Eigenvalue in BModes

[Ran.Tu]

@Jason.Jonkman

*Because the stiffness-proportional constant is calculated only for the isolated tower, the damping of the tower-bending modes when coupled with the platform and RNA may be different than specified (i.e., the damping ratio derived for the tower-bending modes through a FAST linearization analysis of the full wind turbine system may differ from what is specified for the isolated tower in the FAST input file).

Dear Jason,

After reading your reply, I get something new. Could you please help me to correct my understanding?

1. In Elastodyn, we defined a critical damping ratio for blade and tower. But when implementing this critical damping ratio in code, it is transformed to a stiffness-proportional constant.

2. After doing linearization and running runCampbell.m Matlab code, we also get a damping ratio:
   

   
   
   In above figure, Damping ratio is a stiffness-proportional constant for entire system’s stiffness matrix.

3. Here damping ratio (stiffness-proportional constant) = 0.003683, natural frequency = 0.313523, so the critical damping ratio:

critical damping ratio = stiffness-proportional constant * pi * natural frequency
                       =  0.003683 * 3.14159 * 0.313523
                       = 0.00362
                       = 0.36 %

I am not sure whether this derived critical damping ratio is reasonable. This is an onshore wind turbine, without wind and wave. I assigned 1% critical damping ratio for both blade and tower in Elastodyn. No intial rotor speed was assigned. I would assume that hub mass and nacelle mass increase the mass matrix for entire system, and then decrease the critical damping ratio to 0.36% for entire system.
Regards,
Ran