Dear Charlie,
I think the natural frequencies you’ve derived for the OC4-DeepCwind semisubmersible are quite reasonable. Please note that Test25 is a model of the NREL 5-MW turbine atop the OC4-DeepCwind semisubmersible design, which was analyzed in IEA Wind Task 30 OC4 Phase II. The actual DeepCwind wave-tank tests used a scaled system with similar, but not identical, properties (at scale). So, the modeling results from Test 25 should be more similar to the results published in the IEA Wind Task 30 paper than in the Coulling et al paper.
The approach you are using to derive the natural frequencies is quite reasonable, except for the tower modes, which may be off a bit. The natural frequencies of a tower cantilevered to a floating platform are typically a bit higher than the natural frequencies of a tower cantilevered to the inertial frame, due the different tower-base boundary conditions. You can derive a more accurate frequency e.g. through free-decay of the tower with the platform DOFs (and still-water hydrodynamics and moorings) enabled, or through post-processing of a simulation with white-noise excitation (there are other posts on this forum that discuss these topics). That said, we are currently working on the addition of linearization functionality for floating offshore wind turbines within OpenFAST, which will enable full-system eigenanalysis, including the effects of platform DOFs, hydrodynamics, and moorings. We are presenting the theoretical basis for this new functionality next week at the IOWTC conference in San Francisco, CA (USA) and expect to present the verification results at the DeepWind 2019 conference next January in Trondheim, Norway.
Best regards,