Dynamics and control of ship-mounted cranes

When deep water ports are not accessible, cargo is transferred from/to larg er ships to/from smaller ships offshore. A typical arrangement is to place three ships side by side. In the middle is a ship with cranes. Along one si de of the crane ship is the large container ship, and along the other side is the small ship or lighter, which shuttles back and forth between the shi ps and shore. The sea state is a very important factor in this operation. T he sea-excited motion of the crane ship can excite large pendulations of th e containers while they are suspended by the cables of the cranes. The larg e motions can be due to either large excitation amplitudes or small excitat ion amplitudes near resonant conditions. In this study, the cable-suspended load is modeled as an elastic spherical pendulum. The method of multiple s cales is used to derive four nonlinear ordinary-differential equations that describe the amplitudes and phases of the excited modes. These equations a re used to investigate instabilities and provide information for controllin g the pendulations. The results show that a parametric excitation at twice the natural frequency leads to a sudden jump in the response as the cable i s unreeled. Introducing a harmonic change in the cable length at the same f requency as the excitation can suppress this dynamic instability and result in a smooth response. The analytical results are verified by numerical sim ulations of the original full nonlinear equations.