Inertial and hydrodynamic inertial loads on floating units

The analysis of the dynamic behavior of floating units usually employs a coordinate system with origin in the unit's center of gravity, which significantly simplifies the global mass matrix. Hydrodynamic coefficients are then computed considering the same coordinate system. However, to analyze other conditions of mass distribution and maintain the simplicity of a global mass matrix, it is necessary to determine again the hydrodynamic coefficients, thereby reducing the efficiency of the entire process. Another important point is that the geometries frequently used in floating units are such that the cross-terms of an added mass are relatively unimportant when compared with the main terms, and it is, therefore, common to use only some of them to analyze the unit's dynamic behavior. Recently, however, in the search for production systems suitable for water depths greater than 3000 m, other geometries have been considered in technical and economic feasibility studies. It is possible that for these new geometries all terms of the added mass matrix must be included in the analysis. This paper presents the full development used to determine the complete global mass matrix, the inertial and hydrodynamic inertial loads that make use of the added mass matrices considering any coordinate system and the six degrees of freedom, including all cross-terms.