. An analytical approach is more preferable as it provides the answer almost instantaneously and doesn't suffer from the drawback of requiring multiple realizations for statistical confidence. Analytical solutions only exist for simple systems and hence there is a need to simplify the nonlinear coupled differential equations into a simplified 1-degree of freedom system. While simplified methods make the problem tenable, it is important to check that the system still reflects the dynamics of the complicated system. In this paper we systematically compare the existing simplified parametric roll models in the literature against a nonlinear coupled time domain simulation tool to check their veracity and discuss the extent to which each model can capture the nonlinear phenomenon accurately.
Keywords: Parametric roll; Simplified roll model; Volterra series; Grim effective wave; Improved Grim effective wave (IGEW); Coupled nonlinear simulation; GM variation; 1-DOF Parametric roll models