Nonlinear effects on motions and loads using an iterative time-frequency solver

A weakly nonlinear seakeeping methodology for predicting motions and loads is presented in this paper. This methodology assumes linear radiation and diffraction forces, calculated in the frequency domain, and fully nonlinear Froude-Krylov and hydrostatic forces, evaluated in the time domain. The particular approach employed here allows to overcome numerical problems connected to the determination of the impulse response functions. The procedure is divided into three consecutive steps: evaluation of dynamic sinkage and trim in calm water that can significantly influence the final results, a linear seakeeping analysis in the frequency domain and a weakly nonlinear simulation. The first two steps are performed employing a three-dimensional Rankine panel method. Nonlinear Froude-Krylov and hydrostatic forces are computed in the time domain by pressure integration on the actual wetted surface at each time step. Although nonlinear forces are evaluated into the time domain, the equations of motion are solved in the frequency domain iteratively passing from the frequency to the time domain until convergence. The containership S175 is employed as a test case for evaluating the capability of this methodology to correctly predict the nonlinear behavior related to wave induced motions and loads in head seas; numerical results are compared with experimental data provided in literature.