Keywords: nonlinear ship rolling, statistical linearization, capsizing failure, stochastic averaging, seakeeping reliability, sea-wave evolutionary power spectrum.

An approximate analytical technique is developed for assessing the capsizing risk of ships rolling in beam seas subjected to non-white sea-wave excitations. The ship motion is modeled as a nonlinear roll system incorporating both softening and hardening restoring characteristics, nonlinear damping, and evolutionary stochastic excitation representative of ocean conditions. A stochastic averaging method is employed to derive time-dependent seakeeping probabilities in a computationally efficient manner. The method accounts for both bounded and unbounded ship roll motion associated with negative stiffness regions by introducing a tailored form of the non-stationary response amplitude probability density function (PDF), specifically designed to capture this critical ship dynamics behavior. A notable strength of the approach is its ability to handle stochastic excitations with time-varying intensity and frequency content, as commonly encountered in open-sea environments. Numerical examples involving nonlinear ship roll models are presented whereas comparisons with pertinent Monte Carlo simulation data demonstrate the efficiency and accuracy of the proposed technique.

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