4.5. Response Amplitude Operators with Additional Input

In the previous section, it is assumed that each structure in a hydrodynamic interaction structure system is purely modeled by panel elements. The response amplitude operators (RAOs) of a free-floating hydrodynamic interaction structure system are determined by Equation 4–49.

In Aqwa, it is also possible to model each structure by a mixture of panels and Morison elements (discussed in Morison Element Forces). The following parameters of Morison elements are added in the equation of motion in the frequency domain:

  • Tube and slender tube structural mass and moment of inertia with respect to the center of gravity of structure

  • Hydrostatic stiffness matrix due to tube and slender tube elements

  • Added mass matrix of tube and slender tube elements and flooded fluid mass inside the opened tube elements

  • Froude-Krylov and wave inertia force and moment on tube and slender tube elements

In addition, the wave frequency dependent hydrodynamic parameters and the linear hydrostatic stiffness matrix of one or more structures can be changed or appended. The additional structural stiffness matrix can also be defined.

The equation of motion given by Equation 4–49 may be extended as

(4–52)

where is the total structural mass matrix, is the total added mass matrix due to diffracting panels and Morison elements (or the amended added mass matrix input), is the user-defined additional added mass matrix, is the hydrodynamic damping matrix by the diffracting panel elements (or the amended hydrodynamic damping matrix input), is the user-defined additional linear hydrodynamic damping (which could be the equivalent linear damping values to compensate for the viscous and eddy drag effects), is the assembled hydrostatic stiffness matrix (calculated or user-defined), is the user-defined additional hydrostatic stiffness matrix, is the additional structural stiffness matrix, and are the total Froude-Krylov and diffracting force and moments (calculated or user-defined).