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Dynamic Analysis of Flexible Hoisting Rope with Time-Varying Length*

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The governing equations of flexible hoisting rope are developed employing Hamilton’s principle. Experiments are performed. It is found that the experimental data agree with the theoretical prediction very well. The results of simulation and experiment show that the flexible hoisting system dissipates energy during downward movement but gains energy during upward movement. Further, a passage through resonance in the hoisting system with periodic external excitation is analyzed. Due to the time-varying length of the hoisting rope, the natural frequencies of the system vary slowly, and transient resonance may occur when one of the frequencies coincides with the frequency of external excitation

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References

  1. M. F. Glushko and A. A. Chizh, “Differential equations of motion for a mine lift cable,” Int. Appl. Mech., 5, No. 12, 17–23 (1969).

    Google Scholar 

  2. O. A. Goroshko, “Evolution of the dynamic theory of hoist ropes,” Int. Appl. Mech., 43, No. 1, 64–67 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Kaczmarczyk and P. Andrew, “Vibration analysis of elevator rope,” Elev. World., 6, 126–129 (2005).

    Google Scholar 

  4. W. D. Zhu and G. Y. Xu, “Vibration of elevator cables with small bending stiffness,” J. Sound Vib., 263, 679–699 (2003).

    Article  ADS  Google Scholar 

  5. P. Zhang, C. M. Zhu, and L. J. Zhang, “Analyses of forced coupled longitudinal-transverse vibration of flexible hoisting systems with varying length,” Eng. Mech., 25, No. 12, 202–207 (2008).

    Google Scholar 

  6. L. H. Wang, Z. H. Hu, and Z. Zhong, “Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length,” Acta Mech., 214, 225–244 (2010).

    Article  MATH  Google Scholar 

  7. S. Y. Lee and M. Lee, “A new wave technique for free vibration of a string with time-varying length,” J. Appl. Mech., 69, 83–87 (2002).

    Article  ADS  MATH  Google Scholar 

  8. R. M. Chi and H. T. Shu, “Longitudinal vibration of a hoist rope coupled with the vertical of an elevator car,” J. Vib. Acoust., 148, No. 1, 154–159 (1991).

    Google Scholar 

  9. Y. Terumichi, M. Ohtsuka, M. Yoshizawa, and Y. Tsujioka, “Nonstationary vibrations of a string with time-varying length and a mass-spring system attached at the lower end,” Nonlin. Dynam., 12, 39–55 (1997).

    Article  MATH  Google Scholar 

  10. R. F. Fung and J. H. Lin, “Vibration analysis and suppression control of an elevator string actuated by a pm synchronous servo motor,” J. Sound Vib., 206, No. 3, 399–423 (1997).

    Article  ADS  Google Scholar 

  11. S. Kaczmarczyk and W. Ostachowicz, “Transient vibration phenomena in deep mine hoisting cables. Part 2: Numerical simulation of the dynamic response,” J. Sound Vib., 262, 245–289 (2003).

    Article  ADS  Google Scholar 

  12. Y. H. Zhang and Sunil Agrawal, “Coupled vibrations of a varying length flexible cable transporter system with arbitrary axial velocity,” Proc. 2004 Am. Control Conf., 5455–5460 (2004).

  13. W. D. Zhu and Y. Chen, “Theoretical and experimental investigation of elevator cable dynamics and control,” J. Vib. Acoust., 128, 66–78 (2006).

    Article  Google Scholar 

  14. Y. H. Zhang, “Longitudinal vibration modeling and control a flexible transporter system with arbitrarily varying cable lengths,” J. Vib. Control., 11, 431–456 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Zhang, C. M. Zhu, and L. J. Zhang, “Analyses of longitudinal vibration and energetic on flexible hoisting systems with arbitrarily varying length,” J. Shanghai JiaoTong Univ., 42, No. 3, 481–488 (2008).

    Google Scholar 

  16. A. Kumaniecka and Niziol, “Dynamic stability of a rope with slow variability of the parameters,” J. Sound Vib., 178, 211–226 (1994).

    Article  ADS  Google Scholar 

  17. W. D. Zhu and J. Ni, “Energetics and stability of translating media with an arbitrarily varying length,” J. Vib. Acoust., 122, No. 7, 295–304 (2000).

    Article  Google Scholar 

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Authors and Affiliations

  1. Hefei General Machinery Research Institute, Hefei, People’s Republic of China

    Ji-hu Bao

  2. State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University, Shanghai, People’s Republic of China

    Peng Zhang

  3. School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, People’s Republic of China

    Chang-ming Zhu

Authors
  1. Ji-hu Bao
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  2. Peng Zhang
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  3. Chang-ming Zhu
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Correspondence to Ji-hu Bao.

Additional information

Published in Prikladnaya Mekhanika, Vol. 51, No. 6, pp. 128–141, November–December 2015. Original article submitted December 27, 2012.

*This research work was supported by the State Key Laboratory of Mechanical System and Vibration, Shanghai Jiaotong University (MSV-2010-06).

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Bao, Jh., Zhang, P. & Zhu, Cm. Dynamic Analysis of Flexible Hoisting Rope with Time-Varying Length* . Int Appl Mech 51, 710–720 (2015). https://doi.org/10.1007/s10778-015-0729-z

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  • DOI: https://doi.org/10.1007/s10778-015-0729-z

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