Analytical models for calculating natural frequencies of wind turbines considering soil-structure interaction

Abstract

Wind energy plays a key-role in the sustainable energy scenario. With the increasing demand for wind energy, taller towers are becoming more common. This has a crucial impact on the design and analysis of wind turbine towers. The soil-structure interaction (SSI) can considerably affect the first natural frequency. Thus, tools used to predict the natural frequencies of wind turbine towers become increasingly necessary. In this context, this work aims at developing reduced-order models (ROMs) for obtaining the natural frequencies and representation of the modal forms of wind turbines considering SSI. Themathematical models handle SSI by means of three springs characterized by lateral stiffness, rotational stiffness, and cross-coupling stiffness and by means of springs representative of the soil stiffness distributed along the monopile. Both methodologies allow obtaining any frequency of interest and representing its modal form. For the first model of SSI, case studies were carried out with wind turbines available in the literature. Good agreement was observed between the predicted and the measured data, with errors below 8.2%.The results of natural frequencies and modal forms obtained with the ROMs were also compared with those obtained with models formulated via the finite element method, with excellent agreement. For the model with SSI given by distributed springs, three modeling strategies for the determination of the projection function for the monopile section were studied. An important discussion about the choice of the shape function in the use of Galerkin's method was carried out, verifying the need to adopt approaches the one take into account the boundary conditions of the problem, obtaining the best strategy for representing the modal analysis. The responses predicted by the ROMs for two reference turbines were compared with those obtained from the application of the finite element method (considered as reference values) and showed great agreement both in the prediction of both the natural frequencies and the modal shapes. Therefore, this study contributes to the prediction of natural frequencies of wind turbines from mathematical models that require few input parameters and provide information quickly and with good accuracy. The ROMs herein developed may be of importance in the early stages of design, provided that can simulate a number of conditions with low computational cost. (AU)