Stochastic bifurcation and chaos analysis for a class of ships rolling motion under non-smooth perturbation and random excitation

Abstract

The actions of wind and wave have a great influence on the ship rolling motion, which may cause chaotic situation even capsizing. Stochastic bifurcation and chaos for a class of ships rolling motion in longitudinal waves under non-smooth perturbation and random excitation, i.e., the effects of wind and wave, is studied by analytical and numerical methods. The stationary probability density function (SPDF) for rolling motion is obtained through the stochastic averaging method as well as stochastic phenomenological (P) bifurcation is analysed by the qualitative change of it. The parameter conditions for chaos are strictly derived through Melnikov method and random Melnikov method, respectively. Chaotic regions and characteristics of systems parameters are illustrated and discussed in detail. In addition, taking the maritime patrol ship as an example, the analytical results as well as the effects of parameter excitation and noise on chaos are verified and analysed by relevant numerical simulations. These results demonstrate that changing parameter excitation amplitude or noise intensity can induce or suppress chaos.