Abstract
Generalized methods for deriving the harmonic balance equations are illustrated using a ship roll model with angle dependent cubic damping, and cubic stiffness terms. The balance equations are then solved subject to a phase constraint which identifies the resonant solution only. The amplitude of the response at resonance, and the frequency at which resonance occurs, can therefore be obtained without needing to compute the response over a wide frequency range. This provides an efficient tool for investigating the dependence of the resonant response on the level of input excitation, with results which agree well with more time-consuming simulation methods.
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