Introduction Some of the classical nonlinear and time-varying equations of engineering mathematics appear in the modeling of the dynamic behavior of offshore structures. The dynamics of free-hanging risers, tension leg platforms and suspended loads can be cast in the form of Mathieu's equation; wave excitation causes the time variation of the spring parameter (references Disturbingly large subharmonic resonances or chaotic motions can result if the nonlinear equations (reference [4]) or the spring in the Mathieu equation varies harmonically (reference [1] ). This paper presents physical and mathematical arguments which indicate that these large responses are caused by a phase lock between the motion of the structure and the external excitation, something which is generally unlikely to last for long if a structure is subject to a random excitation. To test these predictions, two typical systems are simulated and randomness is introduced into the previously regular forcing in three different ways; as additive white noise, as frequency wander and as bandwidth spread. The responses are Fourier analyzed and maximum, minimum, mean and rms values are recorded. Random inputs cause the Poincare points to wander in a "Poincare region"; these are displayed as a function of the randomness parameter. The size of the subharmonic motions decays quickly with increasing values of the randomness parameter and they are generally small for realistically random wave forcing signals. Where the motion of a vessel is a significant input to a dynamic system, the filtering action of the vessel's dynamics driven by the wave action can generate a relatively regular motion; Pate
