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Nonlinear Flap-Wise Vibration Characteristics of Wind Turbine Blades Based on Multi-Scale Analysis Method

Qifa Lang, Yuqiao Zheng*, Tiancai Cui, Chenglong Shi, Heyu Zhang

School of Mechanical and Electrical Engineering, Lanzhou University of Technology, Lanzhou, 730050, China

* Corresponding Author: Yuqiao Zheng. Email: email

Energy Engineering 2024, 121(2), 483-498.


This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle. We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory (NREL), to research the effects of the nonlinear flap-wise vibration characteristics. The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam, and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first. Then, the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force. Lastly, it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method, and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration. The results indicated that the rotational speed of the impeller has a significant impact on blade vibration. When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16. From the amplitude-frequency curve, it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity. Closed phase trajectories in blade nonlinear vibration, exhibiting periodic motion characteristics, are found through phase diagrams and Poincare section diagrams.


Cite This Article

Lang, Q., Zheng, Y., Cui, T., Shi, C., Zhang, H. (2024). Nonlinear Flap-Wise Vibration Characteristics of Wind Turbine Blades Based on Multi-Scale Analysis Method. Energy Engineering, 121(2), 483–498.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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