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Abstract

The stochastic chaotic motion and the threshold intensity of the external excitation force for onset of chaos of the ships in random beam waves are studied by the nonlinear stochastic dynamics theory. The random differential equation of ships’ rolling motion is established with considering the nonlinear damping, nonlinear restoring moment and the white noise wave excitation. The random Melnikov mean-square criterion is used to determine the threshold intensity for onset of chaos. The probability density function of the rolling response is calculated through solving the stochastic differential equations by applying the path integral method in the chaotic region. It is found that the ships undergo stochastic chaotic motion when the real intensity of the white noise exceeds the threshold intensity, the stable probability density function of the roll response has two peaks and the random jump happens in the response of the system for high intensity of the white noise excitation. The chaotic response is further investigated via numerical results of the system.

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