Analytical approach for seismic analysis of onshore wind turbines considering soil-structure interaction

The aim of this study is to present an efficient analytical approach, based on a combination of transfer matrix formulations and modal superposition, to perform seismic response analysis of onshore wind turbines (WT) incorporating the effects of soil-structure interaction (SSI). The WT tower and rotor-nacelle assembly (RNA) are idealised as a segmented Timoshenko beam-column and lumped mass, respectively. SSI is taken into account using elastic springs at the bottom of the tower to model soil flexibility. The mass of the foundation is also considered in the mathematical model as a lumped mass at the base of the tower. As the serviceability limit state tends to be the governing design condition for WTs, the soil behaviour is idealised as linear-elastic with equivalent linear stiffness. Firstly, natural frequencies and mode shapes of the WT are obtained using the transfer matrix method (TMM), which is based on analytically-calculated state vectors of beam-column members, and state vectors of joints at the top and bottom of the tower. The entire vibrating structure is simplified into an equivalent single-degree-of-freedom (SDOF) system using mode shapes calculated from TMM. The seismic re-sponses are derived using the Newmark-Beta method and modal superposition. The application of TMM for free vibration analysis is validated with reference to results from existing literature. Additionally, the accuracy of the method for calculation of seismic responses is verified using finite-element software. Three different ground models are considered, namely stratum over half-space, stratum over rigid base, and elastic half-space; and the effect of each on the free vibration and seismic responses are examined in terms of displacement and base shear time-histories of the WT with varying foundation geometries. The effects of varying soil properties on the natural frequencies and seismic responses of the WT are also investigated. Finally, the dynamic responses of the model subjected to different seismic time-histories are presented comparatively, to highlight the significant effects of the frequency content of ground motion records.