Frequency-domain seakeeping

Frequency-domain seakeeping is linear analysis of ship motions in waves using response amplitude operators (RAOs), the complex transfer functions giving motion amplitude and phase per unit wave amplitude at each encounter frequency. Linearized equations of motion (mass plus frequency-dependent added mass, radiation damping, and hydrostatic restoring, forced by Froude-Krylov plus diffraction excitation) are solved for the six rigid-body modes by strip theory or three-dimensional panel methods. The response spectrum of any motion or load follows by multiplying the squared RAO by the wave spectrum, and short-term statistics come from the response spectral moments under a Rayleigh assumption. It is fast and underlies operability and long-term load prediction, but omits nonlinear effects like large-amplitude roll and slamming.