Traditional naval architecture analysis of ship survival-ability involves analyzing the vessel righting arm curve in isolation or as compared to a steady wind heeling moment. It is well known that ships do not capsize in calm water and infinite time but do so in rough seas and do so dynamically in short time. Understanding the shortcomings of the traditional approach especially for advanced vessels numerous researchers in the ship dynamics field have proposed an alternative view of ship stability analysis, which involves dynamical analysis. Unfortunately, most ship motions analysis is linear and uses ideal flow theory both of which are inadequate descriptions of large amplitude ship rolling motion. Moreover, much of engineering nonlinear vibrations analysis involves perturbation methods where the nonlinearity is assumed small. Numerical simulation and physical model testing to find this critical behavior is time consuming and expensive. An alternative approach involves directly calculating critical behavior. This approach was originally developed for periodic forcing at a single frequency possibly the linear natural frequency. However, nonlinear resonance is much more complicated than linear resonance and more than a single frequency, multi-valued behavior can occur over a range of frequencies. Moreover, the phenomena which are possible for a nonlinear system are much more varied and diverse. In this paper we will analyze a traditional displacement hull form’s critical response in harmonic waves at the system’s linear natural frequency and compare this to the system’s critical response in random waves. We will compare these responses for different values of damping using these different analysis techniques.

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