Theoretical estimation of joint probability density function of roll angle and angular acceleration in beam seas using PDF line integral method
So far, we have developed a calculation method for roll angular acceleration and its derivative, which is a jerk. In this study, using the probability density function (PDF) line integral method and the joint PDF (JPDF) of roll angle and angular rate, we obtain a theoretical method for the evaluation of the two properties. In particular, the estimation method of acceleration is considered crucial, as the angular acceleration is directly related to inertial forces or moments of onboard objects. Moreover, to consider the strength of container stacks, as well as the lashing strength of cargo and track on board, a separate evaluation of roll angle and roll angular acceleration is insufficient. Further, although the new-generation intact stability criteria for excessive acceleration have been discussed by the International Maritime Organization, the evaluation of JPDF of roll angle and roll angular acceleration could contribute to the efficient evaluation of the safety of crews on board. Meanwhile, no JPDF of roll angle or angular acceleration has been calculated for an arbitrary nonlinear system so far, and there is no doubt that it is a challenging problem. In this study, by applying and extending the idea of the PDF line integral method, we proposed a method for evaluating the JPDF of roll angle and angular acceleration.
Irregular beam seas
Joint PDF of roll angle and angular acceleration
PDF line integral method