Eigenvalue calculation

Natural periods and eigen vectors are calculated for selected modes. The calculation is based on a linearized model of the system. Mass and stiffness matrices are calculated, and the system solved by a standard Jacobian solver. The effect of damping is not included in the analysis.

The mass matrix is built from the virtual mass matrix, including both structural and hydrodynamic mass. The frequency dependency of the latter is not accounted for in the analysis as asymptotic values are used. For bodies of type 1 (see the chapter Body) this means added mass at infinite frequency, while the added mass at zero frequency is used for bodies of type 2.

The secant stiffness for the user selected modes is calculated at the initial position. The user may choose to specify the secant excursion used in the calculation for each mode. The stiffness matrix is made symmetric.

For each natural period, the eigen vectors expresses the relative contribution from each mode. Translations are given in the length unit \(\mathrm{[L]}\) and rotations in degrees \(\mathrm{[deg]}\).

In the interpretation of the results, it should be kept in mind that damping is not included in the analysis. Modes that are heavily damped may thereby not be recognized in time domain simulation results.

Observe also that environmental forces are not included. Thus, the yaw motion of a turret moored or a single point moored vessel can not be checked by an eigenvalue analysis.