# Damping and shift in natural frequency

Hello everyone,

I am doing a MDOF model for the IEA 15 MW. I obtained good agreement with the natural frequency in the technical report. However, when I add the damping matrix and doing a free decay for the tower in FA direction, the PSD shows a shift in the frequency around 4.5 % . I repeated the same test but for the undamped system and the PSD gives me the exact value !

Has anyone encountered this problem and succeeded in solving it?

Best regards,

If I understand what you are saying, the frequency you derive from a tower free-decay simulation shifts by 4.5% when adding damping; is that correct? Can you clarify what you mean by “add the damping matrix”? Are you referring to ElastoDyn tower input `TwrFADmp`(1)? What level of damping did you add?

Best regards,

Dear @Jason.Jonkman,

I swear to God i don’t know what happened !!!
When i am writing to reply, i want to attach some figures and here is the surprise. It works !!!

In fact, you are right . I was extracting the natural frequencies and the eigenvectors using
|-omega_square*[M] + [K]| = 0. And to be more sure, i was running a decay test without damping and doing a PSD for the response. I was doing this for the tower in FA and i obtained nearly the same results. But, when i added damping matrix then doing a decay test for the tower in FA and doing a PSD, the frequency that i obtained was shifted a little bit.
But now the problem is solved !!!

Sorry for bothering you !

Kindly find attached the frequency obtained using det(-omega_square*[M]+[K]) = 0 :

Also, kindly find attached the PSD in dB in the presence of damping :

Thank you again and sorry for bothering you

Best regards,