Skip to main content
SpringerLink
Log in

Analytical Estimation of Natural Frequencies of Offshore Monopile Wind Turbines

  • Conference paper
  • First Online:
Advances in Computational Mechanics and Applications (OES 2023)

Part of the book series: Structural Integrity ((STIN,volume 29))

Included in the following conference series:

  • 127 Accesses

Abstract

A comprehensive analytical solution for the estimation of natural frequencies of monopile supported Offshore Wind Turbines (OWTs) is proposed in this paper. The solution is based on the non-dimensional equations established using the Euler-Bernoulli beam theory and relevant boundary conditions. The equations of motion for above water and underwater are separated to compensate for the effect of added mass. Therefore, three equations of motion are established to simulate the motion of the monopile underwater, above water, and tower. The tower is considered a tapered tubular structure that linearly varies in diameter from bottom to top. Four sets of boundary conditions are also established at the seabed, seawater, platform, and nacelle levels. The seabed boundary conditions are to model the effect of the monopile section under the seabed by using the coupled springs. The seawater and platform level boundary conditions are the continuity conditions to link the monopile underwater, above water, and tower. The translational and rotational masses of the nacelle-rotor assembly are also included in the boundary conditions at the nacelle level. The non-dimensional equations are solved for a DTU 10 MW OWT case, and the results are compared to similar works. Besides, the 1st natural frequency of the system is evaluated for different values of monopile length and cross-section. The proposed method can easily be programmed to estimate the natural frequencies of the OWT structures.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Pezeshki, H., Adeli, H., Pavlou, D.G., and Siriwardane, S. C. State of the art in structural health monitoring of offshore and marine structures, Proceedings of the Institution of Civil Engineers-Maritime Engineering, Volume 0: 1–8, (2022), https://doi.org/10.1680/jmaen.2022.027.

  2. Pezeshki, H., Pavlou, D.G., Adeli, H., and Siriwardane, S. C. Modal analysis of offshore monopile wind turbine: An analytical solution, Journal of Offshore Mechanics and Arctic Engineering 145(1): 010907, (2022), doi: https://doi.org/10.1115/1.4055402.

  3. Sajedi, S., and Liang, X. Dual Bayesian Inference for Risk-Informed Vibration-Based Damage Diagnosis, Computer-Aided Civil and Infrastructure Engineering 36 (9): 1168–84, (2021). https://doi.org/10.1111/mice.12642.

  4. Sajedi, S.M. and Liang, X., Deep Generative Bayesian Optimization for Sensor Placement in Structural Health Monitoring, Computer-Aided Civil and Infrastructure Engineering, 37:9, 1109-1127, (2022). https://doi.org/10.1111/mice.12799.

  5. Zhang, Y. and Lin, W., Computer Vision-based Differential Remeshing for Updating the Geometry of Finite Element Model, Computer-Aided Civil and Infrastructure Engineering, 37:2, 185-203, (2022). https://doi.org/10.1111/mice.12708.

  6. Zhao, J., Hu, F., Xu, Y., Zuo, W., Zhong, J., and Li, H., Structure-PoseNet for identification of dense dynamic displacement and 3D poses of structures using a monocular camera, Computer-Aided Civil and Infrastructure Engineering, 37:6, 704-725, (2022). https://doi.org/10.1111/mice.12761.

  7. Zhang, Q. and Zhang, J., Internal Force Monitoring and Estimation of a Long-Span Reinforced Concrete Ring Beam using Long-gauge Strain Sensing, Computer-Aided Civil and Infrastructure Engineering, 36:1, 109-124, (2021). https://doi.org/10.1111/mice.12569.

  8. Civera, M., Pecorelli, M.L., Ceravolo, R., Surace, C., and Fragonara, L.Z., A Multi-objective Genetic Algorithm Strategy for Robust Optimal Sensor Placement, Computer-Aided Civil and Infrastructure Engineering, 36:9, 1185-1202, (2021). https://doi.org/10.1111/mice.12646.

  9. Jauhiainen, J., Pour-Ghaz, M., Valkonen, T., and Seppänen, A., Non-planar sensing skins for structural health monitoring based on electrical resistance tomography, Computer-Aided Civil and Infrastructure Engineering, 36:12, (2021). https://doi.org/10.1111/mice.12689.

  10. Nasimi, R. and Moreu, F., A methodology for measuring the total displacements of structures using a laser-camera system, Computer-Aided Civil and Infrastructure Engineering, 36:4, 421-437, (2021). https://doi.org/10.1111/mice.12652.

  11. Shen, J., Yan, W., Li, P., and Xiong, X., Deep Learning-based Object Identification with Instance Segmentation and Pseudo-LiDAR Point Cloud for Work Zone Safety, Computer-Aided Civil and Infrastructure Engineering, 36:12, 1549-1567, (2021). https://doi.org/10.1111/mice.12749.

  12. Li, X., Liu, H., Zhou, F., Chen, Z., Giannakis, I., and Slob, E., Deep learning-based nondestructive evaluation of reinforcement bars using ground-penetrating radar and electromagnetic induction data, Computer-Aided Civil and Infrastructure Engineering, 37:14, 1834-1853, (2022). https://doi.org/10.1111/mice.12798.

  13. Tian, Y., Zhang, C., Jiang, S., Zhang, J., and Duan, W., Noncontact Cable Force Estimation with Unmanned Aerial Vehicle and Computer Vision, Computer-Aided Civil and Infrastructure Engineering, 36:1, 73-88, (2021). https://doi.org/10.1111/mice.12567.

  14. Qarib, H. and Adeli, H., A Comparative Study of Signal Processing Methods for Exponentially Damped Signals, Journal of Vibroengineering, 18:4, NoP (2027-2079), pp. 2186-2204, (2016). https://doi.org/10.1111/mice.12567.

  15. Sajedi, S., and Liang, X., Uncertainty-Assisted Deep Vision Structural Health Monitoring, Computer-Aided Civil and Infrastructure Engineering 36 (2): 126–42, (2021). https://doi.org/10.1111/mice.12580.

  16. Adeli, H., & Hung, S. L.. Machine learning–neural networks, genetic algorithms, and fuzzy systems. John Wiley and Sons, New York, (1995).

    Google Scholar 

  17. Ahmadlou, M., & Adeli, H., Enhanced probabilistic neural network with local decision circles: A robust classifier. Integrated Computer-Aided Engineering, 17(3), 197–210, (2010). DOI: https://doi.org/10.3233/ICA-2010-0345.

  18. Rafiei, M. H., & Adeli, H., A new neural dynamic classification algorithm. IEEE Transactions on Neural Networks and Learning Systems, 28(12), 3074–3083, (2017). https://doi.org/10.1109/TNNLS.2017.2682102.

  19. Sørensen, R.A., Michael N., and Henrik K., Routing in Congested Baggage Handling Systems Using Deep Reinforcement Learning, Integrated Computer-Aided Engineering 27 (2): 139–52, (2020). https://doi.org/10.3233/ICA-190613.

  20. Gil-Gala, F.J., Carlos M., María R.S., and Ramiro V., Learning Ensembles of Priority Rules for Online Scheduling by Hybrid Evolutionary Algorithms, Integrated Computer-Aided Engineering 28: 65–80 (2021). DOI:https://doi.org/10.3233/ICA-200634.

  21. Gao, Y., Zhai, P., and Mosalam, K.M. Balansced Semi-Supervised Generative Adversarial Network for Damage Assessment from Low-Data Imbalanced-Class Regime, Computer-Aided Civil and Infrastructure Engineering, 36:9, 1094-1113, (2021). DOI: https://doi.org/10.1111/mice.12741.

  22. Sarmadi, H. and Yuen, K.V. Early damage detection by an innovative unsupervised learning method based on kernel null space and peak-over-threshold, Computer-Aided Civil and Infrastructure Engineering, 36:9, 1150-1167, (2021). DOI: https://doi.org/10.1111/mice.12635.

  23. Maeda, H., Kashiyama, T., Sekimoto, Y., Seto, T., Omata, H., Generative Adversarial Networks for Road Damage Detection, Computer-Aided Civil and Infrastructure Engineering, 36:47-60, (2021). DOI: https://doi.org/10.1111/mice.12561.

  24. Chun, P.J., Yamane, T., and Maemura, Y., A deep learning based image captioning method to automatically generate comprehensive explanations of bridge damage, Computer-Aided Civil and Infrastructure Engineering, 37:11, 1387-1401, (2022). https://doi.org/10.1111/mice.12793.

  25. Rafiei, M. H., & Adeli, H., A novel machine learning based algorithm to detect damage in highrise building structures. The Structural Design of Tall and Special Buildings, 26, 18, (2017). https://doi.org/10.1002/tal.1400.

  26. Amezquita-Sanchez, J. P., Park, H.P., and Adeli, H., A Novel Methodology for Modal Parameters Identification of Large Smart Structures Using MUSIC, Empirical Wavelet Transform, and Hilbert Transform. Engineering Structures 147 (September): 148–59, (2017). https://doi.org/10.1016/j.engstruct.2017.05.054.

  27. Lin, Z., Dubravka Pokrajac, D., Guo, Y., Jeng, D.S., Tang, T., Rey, N., Zheng, J., and Zhang, J., Investigation of Nonlinear Wave-Induced Seabed Response around Mono-Pile Foundation. Coastal Engineering 121: 197–211, (2017). https://doi.org/10.1016/j.coastaleng.2017.01.002.

  28. Damgaard, M., Ibsen, L. B., Andersen, L. V., and Andersen, J. K.F., Cross-Wind Modal Properties of Offshore Wind Turbines Identified by Full Scale Testing, Journal of Wind Engineering and Industrial Aerodynamics 116: 94–108, (2013). https://doi.org/10.1016/j.jweia.2013.03.003.

  29. Prendergast, L. J., Gavin, K., and Doherty, P., An Investigation into the Effect of Scour on the Natural Frequency of an Offshore Wind Turbine, Ocean Engineering 101: 1–11, (2015). https://doi.org/10.1016/j.oceaneng.2015.04.017.

  30. Prendergast, L. J., Reale, C., and Gavin, K., Probabilistic Examination of the Change in Eigenfrequencies of an Offshore Wind Turbine under Progressive Scour Incorporating Soil Spatial Variability. Marine Structures 57: 87–104, (2018). https://doi.org/10.1016/j.marstruc.2017.09.009.

  31. Norén-Cosgriff, K., and Kaynia, A.M. Estimation of Natural Frequencies and Damping Using Dynamic Field Data from an Offshore Wind Turbine, Marine Structures 76: 102915, (2021). https://doi.org/10.1016/j.marstruc.2020.102915.

  32. Luan, M., Qu, P., Jeng, D.S., Guo, Y., and Yang, Q., Dynamic Response of a Porous Seabed–Pipeline Interaction under Wave Loading: Soil–Pipeline Contact Effects and Inertial Effects. Computers and Geotechnics 35 (2): 173–86, (2008). https://doi.org/10.1016/j.compgeo.2007.05.004.

  33. Chang, K.T., and Jeng, D.S., Numerical Study for Wave-Induced Seabed Response around Offshore Wind Turbine Foundation in Donghai Offshore Wind Farm, Shanghai, China. Ocean Engineering 85: 32–43, (2014). https://doi.org/10.1016/j.oceaneng.2014.04.020.

  34. Sui, T., Zhang, C., Guo, Y., Zheng, J., Jeng, D., Zhang, J., and Zhang, W., Three-Dimensional Numerical Model for Wave-Induced Seabed Response around Mono-Pile. Ships and Offshore Structures 11 (6): 667–78, (2015). https://doi.org/10.1080/17445302.2015.1051312.

  35. Zhang, C., Zhang, Q., Wu, Z., Zhang, J., Sui, T., and Wen, Y., Numerical Study on Effects of the Embedded Monopile Foundation on Local Wave-Induced Porous Seabed Response. Mathematical Problems in Engineering 2015: 1–13, (2015). https://doi.org/10.1155/2015/184621.

  36. Alkhoury, P., Soubra, A.H., Rey, V., and Aït-Ahmed, M., A Full Three-Dimensional Model for the Estimation of the Natural Frequencies of an Offshore Wind Turbine in Sand. Wind Energy 24 (7): 699–719, (2021). https://doi.org/10.1002/we.2598.

  37. Graff, K F., Wave Motion in Elastic Solids. Dover Publications, New York, 2012.

    Google Scholar 

  38. Meirovitch, L, Analytical Methods in Vibrations. Macmillan, New York.

    Google Scholar 

  39. Pavlou, Dimitrios G. “Soil–Structure–Wave Interaction of Gravity-Based Offshore Wind Turbines: An Analytical Model.” Journal of Offshore Mechanics and Arctic Engineering 143 (3), 2021. https://doi.org/10.1115/1.4048997.

  40. Darvishi-Alamouti, S., Bahaari, M.R., and Moradi, M., Natural Frequency of Offshore Wind Turbines on Rigid and Flexible Monopiles in Cohesionless Soils with Linear Stiffness Distribution. Applied Ocean Research 68: 91–102 (2017). https://doi.org/10.1016/j.apor.2017.07.009.

  41. Polyanin A.D, Zaitsev. Handbook of Exact Solutions for Ordinary Differenctial Equations. Chapman & Hall/CRC, NewYork, 2003.

    Google Scholar 

  42. Sanger, D. J., Transvers vibration of a class of non-uniform beams, Journal of Mechanical Engineering science, Vol 10 (2): 111-120, 1967.

    Google Scholar 

  43. Bak, Christian, Frederik Zahle, Robert Bitsche, Taeseong Kim, Anderes Yde, Lars Christian Henriksen, Anand Natarajan, and Morten Hansen., Description of the DTU 10 MW Reference Wind Turbine, 2013. https://dtu-10mw-rwt.vindenergi.dtu.dk.

  44. Veritas, Det Norske. Environmental Conditions and Environmental Loads.” NNV no. October: 9–123, 2010.

    Google Scholar 

  45. Morison, J R, J W Johnson, and S A Schaaf. The Force Exerted by Surface Waves on Piles.” Journal of Petroleum Technology 2 (05): 149–54, (1950). https://doi.org/10.2118/950149-g.

Download references

Author information

Authors and Affiliations

  1. University of Stavanger, 4021, Stavanger, Norway

    Hadi Pezeshki, Dimitrios Pavlou & Sudath C. Siriwardane

Authors
  1. Hadi Pezeshki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dimitrios Pavlou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sudath C. Siriwardane
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Pezeshki .

Editor information

Editors and Affiliations

  1. University of Stavanger, Stavanger, Norway

    Dimitrios Pavlou

  2. Ohio State University, Columbus, OH, USA

    Hojjat Adeli

  3. Faculty of Engineering, University of Porto, Porto, Portugal

    José A. F. O. Correia

  4. University of Bologna, Bologna, Italy

    Nicholas Fantuzzi

  5. Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus

    Georgios C. Georgiou

  6. Faculty of Science and Technology, University of Stavanger, Stavanger, Norway

    Knut Erik Giljarhus

  7. University of Stavanger, Stavanger, Norway

    Yanyan Sha

Appendix 1: Nomenclature

Appendix 1: Nomenclature

Symbol

Structural properties

\(L\)

Nacelle level from the seabed (\(m\))

\({L}_{Tow}\)

Tower length (\(m\))

\({L}_{Plat}\)

Platform level from the seabed (\(m\))

\(d\)

Water depth (\(m\))

\({D}_{top}\)

Tower top cross-section diameter (\(m\))

\({D}_{bot}\)

Tower bottom cross-section diameter (\(m\))

\({t}_{Tow}\)

Tower average thickness (\(m\))

\({m}_{bot}\)

Tower mass of unit length at the bottom cross-section (\(Kg/m\))

\({E}_{Tow}\)

Tower Young’s modulus (\(GPa\))

\(E{I}_{Tow}\)

Flexural rigidity of the tower, i.e., \({E}_{Tow}{I}_{Tow}\) (\(GPa.{m}^{4})\)

\({M}_{N}\)

Nacelle-Rotor assembly mass (\(Kg\))

\({J}_{N}\)

Nacelle-Rotor assembly rotational inertia (\(Kg.{m}^{2}\))

\({D}_{Mon}\)

Monopile average diameter (\(m\))

\({t}_{Mon}\)

Monopile average thickness (\(m\))

\({A}_{Mon}\)

Monopile cross-sectional area (\({m}^{2}\))

\({m}_{Mon}\)

Monopile mass of unit length (\(Kg/m\))

\({E}_{Mon}\)

Monopile Young's modulus (\(GPa\))

\(E{I}_{Mon}\)

Flexural rigidity of the monopile, i.e., \({E}_{Mon}{I}_{Mon}\) (\(GPa.{m}^{4})\)

\({\rho }_{s}\)

Material Density (\(Kg/{m}^{3}\))

\({K}_{L}\)

Lateral stiffness (\(GN/m\))

\({K}_{LR}\)

Cross stiffness (\(GN\))

\({K}_{R}\)

Rotational stiffness (\(GN.m\))

\({C}_{A}\)

Added mass coefficient

\({\rho }_{w}\)

Sea water density (\(Kg/{m}^{3}\))

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pezeshki, H., Pavlou, D., Siriwardane, S.C. (2024). Analytical Estimation of Natural Frequencies of Offshore Monopile Wind Turbines. In: Pavlou, D., et al. Advances in Computational Mechanics and Applications. OES 2023. Structural Integrity, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-031-49791-9_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-49791-9_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-49790-2

  • Online ISBN: 978-3-031-49791-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation