Closed form solution of Eigen frequency of monopile supported offshore wind turbines in deeper waters incorporating stiffness of substructure and SSI

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 (>30 m) 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

Design of monopiles for offshore wind turbines in 10 steps

“…Arany et al (2016)), it is suggested that the best approach to estimate the foundation stiffness is the methods of Poulos and Davis (1980) and Randolph (1981). Furthermore, in the authors' experience the slender pile formulae give stiffness results that produce better approximations of the Eigen frequency of the structure than the formulae for stocky (rigid) piles.…”

“…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.…”

“…The chosen value is conservatively small for the relevant wind speed ranges, see e.g. Camp et al (2004), or the discussion on damping in Arany et al (2016). The dynamic amplification factors are calculated as…”

Predicting long term performance of offshore wind turbines using cyclic simple shear apparatus

“…However, the frequency of this loading is extremely low and is in the order of magnitude of 100s (see Figure 1). Typical period of wind turbine structures being in the range of about 3 seconds [22] no resonance of structure due to wind turbulence is expected resulting in cyclic soil-structure interaction. On the other hand, the wave loading will also apply overturning moment at the mudline and the magnitude depends on water depth, significant wave height and peak wave period.…”

Distinct-element analysis of an offshore wind turbine monopile under cyclic lateral load

“…The wave loading can be mildly dynamic or severely dynamic depending on the turbine size. The interactions of these loads could be complicated (Arany et al, 2016), but they are not considered in this paper. The typical excitation ranges are 1P (0·18$0·32 Hz) and 3P (0·5$1 Hz).…”