THE EFFECT OF A CONSTANT HEELING MOMENT ON THE MAIN AND SUPERHARMONIC ROLL RESPONSE OF A SHIP IN REGULAR BEAM SEAS

The generalised harmonic balance method is used to investigate the dc, fundamental, second and third harmonic components in the roll response of a biased ship in regular beam waves. The resulting four balance equations then yield both the main resonance response, and the dominant superharmonic resonances (if any), which are compared to the unbiased case. Differences in the behaviour of ship models with roll stiffening, or roll softening righting moments under biased conditions are also investigated, and are found to be significant. The results for all these cases have been validated against simulation, and the two show excellent agreement across the frequency range considered.