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University of New South Wales, Australia

The computed results seem to show that there is much more nonlinearity in the responses for the forces and moments than for the motions themselves. Is this simply due to the factor that the frequencies associated with the harmonics are higher and that the forces and moments depend on temporal derivatives of the motions?


As mentioned by the discussor, the measured hull girder loads showed a much more pronounced nonlinear behavior than the motions did. To explain this phenomenon, it is necessary to explain the physical origin of the loads. In general, hull girder loads are defined as the forces and moments in a hull cross-section, i.e., the “internal loads,” which make equilibrium with the net external forces and moments and the inertial reactions of the ship. The external loads are the net result of a pressure integration over the hull surface.

There are two reasons for the observation of much more pronounced nonlinearities in the hull-girder loads than in the motion responses. The first reason is the dominance of inertial effects in the hull girder loads. As illustrated by equation (2), the relative magnitudes of amplitudes of higher order effects in time-varying signals are increased simply by a time-derivation of the signal. It should be understood that the acceleration of the vessel is the net result of the global mass inertia characteristics of the vessel and of the overall excitation forces. The second reason is the sensitivity of hull girder loads to local external forces. Locally, the external forces acting on a part of the vessel can behave much more nonlinearly than the overall forces. This is because the local nonlinear force contributions are smoothed out over the whole surface. The internal loads are directly affected by these local nonlinearities in the bow and aft region of the vessel, especially in the case of bow flare in combination with large relative motions. Even then, it is possible that hardly any nonlinear behavior can be observed in the motion responses.

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