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Finite Element Investigation of Offshore Wind Turbines Natural Frequency with Monopile Foundations System

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Abstract

Background

The estimation of the natural frequency is a key step in the design of an offshore wind turbine (OWT). In the literature, the natural frequency can be evaluated through two steps, the first one is the estimation of the fixed base natural frequency using formulas from the literature, and the second one is the estimation of the foundation system effect. These formulas are efficient for simple shapes of OWTs but become hard to use for recent OWTs.

Method

The finite element method and the Fourier series have been used to develop a computer code under the name of “TurbiSoft” to compute the natural frequency of the OWT with the foundation system. Each of the linear, the quadratic volume elements, and the joint element was employed in TurbiSoft to model the whole system to examine the influence of the element type, the soil profile, and the interaction soil–pile state on the natural frequency.

Results

The outcomes of TurbiSoft for several OWTs were compared with the measured frequencies to define the range error of each parameter. The results show that the quadratic elements are more suitable for the natural frequency calculation. Also, this study demonstrates that the natural frequency value is strongly related to the interaction soil–pile state, and is slightly affected by the soil profile variation.

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Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

\({f}_{\mathrm{FB}}\) :

Fixed base natural frequency

\({f}_{\mathrm{n}}\) :

Natural frequency of tower/monopile/soil

\({f}_{RB(tapered)}\) :

Natural frequency of wind turbines with linearly tapered towers

\({\mathrm{k}}_{0}\) :

Earth pressure coefficient at rest

\({m}_{T}^{^{\prime}}\) :

Global masse

\({m}_{T(trapered)}\) :

Mass of the tapered tower

\({m}_{RNA}\) :

Total mass of the Rotor nacelle assembly

\(\left[m\right]\) :

Elementary mass matrices

\({t}_{p}\) :

Monopile wall thickness

\({t}_{s}\) :

Substructure wall thickness

\({t}_{T}\) :

Tower wall thickness

w:

Angular frequency

\(\left[B\right]\) :

Strain–displacement matrix

\({\mathrm{C}}_{\mathrm{L}}\) and \({\mathrm{C}}_{\mathrm{R}}\) :

Foundation flexibility coefficients

Dtop:

Tower top diameter

Dbottom :

Tower bottom diameter

\({\mathrm{D}}_{\mathrm{r}}\) :

Sand relative density

\({D}_{p}\) :

Monopile diameter

\(\left[D\right]\) :

Material property matrix

\({D}_{pile}\) :

Monopile diameter

\({E}_{T}{I}_{T}\) :

Flexural rigidity

\({E}_{s}\) :

Soil modulus

\({E}_{sD}\) :

Soil modulus at z depth equal to monopile diameter

\({E}_{T}\) :

Tower material Young’s modulus

\(\left[\mathrm{K}\right]\) :

Stiffness matrix

\({\left[\mathrm{K}\right]}_{\mathrm{int}}\) :

Joint element stiffness matrix

\({\left[\mathrm{K}\right]}_{\mathrm{i}}^{\mathrm{n}}\) :

Stiffness matrix of an element I associated with n harmonic

\({\mathrm{K}}_{\mathrm{L}}\) :

Lateral stiffness

\({\mathrm{K}}_{\mathrm{LR}}\) :

Cross-coupling stiffness

\({K}_{n}\) :

Interface normal stiffness

\({\mathrm{K}}_{\mathrm{R}}\) :

Rotational stiffness

\({K}_{s}\) :

Interface shear stiffness

\({\mathrm{K}}_{T(tapered)}\) :

Lateral stiffness of a tapered tower

L:

Tower height

\({L}_{p}\) :

Monopile embedded length

\({L}_{s}\) :

Substructure height

\({L}_{T}\) :

Tower height

\(\left[M\right]\) :

Global mass matrices

\({\mathrm{N}}_{\mathrm{b}}\) :

Number of the blades

\({\mathrm{N}}_{\mathrm{i}}\) :

Shape function associated with node I

\({\left[\mathrm{N}\right]}^{\mathrm{n}}\) :

Shape function matrix associated with n harmonic

RNA:

Rotor nacelle assembly

\({\eta }_{L}\), \({\eta }_{R}\),\({\eta }_{LR}\) :

Non-dimensional foundation stiffness parameters

ϒ :

Soil density

\(\nu\) :

Poisson’s ratio

\({\upsigma }_{\mathrm{v}0}\) :

Vertical stress due to the overburden

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Science and Applied Science, University of Bouira, Bouira, Algeria

    R. Bakhti & A. Laib

  2. Development Laboratory in Mechanics and Materials, University of Djelfa, Djelfa, Algeria

    R. Bakhti & B. Benahmed

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  1. R. Bakhti
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  2. B. Benahmed
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Bakhti, R., Benahmed, B. & Laib, A. Finite Element Investigation of Offshore Wind Turbines Natural Frequency with Monopile Foundations System. J. Vib. Eng. Technol. 12, 2437–2449 (2024). https://doi.org/10.1007/s42417-023-00989-3

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