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

Abstract

An analytical model to predict the natural frequency of offshore wind turbines on three-spring flexible foundations using two different beam models. Soil Dynamics and Earthquake Engineering, 74,[40][41][42][43][44][45] ABSTRACT: 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 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.

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“…Timoshenko beam theory accounts for shear deformation and the effect of rotational inertia and the nacelle and rotor assembly is modelled as a top head mass with mass moment of inertia. Due to the rigidity of the foundation when compared to the tower, the resonant frequency is very close to fixed base frequency, see Arany et al (2015). Other aspects related to dynamic soil-structure interaction of the system can be found in Bhattacharya and Adhikari (2011), Bhattacharya (2014).…”

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“…The loads acting on the wind turbine rotor and substructure are ultimately transferred to the foundation and can be classified into two types: static or dead load due to the self-weight of the components and the cyclic/dynamic loads arising from the wind, wave, 1P and 3P loads, for further details see Arany et al (2015b). However, the challenging part is the dynamic loads acting on the wind turbine and the salient points are discussed below: (a) The rotating blades apply a cyclic/dynamic lateral load at the hub level (top of the tower) and this load is determined by the turbulence intensity in the wind speed.…”

“…A calculation procedure is developed in Arany et al (2015b) which can be easily carried out in a spreadsheet program. The output of such a calculation will be relative wind and the wave loads and an example is shown in Figure 5 where it is assumed that the wind and wave are perfectly aligned.…”

“…This is because the structure is excited in a wide frequency band from wind turbulence, waves, aerodynamic and mass imbalance loads at the rotational frequency range (1P) and blade passage and rotational sampling loads at the blade passing frequency (2P or 3P). More information on the complexity of loading of offshore wind turbine foundations can be found in Burton et al (2011);Arany et al (2015b) The importance of dynamics in foundation design is demonstrated in , Kühn (1997); Zaaijer (2006); Lombardi et al (2013), Bhattacharya (2012, 2011). Figure 10 shows a typical wind turbine's excitations in terms of frequency content.…”

“…The natural frequency is calculated following Arany et al (2015a) and Arany et al (2016), as shown in Section 2.6. The first natural frequency and the damping of the first mode in the along-wind and cross-wind directions are used to obtain the dynamic amplification factors (DAF) that affect the structural response.…”