Abstract
The transfer operation of a crane ship becomes dangerous when sea state 3 is reached. The sea state may directly or indirectly cause large motions of the container being hoisted by creating instabilities of the crane load's motion. A simplified model is studied and used to illustrate how the instabilities could arise due to the combination of a one-to-one internal resonance and a primary (additive) resonance or a parametric (multiplicative) resonance. The method of multiple scales is used to derive four ordinarydifferential equations describing the amplitudes and phases of the two modes. The resulting two sets of modulation equations are used to study the equilibrium and dynamic solutions and their stability. The response could be a single-mode solution or a twomode solution. A combination of a shooting technique and Floquet theory is used to calculate limit cycles and ascertain their stability. The numerical results indicate the existence of a sequence of perioddoubling bifurcations that culminates in chaos, multiple attractors, intermittency of type I, and cyclicfold bifurcations. The excitation parameters that lead to complex motions, including chaos, are identified.
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