# Hub Height vs. First Natural Frequency

Dear all,

does anybody know if there is a specific relationship between the hub height and the first natural frequency (which I suppose corresponds to the bending mode along the for-aft direction) of a wind turbine? I assume the wind turbine is onshore with tapered tower and concrete surface foundation.

Thank you.
Regards

Dear Francesca,

Most modern utility-scale wind turbine towers, regardless of hub height, have their first natural frequency (for the first fore-aft and side-to-side bending modes) located between the once-per revolution (1P) and three-per revolution (3P) frequency. This is known as a “soft-stiff” design. To be precise, for a variable-speed 3-bladed rotor, the lower bound is the 1P frequency at rated rotor speed and the upper bound is the 3P frequency at cut-in rotor speed. (A “soft-soft” design would have the first tower natural frequency below 1P and “stiff-stiff” design would have the first natural frequency above 3P, but these designs are not common.)

I hope that helps.

Best regards,

Just to clarify Jason’s statement in case there is a misunderstanding, the natural frequencies are not actually innate to the towers, but designers typically choose tower properties (mass and stiffness) that will result in soft-stiff designs.

Marshall

Hi

I am trying to simulate the response of the NREL 5 MW OWT on a jacket substructure in 70m water depth, idling under an extreme wind load of 50 m/s. I have built my FE model in DNV-USFOS, with a hub-height of 90m above the MSL. My tower is 68.75 m long, from above the transition piece.

However, when i do a eigen value analysis, the first natural frequency is found to be dipping into the 3P zone (I’m in fact getting values around 0.35 Hz which is along the boundary of the 3P zone). I have modelled the tower using steel density of 8500 kg/m3, as specified in your report, disregarding the bolts and flanges. The only way i could shift my structure into the “soft-stiff” zone is by increasing the tower/hub-height. However, this, i believe, would not be ideal, as the aerodynamic calculations in FAST are based on a hub-height value of 90m.

As Marshall pointed out in the above post, i could reduce the stiffness of the tower (use a lower value for Young’s modulus), which would set my natural frequency in the “soft-stiff” zone, without increasing the tower height. The question i would like to ask is whether such tuning of natural frequencies by changing stiffness properties to avoid the resonance be valid for a theoretical study as the one i am doing?

Sincerely

Abhinav K A.

Dear Abhinav,

You should be able to change the FAST input parameters so as to increase the hub height. How is USFOS coupled to FAST?

It may be OK to artificially change the support structure stiffness to obtain a desired natural frequency, but then you may lose a sense of how to construct the real system, if that interests you. When dropping the stiffness, you should also ensure that you don’t it so far so as to increase the tower deflection to unrealistic values.

Best regards,

Dear Jason

Thanks for the reply. There is no coupling between USFOS and FAST in my study. The idea is to model the jacket as an equivalent monopile in FAST for a decoupled analysis. I would like to keep the material properties as real as possible, so i will raise the hub height such that natural frequency falls in the soft-stiff regime.

I would like to know one more thing. I was going through the tower properties in your user manual.

TMassDen - I divided this value with the corresponding cross-sectional area and got mass density 1.1033e+04 kg/m3 - you have specified 8500 kg/m3

TwFAStif - I divided this value with the corresponding MoI and got Young’s modulus as 2.7179e+11 N/m2 you have specified 2.1e+11 N/m2

Is there something wrong with my calculations/formulae?

Sincerely

Abhinav

Dear Abhinav,

I would guess there is something wrong in your calculations, because qualitatively your approach sounds correct.

Best regards,

Hi Jason

It was my mistake. You have mentioned that you have increased the thickness values by 30% to account for the natural frequency. I used the original thickness values. When i use the modified thickness values i’m getting your tower properties.

Thanks

Abhinav