RESPONSES OF A NONLINEARLY COUPLED PITCH-ROLL SHIP MODEL UNDER HARMONIC EXCITATION

Stationary responses of nonlinearly coupled pitch and roll ship modes are studied using a modified averaging method, along with two second o rder multiple time scale (MTS) methods for comparison. Stability of th e solutions is also studied. In the case of harmonic excitation all th e three methods give fairly accurate results to the original problem b ut the averaging method is the most efficient. Analytic solutions are obtained from the averaged equations, which can be used to predict sta tionary responses both for small and for large excitations. From the a veraging method several qualitatively different phenomena which cannot be addressed by the first order theory have been obtained: (i) the sa turation phenomenon is lost, (ii) the bifurcation points are altered a nd (iii) a drift term is present which, although small, appears to hav e a significant effect on the accuracy of the solutions.