Ship rolling equation: Comparison of the different damping models

In the paper, a comparison of the ship rolling numerical simulations results for four roll damping models is presented. In the first two models, constant damping coefficients are used, in linear and nonlinear notation. These damping models are commonly used, however have a significant disadvantage - the damping coefficients are independent of the roll amplitude and frequency. In the next two models, the damping coefficients are dependent on rolling amplitude and frequency and are implemented in roll equation with linear and nonlinear notation. The overall goal of the study is to test the effect of value and notation of damping on the results of the ship rolling numerical simulations. However, the main goal is to test if the damping dependent on roll amplitude and frequency will have an effect on ship rolling numerical simulations results. Comparison of roll damping models comprises three tests. The first two tests refer to the frequency response curve while the third test concerns the rolling equation unstable solution area. Research shows that the rolling equation is sensitive to the applied damping model and that the damping dependent on roll amplitude and frequency can have a significant impact on the results of ship rolling numerical simulations. © 2023 Elsevier Ltd