Abstract
Preliminary design of offshore wind turbines requires high precision simplified methods for the analysis of the system fundamental frequency. Based on the Rayleigh method and Lagrange’s Equation, this study establishes a simple formula for the analysis of system fundamental frequency in the preliminary design of an offshore wind turbine with a monopile foundation. This method takes into consideration the variation of cross-section geometry of the wind turbine tower along its length, with the inertia moment and distributed mass both changing with diameter. Also the rotational flexibility of the monopile foundation is mainly considered. The rigid pile and elastic middle long pile are calculated separately. The method is validated against both FEM analysis cases and field measurements, showing good agreement. The method is then used in a parametric study, showing that the tower length Lt, tower base diameter d0, tower wall thickness δt, pile diameter db and pile length Lb are the major factors influencing the fundamental frequency of the offshore wind turbine system. In the design of offshore wind turbine systems, these five parameters should be adjusted comprehensively. The seabed soil condition also needs to be carefully considered for soft clay and loose sand.
Similar content being viewed by others
References
Adhikari S and Bhattacharya S (2011), “Vibrations of Wind-Turbines Considering Soil-Structure Interaction,” Wind and Structures, 14(2): 85–112.
Arany L, Bhattacharya S, Macdonald JHG and Hogan SJ (2016), “Closed Form Solution of Eigen Frequency of Monopile Supported Offshore Wind Turbines in Deeper Waters Incorporating Stiffness of Substructure and SSI,” Soil Dynamics and Earthquake Engineering, 83: 18–32.
Arany L, Bhattacharya S, Macdonald JHG and Hogan SJ (2017), “Design of Monopiles for Offshore Wind Turbines in 10 Steps,” Soil Dynamics and Earthquake Engineering, 92: 126–152.
Bhattacharya S and Adhikari S (2011), “Experimental Validation of Soil-Structure Interaction of Offshore Wind Turbines,” Soil Dynamics and Earthquake Engineering, 31: 805–816.
Byrne B (2011), Foundation Design for Offshore Wind Turbines, Géotechnique Lecture.
Cao ZY (1990), “Free Vibration Analysis of Tower Structure with Variable Cross-Section,” Journal of Vibration and Shock, 36(4): 40–46. (in Chinese)
Chen JB, Liu YK and Bai XY (2015), “Shaking Table Test and Numerical Analysis of Offshore Wind Turbine Tower Systems Controlled by TLCD,” Earthquake Engineering and Engineering Vibration, 14(1): 55–75.
Clough RW and Penzien J (1975), Dynamics of Structures, McGraw-Hill.
DNV-OS-J101 (2014), Design of Offshore Wind Turbine Structures, Det Norske Veritas.
Dyson GJ and Randolph MF (2001), “Monotonic Lateral Loading of Piles in Calcareous Sand,” Journal of Geotechnical and Geoenvironmental Engineering, 127(4): 346–352.
Etienne AA (2011), “Experimental Modelling of Lateral Loads on Large Diameter Monopile Foundations in Sand,” Master of Science Thesis, Delft University of Technology, Netherlands.
Fan CC and Long JH (2005), “Assessment of Existing Methods for Predicting Soil Response of Laterally Loaded Piles in Sand,” Computers and Geotechnics, 32: 274–289.
GB/T (2008), Technical Code for Building Pile Foundation, Beijing. (in Chinese)
GB/T (2012), Code for Seismic Design of Special Structures, Beijing. (in Chinese)
Geogiadis M, Anagnostopoulos C and Saflekou S (1992), “Centrifugal Testing of Laterally Loaded Piles in Sand,” Canadian Geotechnical Journal, 29: 208–216.
Huang MS and Zhong R (2014), “Coupled Horizontal-Rocking Vibration of Partially Embedded Pile Groups and Its Effect on Resonance of Offshore Wind Turbine Structures,” Chinese Journal of Geotechnical Engineering, 36(2): 286–294. (in Chinese)
Huang MS, Yu J and Zhang CR (2015), “p–y Curves of Laterally Loaded Piles in Clay Based on Strain Path Approach,” Chinese Journal of Geotechnical Engineering, 37(3): 400–409. (in Chinese)
Kim BT, Kim NK, Lee WJ and Kim YS (2004), “Experimental Load Transfer Curves of Laterally Loaded Piles in Nak-Dong River Sand,” Journal of Geotechnical and Geoenvironmental Engineering, 130(4): 416–425.
Kuhn MJ (2001), “Dynamics and Design Optimization of Offshore Wind Energy Conversion Systems,” PhD Thesis, Delft University of Technology, Netherlands.
Lombardi D, Bhattacharya S and Wood DM (2013), “Dynamic Soil-Structure Interaction of Monopile Supported Wind Turbines in Cohesive Soil,” Soil Dynamics and Earthquake Engineering, 49: 165–180.
Mabie HH and Rogers CB (1964), “Transverse Vibrations of Tapered Cantilever Beams with End Loads,” Journal of the Acoustical Society of America, 36: 463–469.
Qiu JB, Xiang SH and Zhang ZP (2006), Computational Structural Dynamics, University of Science and Technology of China. (in Chinese)
Rosquoet F, Thorel L, Garnier J and Canepa Y (2007), “Lateral Cyclic Loading of Sand-Installed Piles,” Soil and Foundations, 47(5): 821–832.
Snyder B and Kaiser MJ (2009), “A Comparison of Offshore Wind Power Development in Europe and The US: Patterns and drivers of development,” Applied Energy, 86: 1845–1856.
Tempel JVD (2006), “Design of Support Structures for Offshore Wind Turbines,” PhD Thesis, Delft University of Technology, Netherlands.
Vugts JH (2000), Considerations on The Dynamics of Support Structures for An OWEC, Delft University of Technology, Netherlands.
Wang GY (1978), Vibration of Building and Structures, Science and Technology Press, Beijing. (in Chinese)
Zaaijer M (2006), “Foundation Modelling to Assess Dynamic Behavior of Offshore Wind Turbines,” Applied Ocean Research, 28: 45–57.
Zhao SZ (2013), “The Study of Centrifugal Modeling Test on Bearing Capacity of Single Pile under Horizontal Load,” Master Thesis, Dalian University of Technology, China. (in Chinese)
Zhu B, Xiong G, Liu JC, Sun YX and Chen RP (2013), “Centrifuge Modelling of A Large-Diameter Single Pile under Lateral Loads in Sand,” Chinese Journal of Geotechnical Engineering, 10(35): 1807–1815. (in Chinese)
Acknowledgement
The authors gratefully acknowledge support for this research from the National Natural Science Foundation of China (Grant Nos. 51678346 and 51038007), and the State Key Laboratory of Hydroscience and Engineering Project (Grant Nos. 2014-KY-03 and 2015-KY-03).
Author information
Authors and Affiliations
Corresponding author
Additional information
National Natural Science Foundation of China under Grant Nos. 51678346 and 51038007, and the State Key Laboratory of Hydroscience and Engineering Project under Grant Nos. 2014-KY-03 and 2015-KY-03
Rights and permissions
About this article
Cite this article
Yang, C., Wang, R. & Zhang, J. A simplified method for analyzing the fundamental frequency of monopile supported offshore wind turbine system design. Earthq. Eng. Eng. Vib. 17, 893–901 (2018). https://doi.org/10.1007/s11803-018-0482-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-018-0482-5