An aid to operating decisions based on nonlinear response of a crane bargein waves

A nine-degree-of-freedom time domain mathematical model was used to numeric ally simulate crane ship dynamics. This model considers the elasticity and damping of the hoisting rope assembly and includes arbitrary, biangular swi ng of the suspended hook-load coupled with surge, sway, heave, roll, pitch, and yaw motions of the hull. The linear frequency-dependent hydrodynamic r esponse to the hull's own motions accounted for memory effects that were ap proximated in the time domain by a finite state space model. The nonlinear hydrodynamic drag force acting on the oscillating hull was quadratically ap proximated using an empirical drag coefficient. The incident wave force on the hull consisted of the first-order force oscillating at wave frequency a nd the second-order slowly varying wave drift force; The nonlinear horizont al mooring system restoring force was approximated by a third-order polynom ial. To specify operating limits for a shear-leg crane barge in a heavy lif t offshore operation, a stochastic analysis was performed based on the syst em's simulated dynamic response in an ensemble of natural seaways.