1P and 3P frequency ranges

Wind & Water Structural Analysis
1

Hi,

I have a question related to the 1st and 2nd natural frequencies of a wind turbine. For the nrel 5mw reference wind turbine, I have calculated the 1st tower Fa and ss as 0,326 Hz and 0,3155 Hz respectively and the 1st drive train torsion as 0,632 Hz. These are out of the 1P and 3P frequency ranges of 0,115 to 0,20 Hz and 0,35 to 0,61 Hz respectively. For a floating offshore wind turbine I would think that again one would want to stay clear of 1P and 3P intervals, but looking into the nrel report for the MIT tlp by Denis Matha, I find that the first platform heave is 0,47 Hz and the 1st tower Fa and ss are 0,63 and 0,57 Hz respectively. Any thoughts on this would be greatly appreciated.

1 Like
2

Dear Jacob,

I agree that one should generally avoid locating structural natural frequencies that coincide with 1P and 3P frequencies in the operational speed range of the wind turbine. However, this may be OK if the excitations that occur at 1P or 3P don’t resonate the mode in question. It is also possible for the control system to be modified to add damping to the modes getting excited or to bypass the resonance altogether–e.g. by adding a notch filter to keep the rotor from resonating a structural natural frequency for long.

For the MIT/NREL TLP, we were aware that the compliance of the TLP raised the tower natural frequency so that it crossed 3P instead of falling between 1P and 3P. However, in our study of the MIT/NREL TLP, we did not notice strong resonance of the tower as a result, so, we did not try to modify the tower design or controller to avoid this.

I hope that helps.

Best regards,

3

Dear Jason,

Once again thank you very much for your quick and great explanation. That helps me a lot.

4

Dear Jason,
I recently built a FWT (semi-submersible type) aeroelastic model in Bladed. The uncoupled tower frequencies seem to avoid the 1P and 3P frequencies. However, the coupled tower natural frequencies from the Campbell diagram are higher and fall into the 3P range. My question is:

  1. Do you think it will be okay to neglect the coupled modes and use the uncoupled mode frequencies as my criteria? Do I risk resonance doing this?
  2. Why are coupled mode frequencies of tower higher than uncoupled frequencies?
    Looking forward to you reply.
    Regards
    Salem
5

Dear @Salem.Okpokparoro,

It is the coupled frequencies of the tower that are important for floating wind applications. By “coupled”, I mean tower natural frequencies that depend on the appropriate boundary conditions at the tower base and tower top. At the tower top, the mass, center of mass, and inertia of the rotor-nacelle assembly will impact the tower natural frequencies. At the tower base, the mass, center of mass, and inertia of the floating substructure, hydrodynamic added mass, and hydrostatic and stationkeeping system stiffness are likely all important. Structurally flexibility of the RNA and substructure could also impact the tower natural frequencies.

Regarding why the natural frequencies of the tower change when the tower is attached to a floating platform, consider the following explanation:

For a uniform beam of length L, mass per unit length m and bending stiffness EI, the analytical solution for the first bending natural frequency (omega_1) of a fixed-free (cantilevered) and free-free beam is:

omega_1 = 3.516SQRT( EI/mL^4 ) for fixed-free (cantilevered)
omega_1 = 22.37SQRT( EI/mL^4) for free-free

(e.g., see: Thomsen, W.T. and Dahleh, M.D., Theory of Vibration with Applications 5th Edition, Prentice Hal, 1998)

While the free-free beam has zero-frequency (rigid-body) modes not seen in the cantilevered beam, the bending modes are actually of higher frequency for the free-free beam. This is because the free-free mode has a node midway along the beam.

While an FOWT is not the same as a uniform free-free beam, the effect is similar. The tower base is cantilevered to a floating substructure that is not fixed, but has mass/inertia (from body mass and hydrodynamic added mass) and stiffness (hydrostatic, mooring). As the mass and stiffness of the floater decrease, the boundary condition would approach a “free” condition; likewise, as the mass and stiffness of the floater increase, the boundary condition would approach a cantilevered condition. Most floaters will lie somewhere in between these two extremes, but in most practical cases, the floating boundary condition increases the tower-bending natural frequencies.

FYI: I can’t speak to how Bladed captures these effects. I would suggest contacting Bladed technical support for Bladed-related questions.

Best regards,

6

Dear @Jason.Jonkman
Many thanks for your copious elucidation. Very much appreciated. Thanks.
Regards
Salem