Abstract
The characteristic features of subharmonic oscillations in the nonlinear rolling of a ship are investigated. The mathematical model used for this purpose is given by a second order differential equation taking into account both the righting moment and the damping nonlinearities. The righting moment is expressed by a cubic polynomial, whereas the damping effects are nonlinear both in angle and angular velocity.
Particular attention is devoted to subharmonics for the case of a ship in upright equilibrium position. It has been proved that a subharmonic oscillation with tuning factor 3 can be present only after the excitation intensity has exceeded a threshold level. The phenomenon can be particularly dangerous for ships whose righting moment shows a strong departure from the linearity. This occurs in particular for modern container ships.
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