Dear Pierre-Yves,
When you say you don’t find the same natural frequencies as reported in the NREL 5-MW specifications report from 2009, how different are the results?
Regarding deriving natural frequencies from the nonlinear solution, natural frequencies can by found through FAST linearization followed by eigenanalysis or by exciting the system with broadband excitation and examining the FFT/PSD of the time-series response, as has been discussed many times in this forum.
Modes (nwtc.nrel.gov/BModes) be used in place of Modes: Tower Eigenfrequencies of NREL 5MW Turbine.
Best regards,