A nonlinear probabilistic method for predicting vessel capsizing in random beam seas

Abstract

The capsizing of vessels in random beam seas is investigated using a single degree-of-freedom model which is limited to the roll motion. Several factors, including sea wave spectrum, nonlinear righting moment characteristics, and nonlinear damping, are taken into account in the analysis. A nonlinear probabilistic method is developed by combining ideas from modern nonlinear dynamics (specifically, the Melnikov function and the phase space area flux) and random vibrations. Conditions for the onset of vessel capsizing are obtained in terms of the sea state characteristics (significant wave height and characteristic wave period) and the vessel parameters (damping and stiffness coefficients). Extensive numerical simulations are carried out to demonstrate the validity of the analytical results. It is found that there exists an excellent correlation between the rate of phase space flux and the probability of capsizing.

Efficient estimation of extreme non-linear roll motions using the first-order reliability method (FORM)

“…Most of these procedures are based on simplifying, but often reasonable, assumptions such as equivalent linear damping (Bulian and Francescutto 7 ), second-or third-order perturbation procedures (Neves and Rodriguez 8 ), Melnikov functions (Hsieh at al. 9 and Spyrou 10 ), and moment closure techniques (Ness et al 11 ).…”

Capsize criteria for ship models with memory-dependent hydrodynamics and random excitation

“…Descriptions of this technique in the context of ship capsize can be found in the literature. The Melnikov theory for the usual roll di¬erential equation has been considered in detail for both harmonic and random excitation (Falzarano et al 1992, Hsieh et al . 1994Jiang et al .…”

Analytical method of capsizing probability in the time domain for ships in the random beam seas

“…Francescutto studied the bifurcation and chaotic phenomena of the ship roll when the wave is assumed as a narrowband spectrum [5]. Troesch et al introduced phase flux rate and studied the capsizing of biased ships [6]. The capsizing probability of ships cannot be predicted quantitatively by all of the above mentioned methods.…”