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Effect of balance weight on dynamic characteristics of a rotating wind turbine blade

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Abstract

Iron pellets are often added in blades to maintain moment balance in the design process of a wind turbine. The balance weight will change the natural vibration characteristics of the wind turbine blade. Resonant frequencies may appear for this reason, so it is necessary to study the effects of balance weight on the dynamic characteristics of a blade. In this paper, the wind turbine blade, after the weight balance process, is modeled as an Euler–Bernoulli beam with lumped masses. A mathematical model for a rotating nonuniform blade with a lumped mass on an arbitrary section is established, while nonlinear partial differential equations governing the coupled extensional–bending–bending vibration are obtained by applying the Hamiltonian principle. The associated modal problem is obtained from the governing equations, and then the differential form of the modal problem is transformed to integral form based on Green’s functions (structural influence functions). A direct numerical approach is applied to calculate natural frequencies and vibrating modes. The effects of the mass and position of the balance weight and the rotating speed on the natural frequencies and mode shapes of the blade are discussed.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (11372257, 11302183), Shanghai Key Laboratory of Mechanics in Energy Engineering, Sichuan Province Project for the Young Research Group of Scientific and Technological Innovations (2013), the Anhui Province Natural Science Foundation (1308085MA13), the Scientific Research Foundation for Returned Overseas Chinese Scholars, and Research Project Funds of Anhui University of Science and Technology.

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Authors and Affiliations

  1. Department of Mechanics, College of Science, Anhui University of Science and Technology, No. 100, Park Road, Huainan, 232001, People’s Republic of China

    L. Li

  2. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, People’s Republic of China

    L. Li, Y. H. Li & B. K. Jiang

  3. Department of Mathematics, Kunming University, Kunming, 650214, People’s Republic of China

    Q. K. Liu

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  1. L. Li
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  2. Y. H. Li
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  3. Q. K. Liu
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  4. B. K. Jiang
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Corresponding author

Correspondence to L. Li.

Appendix: Parametric distributions of the blade

Appendix: Parametric distributions of the blade

The parametric distributions of the blade adopted in this work are shown in Fig. 8.

Fig. 8
figure 8

Parametric distributions of the blade. a mass per unit length; b built-in twist angle; c thicknesswise bending rigidity; d chordwise bending rigidity; e axial rigidity

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Li, L., Li, Y.H., Liu, Q.K. et al. Effect of balance weight on dynamic characteristics of a rotating wind turbine blade. J Eng Math 97, 49–65 (2016). https://doi.org/10.1007/s10665-015-9796-8

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  • DOI: https://doi.org/10.1007/s10665-015-9796-8

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