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On generalized fractional vibration equation

Author

Listed:
  • Dai, Hongzhe
  • Zheng, Zhibao
  • Wang, Wei

Abstract

In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

Suggested Citation

  • Dai, Hongzhe & Zheng, Zhibao & Wang, Wei, 2017. "On generalized fractional vibration equation," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 48-51.
    • Handle: RePEc:eee:chsofr:v:95:y:2017:i:c:p:48-51
    DOI: 10.1016/j.chaos.2016.12.006
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    References listed on IDEAS

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    1. Shen, Yongjun & Yang, Shaopu & Sui, Chuanyi, 2014. "Analysis on limit cycle of fractional-order van der Pol oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 67(C), pages 94-102.
    2. Yang, Yongge & Xu, Wei & Gu, Xudong & Sun, Yahui, 2015. "Stochastic response of a class of self-excited systems with Caputo-type fractional derivative driven by Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 190-204.
    3. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    4. Xu, Beibei & Chen, Diyi & Zhang, Hao & Wang, Feifei, 2015. "Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system," Chaos, Solitons & Fractals, Elsevier, vol. 75(C), pages 50-61.
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