Stationary responses of nonlinearly coupled pitch and roll ship modes are studied using a modified averaging method, along with two second order multiple time scale (MTS) methods for comparison. Stability of the solutions is also studied. In the case of harmonic excitation all the three methods give fairly accurate results to the original problem but the averaging method is the most efficient. Analytic solutions are obtained from the averaged equations, which can be used to predict stationary responses both for small and for large excitations. From the averaging method several qualitatively different phenomena which cannot be addressed by the first order theory have been obtained: (i) the saturation phenomenon is lost, (ii) the bifurcation points are altered and (iii) a drift term is present which, although small, appears to have a significant effect on the accuracy of the solutions.
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Pan, R., Davies, H.G. Responses of a non-linearly coupled pitch-roll ship model under harmonic excitation. Nonlinear Dyn 9, 349–368 (1996). https://doi.org/10.1007/BF01833361
- Averaging method
- internal resonance
- nonlinear oscillation