| The parametric rolling is a severe stability problem of ships,which endanger the crew’s lives and our property. In the present thesis,multi-level numerical models classified by different complexity and nonlinearity are developed to evaluate this phenomenon. The 1DOF Hill Equation is the elementary level, which explains the mechanism of parametric resonance.The second level employs a 3-DOF (heave-roll-pitch) weakly nonlinear model, where Radiation/Diffraction forces are kept linear and represented by impulse response function,while the Froude-Krylov forces and hydrostatic restoring forces are evaluated on the instantaneously wet surface of the ship, which can capture the main cause of parametric resonance. Despite of the fact that the time-domain radiation force represented by impulse response function is widely used, there are still some incorrect places in the basic theory. In the present work, the Cummins’s method combined with STF method to calculate ship motion in time domain is reconstructed and the consistent formulations are formed. The latter model is employed to simulate the parametric rolling of one C11 class containership and numerical results are validated by experimental data. The influence of roll damping and wave steepness on the development of parametric rolling is discussed. The parametric rolling in random waves is also simulated and the influence of random phase and simulation time on the statistical characteristics of parametric rolling in irregular waves are discussed. The numerical simulation results also show that parametric rolling in irregular waves ’comes and goes’, but the occurrences of parametric roll seem to be rather long. The practical non-ergodicity of parametric rolling in irregular waves is one of the governing factors in statistical post-processing of parametric roll records. The statistic and convergence analysis of the parametric rolling show that the data set should include at least 10-20 records for detailed analysis. |
