Theoretical determination of roll angular jerk of ships in irregular beam seas using PDF line integral method

The time derivative of acceleration is called a jerk, which is an important property to evaluate ride comfort in elevators, cars, and so on. Likewise, evaluation of motion sickness or ride comfort on a vessel could be achieved by this jerk property in the future. In this paper, we utilize the PDF Line Integral Method (PLIM), which was newly contrived in our previous research, for calculating not only roll angular acceleration but also roll angular jerk. The derivation of this theory, as well as numerical comparison with Monte Carlo simulation (MCS) results, are presented. Although the utilized restoring curve (GZ curve) exhibits strong asymmetricity, the proposed method successfully calculates roll angular jerk for such a condition. Since roll angular jerk is a high-order differential property, the biggest advantage of PLIM is that it only requires the information of roll and roll rate joint probability density function (PDF) to provide the PDF of jerk.