Abstract
Offshore wind turbines (OWTs) are dynamically loaded structures and therefore the estimation of the natural frequency is an important design calculation to avoid resonance and resonance related effects (such as fatigue). Monopiles are currently the most used foundation type and are also being considered in deeper waters (>30m) where a stiff transition piece will join the monopile and the tapered tall tower. While rather computationally expensive, high fidelity finite element analysis can be carried to find the Eigen solutions of the whole system considering soil–structure interaction; a quick hand calculation method is often convenient during the design optimisation stage or conceptual design stage. This paper proposes a simplified methodology to obtain the first natural frequency of the whole system using only limited data on the WTG (Wind Turbine Generator), tower dimensions, monopile dimensions and the ground. The most uncertain component is the ground and is characterised by two parameters: type of ground profile (i.e. soil stiffness variation with depth) and the soil stiffness at one monopile depth below mudline. In this framework, the fixed base natural frequency of the wind turbine is first calculated and is then multiplied by two non-dimensional factors to account for the foundation flexibility (i.e. the effect of soil–structure interaction). The theoretical background behind the model is the Euler–Bernoulli and Timoshenko beam theories where the foundation is idealised by three coupled springs (lateral, rocking and cross-coupling). 10 wind turbines founded in different ground conditions from 10 different wind farms in Europe (e.g. Walney, Gunfleet sand, Burbo Bank, Belwind, Barrow, Kentish flat, Blyth, Lely, Thanet Sand, Irene Vorrink) have been analysed and the results compared with the measured natural frequencies. The results show good accuracy (errors below 3.5%). A step by step sample calculation is also shown for practical use of the proposed methodology.
Highlights
Offshore wind turbines (OWTs) are currently installed in high numbers in Northern Europe and the industry is rapidly developing worldwide
It has been well established that offshore wind turbines are dynamically sensitive structures [10,11,12,3,35], and dynamics of OWTs must be studied to avoid unplanned resonance which may lead to increased fatigue damage through dynamic amplification of responses
The sources of uncertainty related to the discrepancy can be due to theory or physical idealisation of the system or parameters or a combination of the above and are summarised below: (1) Beam model uncertainty i.e. uncertainty in the mathematical idealisation of the physical system: The current methodology is based on the Euler–Bernoulli beam theory, the authors have found in [6] that more sophisticated beam models including rotary inertia (Rayleigh beam) and shear deformation (Timoshenko beam) do not provide notable improvements in the results
Summary
Offshore wind turbines (OWTs) are currently installed in high numbers in Northern Europe and the industry is rapidly developing worldwide. Estimation of the natural frequency of the whole system is an important design calculation [25] so as to avoid the excitation frequencies arising from wind turbulence loading, wave loading, the rotational frequency of the turbine (1P) and the blade passing frequency (2P/3P).
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