Consequences of a Non-Linear Asymmetric Restoring Force on the Offshore Barge Rolling Motion

A certain barge widely used for offshore operations in Brazil has a ramp to allow riser and pipeline installations. This ramp crosses the free surface, leading to a non-linear restoring force. The restoring force is also asymmetric, since the ramp is placed in starboard side. Because of the irregular geometry, the predicted hydrodynamic behavior obtained considering potential theory is affected. It is usual consider using duffing equation (inclusion of a cubic term in restoring force) to reproduce GZ curve for analysis at large angles. Although non-linear, the behavior of Duffing model (limits of stability) has been stressed by scientific community and can be considered well-known. Unfortunately, for this analysis, duffing model is not the most appropriated to be used, because of the asymmetry. A quadratic model of restoring force may present better results describing roll evolution and should be investigated. Several studies have been done to improve the dynamic behavior of the barge. As a part of this effort, model tests have been conducted to allow the installation of bilge keels to control the rolling behavior. This was a good opportunity to access the non-linear behavior what will permit comparison with theoretical analysis.