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Wind and Structures
  Volume 25, Number 5, November 2017 , pages 459-474

Analytical solution for natural frequency of monopile supported wind turbine towers
Xue-Ning Rong, Ri-Qing Xu, Heng-Yu Wang and Su-Yang Feng

    In this study an analytical expression is derived for the natural frequency of the wind turbine towers supported on flexible foundation. The derivation is based on a Euler-Bernoulli beam model where the foundation is represented by a stiffness matrix. Previously the natural frequency of such a model is obtained from numerical or empirical method. The new expression is based on pure physical parameters and thus can be used for a quick assessment of the natural frequencies of both the real turbines and the small-scale models. Furthermore, a relationship between the diagonal and non-diagonal element in the stiffness matrix is introduced, so that the foundation stiffness can be obtained from either the p-y analysis or the loading test. The results of the proposed expression are compared with the measured frequencies of six real or model turbines reported in the literature. The comparison shows that the proposed analytical expression predicts the natural frequency with reasonable accuracy. For two of the model turbines, some errors were observed which might be attributed to the difference between the dynamic and static modulus of saturated soils. The proposed analytical solution is quite simple to use, and it is shown to be more reasonable than the analytical and the empirical formulas available in the literature.
Key Words
    natural frequency; wind turbine tower; soil-structure interaction; beam theory; stiffness matrix
Xue-Ning Rong: School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
Ri-Qing Xu and Su-Yang Feng: Research center of coastal and urban geotechnical engineering, Zhejiang University,
Hangzhou 310058, China
Heng-Yu Wang: Ningbo institute of technology, Zhejiang University, Ningbo 315100, China

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