This paper investigates methods of simulating the combined wave frequency and low-frequency wave drift forces and motion responses of floating systems. This is motivated by the requirement for estimates of response statistics for systems on nonlinear moorings. Results are given for a linear system for which experimental data are available (an articulated column model); and for a moored barge on mildly and strongly nonlinear moorings. Estimates are obtained for low-frequency spectra, linear and quadratic transfer functions, response probability distributions, and peak distributions.

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