Influence of varying restoring moment curve on parametric roll motion of ships in regular longitudinal waves

Influence of variable acceleration on parametric roll motion of a container ship

“…In this study, restoring moment surface was predicted by only wave crest and wave trough restoring moment levers for practicality and capability of solution in frequency domain. Pesman and Taylan show that the simplification does not affect the results in acceptable accuracy [18]. Analytic restoring moment surface utilized in roll motion equation is given in Figure 2.…”

“…Simple model is based on one degree of freedom parametric roll motion equation which includes ship velocity, heave and pitch effects by means of time in restoring moment variation [17,18]. Restoring moment is also excitation moment in head waves.…”

Numerical and Analytical Approaches for Roll Motion Analysis in Regular Longitudinal Waves

“…6 DOF and 4 DOF time domain simulation approaches were applied by using AQWA-LINE and AQWA-NAUT software which are capable of calculating motions by using 3D diffraction/radiation and potential flow theory. The single -DOF time and frequency domain models based on reducing number of DOF from 3 to 1 by using the quasi-static Froude-Krylov assumption [20,21,22] were used for analytical approaches. In the models, heave and pitch effects were considered by means of time varying restoring moment [20,21,22].…”

“…The single -DOF time and frequency domain models based on reducing number of DOF from 3 to 1 by using the quasi-static Froude-Krylov assumption [20,21,22] were used for analytical approaches. In the models, heave and pitch effects were considered by means of time varying restoring moment [20,21,22]. Basically, three analytical approaches were used in the present study.…”

“…Basically, three analytical approaches were used in the present study. The first is Bulian's PolyFour Model, the other one is the simplified model which may be considered a simplified version of the first model [21,22] , and the other one is linear model [23]. The accuracy of numerical and analytical approaches were evaluated by comparing experimental results obtained for the sample ship form [21].…”