Comparison of the natural frequencies of a reference wind turbine blade using the finite element method with Euler-Bernoulli and Timoshenko beam formulations

Resumo

The development of horizontal axis wind turbines brought longer blades and taller towers, which incurs
in structures more susceptible to vibration problems. The vibrational behavior of the blades and the tower are
studied separately at a first stage and each structure is typically modeled as a cantilever beam, with the aid of the
finite element method. The most common beam models are the Euler-Bernoulli Beam Model and Timoshenko
Beam Model, both used on this work. The key differences between those two models are that the shear stress and
the rotatory inertia effects are ignored on the first one, which generate some discrepancies among the results. In
the present work, a finite element method code is implemented for both beam formulations to determine the natural
frequencies of a reference wind turbine blade, whose properties were obtained in the literature. The code was first
validated by comparing the computed and theoretical results for a cantilever beam with rectangular cross section,
and then applied to the wind turbine blade. For both structures analyzed it is shown that the natural frequencies
obtained with Timoshenko model are lower than the ones obtained with Euler-Bernoulli model, and that the
magnitude of difference increases with mode order.