# Simplified model of wind turbine tower

Hi all,

I’m new on this forum.I’m an Italian student whose graduation thesis is about wind turbine structural analysis.

I know that FAST uses a flexible-multibody approach to model the wind turbine , and that blades and tower are modelled as cantilavier euler-bernoulli beams.
My aim now is to create a “simplified” dynamical model of the tower and make a comparison with FAST results and eventually(I think surely) explain the differences due to my semplification.

Searching on the internet i found out that a common model for the tower is based on a cantilavier euler-bernoulli beam with a lumped mass on the top.

I’d like to know if you think that this model can give me reasonable results( displacement and internal reactions) that can capture the general dynamics of the system and in that case:

1-How would you model the forces acting on this simplified system? (I’m thinkin about an axial force that represents the hub and blades weight,an harmonic force to model the centrifugal force due to the rotation of the blades and a distribuited force along the tower to model the aerodynamic force.)

2-Can you suggest me any reference material that explains the mathematics behind the euler bernoulli theory used in FAST ?(expecially about how you introduced the damping in euler-bernoulli equation) I think that studying this could help me with the comparison I have to do.

Thank you very much !

Alessandro

Dear Alessandro,

If you are interesting in the dynamic response of the tower, without specific interest in blade dynamics/loading, I suppose it would be reasonable to model a cantilevered beam with a lumped mass and inertia at the tower top. Make sure that you include the rotational inertia of the tower top in addition to the mass, as this effect tends to be large for most wind turbines. For a 3-bladed rigid rotor, this inertia would be fixed, but for a 2-bladed rotor, this inertia would be periodic. Depending on the tower-top weight and/or deflection of the tower, geometric nonlinearities (e.g. the axial shortening and p-delta effect) may be important, as are included in the structural model of FAST v7 and ElastoDyn module of FAST v8. For a rigid rotor, the centrifugal forces will balance out with respect to the tower-top loading, but gyroscopic terms may be important. Aerodynamically, you’d want to capture ideally all six components of the rotor load (3 forces including thrust, 3 moments include torque).

Information on the theory basis of the structural model of FAST v7 and the ElastoDyn module of FAST v8 is provided in the following forum topic: http://forums.nrel.gov/t/coupled-blade-modes-in-fast/314/1.

Best regards,

Dear Jason,