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A reduced-order model to predict the natural frequencies of offshore wind turbines considering soil–structure interaction


Analytical reduced-order models (ROMs) are derived aiming at determining the natural frequencies of offshore wind turbines (OWTs). Case studies based on six wind turbines are developed considering two boundary conditions, namely fixed base (perfectly clamped) and elastic base, representing soil–structure interaction (SSI). For the elastic-base boundary condition, the stiffness of the pile-soil system at the seabed is represented by a set of three springs: \(K_{\rm L}\) (lateral spring), \(K_{\rm R}\) (rocking spring) and \(K_{\rm LR}\) (cross-coupling spring). The novel aspect herein is the presentation of an analytical mathematical model that allows obtaining different natural frequencies and the representation of the vibration modes. This mathematical model tackles the problem without the transformation of the beam of a variable section into a beam of a uniform section with equivalent properties that must be adjusted to each case. The different natural frequencies predicted by the ROMs are compared with those obtained by using higher-order hierarchical models using the Finite Element Method (FEM). In addition, the values of the first natural frequency of all OWTs predicted by ROMs are compared with the measured frequencies. The results show that the derived model accurately predicts the fundamental frequency of existing turbines, with errors below 8.2%. This proposed methodology can be of great interest in the early stages of the design of OWTs, provided the expeditious analysis and good accuracy in estimating natural frequencies. It also presents generality of use, since it does not require any previous definition of equivalent properties.

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The first and the second authors acknowledge the São Paulo Research Foundation (FAPESP) for research grants 2015/18220-2, 2016/25457-1 and 2017/16578-2. The third and fourth authors are grateful to the Brazilian National Research Council (CNPq) for the Grants 302470/2017-4 and 305945/2020-3, respectively. The third author also acknowledges FAPESP for the grant 2015/10223-2. The authors thank the valuable support given by MSc. Heloisa Beraldo.

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Appendix 1

Appendix 1

Table 9 Parameters with symbol
Table 10 Matrix B non-null terms for fixed base OWTs
Table 11 Matrix C non-null terms for elastic base OWTs

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Ferreira, Y.A., Vernizzi, G.J., Futai, M.M. et al. A reduced-order model to predict the natural frequencies of offshore wind turbines considering soil–structure interaction. Mar Syst Ocean Technol 17, 80–94 (2022).

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