The Effect of Water on Deck on the Roll Bifurcation of Crafts under Random Waves

Abstract

The stability of the roll motion of crafts is of great importance because of its significant impact on safety, ease of travel, overall performance and potential capsizing of the system. It is important to study this motion and to investigate its dynamic stability, which is completely nonlinear and highly sensitive to atmospheric conditions, asymmetric loads and the presence of water on the deck. In this research, it was tried to study the stability of the roll motion under the pointed conditions and random white-noise waves analytically. To do this, the probability density function of response was obtained using the Fokker Planck Kolmogorov (FPK) method and the stationary solution of the corresponding partial differential equation. Then, the effect of water on the deck, deviation moment due to the asymmetric load or crossing winds, the damping coefficient and the intensity of the random wave was investigated. Introducing non-dimensional parameters, the equation of roll motion was derived so that it could be applied to a wide range types of crafts. The results, as expected, indicate a significant qualitative change i.e. a bifurcation in the behavior when we have water on the deck. The stability of three types of the crafts is also studied and it is shown that in the presence of water on the deck, the type of craft can completely effect on instability phenomenon.

Keywords

• dynamic stability
• roll stability
• fpk equation
• bifurcation
• stochastic analysis