Floating systems, such as ships, barges or semi-submersibles, show a dynamical behavior which is determined by their internal structure and the operating conditions caused by external forces e.g. due to waves and wind. Due to the complexity of the system which commonly includes coupling of multiple components or nonlinear restoring forces, the response can exhibit inherently nonlinear characteristics. In this paper different models of floating systems are considered. For the idealized case of purely harmonic forcing they all show nonlinear behavior such as subharmonic motion or different steady state responses at constant operating conditions. The introduction of random disturbances leads to deviations from the idealized case which may change the overall response significantly. Advantages and limitations of the different mathematical models and the applied numerical techniques are discussed.

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