An analytical model to predict the natural frequency of offshore wind turbines on three-spring flexible foundations using two different beam models

• An analytical model to predict natural frequency of wind turbines considering SSI.
• Foundation modelled by three coupled springs (Lateral, Rotational and Cross-coupling).
• Tower modelled as Euler Bernoulli beam and Timoshenko beam.
• Natural frequency predictions for several operational offshore wind turbines.
• Natural frequency versus different foundation stiffness parameters curves.

In this study an analytical model of offshore wind turbines (OWTs) supported on flexible foundation is presented to provide a fast and reasonably accurate natural frequency estimation suitable for preliminary design or verification of Finite Element calculations. Previous research modelled the problem using Euler–Bernoulli beam model where the foundation is represented by two springs (lateral and rotational). In contrast, this study improves on previous efforts by incorporating a cross-coupling stiffness thereby modelling the foundation using three springs. Furthermore, this study also derives the natural frequency using Timoshenko beam model by including rotary inertia and shear deformation. The results of the proposed model are also compared with measured values of the natural frequency of four OWTs obtained from the literature. The results show that the Timoshenko beam model does not improve the results significantly and the slender beam assumption may be sufficient. The cross-coupling spring term has a significant effect on the natural frequency therefore needs to be included in the analysis. The model predicts the natural frequency of existing turbines with reasonable accuracy.