Stability of ships with water on deck in random beam waves

摘要

We study the stability of small ships with water on deck in random beam waves from a probability perspective. Previous research has shown that this kind of ship motion is governed by two dynamical regions: Homoclinic and heteroclinic, where the heteroclinic model emulates symmetric vessel capsize and the homoclinic model represents a vessel with an initial bias caused by water on deck. We investigate the stability and capsizing of ships in the homoclinic region using the probability method and nonlinear stochastic dynamics theory. Simplifying the random wave excitation to a periodic force and white noise perturbation, the random Melnikov mean square criterion is used to determine the parameter domain for the ship's stochastic chaotic motion. The probability density function of the roll response is calculated by solving the stochastic differential equations using the path integral method. A mathematical example is presented. It is found that in the chaotic parameter region, the probability density function of the system has two peaks. The response of the system will jump from one peak to another for large amplitudes of periodic excitation. This will lead to instability and even capsizing.