Generalized damping is calculated for a quality check of the hydrodynamic damping coefficients.
The structural mass eigen space 
is introduced, such that
 | (4–72) |
where 
is the structural mass matrix, 
, n = 6 x 
(where 
is the number of hydrodynamic interaction structures), and 
.
The eigenvector satisfies
 | (4–73) |
Defining a new diagonal matrix:
 | (4–74) |
the square root mass matrix is written as:
 | (4–75) |
Denoting 
as the hydrodynamic damping matrix at the frequency 
, the normalized damping matrix is given as:
 | (4–76) |
Note: The hydrodynamic damping matrix 
consists of the diffraction panel induced damping and the
frequency-independent damping.
The damping eigensolution is:
 | (4–77) |
where 
and 
(
) is considered the generalized damping at the motion mode i , which should generally be positive.
The generalized damping is checked when the radiation force is evaluated by the convolution integration approach in a time domain analysis (see Radiation Force by Convolution Integration).
If 
is negative, denoting the 
-th eigenvector in the matrix 
as
 | (4–78) |
it is recommended that you add the frequency-independent diagonal damping coefficients for some dominant motions in this eigenvector. The value is suggested to not be less than
 | (4–79) |
where 
is the structural mass or moment of inertia of the 
-th motion of the 
-th structure.