Abstract
For ships, rolling motion is the most critical due to the possibility of capsizing. In a regular (periodic) sea, if no bounded steady state solutions exist, then capsizing may be imminent. Determining for exactly which wave amplitude and frequency the steady-state solutions disappear or become unstable is of great practical importance.
In previous works (Falzarano, Esparza, and Taz Ul Mulk, 1994) and abstracted presentations (Falzarano, 1993), the global transient dynamics of large amplitude ship rolling motion was studied. The effect on the steady-state solutions of changing wave frequency for a fixed wave amplitudes was studied. It was shown how the in-phase and out-of-phase solutions evolve as the frequency passes through the linear natural frequency. For small wave amplitudes (external forcing) there exists a single steady-state throughout the frequency range, for moderate wave amplitudes there exists a frequency range where multiple steady state harmonic solutions exists. As the wave amplitude was increased further there existed a frequency range where no steady-state harmonic solution existed.
In the present work, the very large amplitude ship rolling motion in the region where no steady-state solutions exist will be studied in more detail. Moreover, the mechanisms (bifurcations) that cause this type of behavior to evolve from more simple behavior will be studied using a combination of both frequency response curves and Poincaré maps. It is expected that global chaotic bifurcations such as those previously described (e.g., Thompson and Stewart, 1989) will be identified.
Wavelet Analysis for Ship Rolling Motion of Purse Seiners in North Sulawesi, Indonesia
