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Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions

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  • Jiaquan Xie
  • Yongjiang Zheng
  • Zhongkai Ren
  • Tao Wang
  • Guangxian Shen

Abstract

In practice, due to the fact that the phenomenon of drawing self-excited vibration can be deemed as one of the hunting phenomena of the mechanical system, this study focuses on investigating the drawing self-excited vibration process through proposing the fractional differential equation model of hunting phenomenon of the mechanical system. The fractional Legendre functions together with their fractional differential operational matrices are used to numerically solve the model. In this way, the numerical solutions of vibration displacement of the model are obtained. At the end, the proposed model and algorithm are proved to be effective via analyzing the numerical results and phase position.

Suggested Citation

  • Jiaquan Xie & Yongjiang Zheng & Zhongkai Ren & Tao Wang & Guangxian Shen, 2019. "Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions," Complexity, Hindawi, vol. 2019, pages 1-10, December.
    • Handle: RePEc:hin:complx:9234586
    DOI: 10.1155/2019/9234586
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    References listed on IDEAS

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    1. Jiang, Jingfei & Guirao, Juan Luis García & Chen, Huatao & Cao, Dengqing, 2019. "The boundary control strategy for a fractional wave equation with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 92-97.
    2. Xie, Jiaquan & Yao, Zhibin & Gui, Hailian & Zhao, Fuqiang & Li, Dongyang, 2018. "A two-dimensional Chebyshev wavelets approach for solving the Fokker-Planck equations of time and space fractional derivatives type with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 197-208.
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    Cited by:

    1. Li, Zhongjie & Zhao, Li & Wang, Junlei & Yang, Zhengbao & Peng, Yan & Xie, Shaorong & Ding, Jiheng, 2023. "Piezoelectric energy harvesting from extremely low-frequency vibrations via gravity induced self-excited resonance," Renewable Energy, Elsevier, vol. 204(C), pages 546-555.

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