Maki, AtsuoAtsuoMakiDostal, LeoLeoDostalMaruyama, YuukiYuukiMaruyamaSasa, KenjiKenjiSasaSakai, MasahiroMasahiroSakaiUmeda, NaoyaNaoyaUmeda2022-10-122022-10-122022-11-15Ocean Engineering 264: 112159 (2022-11-15)http://hdl.handle.net/11420/13741So far, the authors have established the theoretical estimation method of the Probability Density Function (PDF) of roll angular acceleration and jerk with the use of PLIM (PDF Line Integral Method), and estimations of the PDF of these properties were successfully achieved. PLIM, on the other hand, necessitates numerical integration along the complex shaped integral path. The integral path, in particular, becomes challenging in the calculation of the jerk property. However, if the restoring term is only represented by a linear component, then explicit expressions of PDF of roll angular acceleration can be obtained using the nonlinearization technique. It is noteworthy that the form of the nonlinear damping component does not constrain the applicability. This paper aims to show the derivation of the theoretical result and comparison with Monte Carlo Simulation (MCS) results. Furthermore, using the current form of the acceleration PDF, the PDF of roll angular jerk was obtained. The variance of roll angular rate determines the PDF form of the acceleration, which is the method's main advantage.en0029-80182022Approximate solutionExcessive accelerationIrregular beam seasPDF Line integral methodRoll angular accelerationJournal Article10.1016/j.oceaneng.2022.112159Other