On the parametric excitation of nonlinear rolling motion in random seas

Abstract

The nonlinear equation of rolling motion in random oblique seas is analysed considering parametric excitation caused by transverse stability variation in realistic seaway. Use of Bogoliubov-Mitropolsky’s method of slowly varying parameters together with Stratanovich-Khasminsky’s stochastic averaging is made to obtain an equation describing the variance of the amplitude of rolling motion as a function of time. The condition for stable motion is then derived. Furthermore, stationary variance is expressed in a closed form.