UC San Diego

The behavior of a system consisting of two ships connected by a ramp subject to external forcing from ocean waves is a relevant issue when considering the possible transportation of cargo. The resulting motions of the interconnected dynamical system can be extremely complex due to the nonlinear nature of the problem. As such, the development of a mathematical model is bypassed in favor of a computer-based method using MATLAB, Simulink, and SimMechanics. In order to maintain a reasonable level of complexity, this method rests on several assumptions and simplifications such as the modeling of the ocean waves as sinusoidal surface forces. The effects of altering the ramp length and the ocean wave incidence angle on the motions of the system are explored, where special attention is given to the angles formed between the ramp and the ships, as they are quantities that need to be minimized. Surface plots are generated which highlight the dependence of these angles on the length of the ramp and wave orientation, and it is concluded that for longer ramp lengths and wavefront angles of about 62⁰ from the ship- ramp-ship axis, the angles are reduced. A penalty function is then created based on the knowledge that increasing the ramp length results in a prohibitive weight and fails to decrease the roll component of the angles. With this penalty included, the surface plots assume a more convex shape with well-defined minima. The method of extremum seeking is then given, and its applicability to this system is discussed