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Transverse vibration of flexible hoisting rope with time-varying length

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Abstract

The nonlinear vibration of a flexible hoisting rope with time-varying length is investigated. The governing equations of the flexible hoisting rope are developed based on Hamilton’s principle. Experiments performed evaluated the theoretical model and found that the experimental data agree well with the theoretical prediction, which validates the mathematical model of the flexible hoisting system. The results of the simulations and experiments show that the flexible hoisting system dissipates energy during downward movement (thus is stabilized) and gains energy during upward movement (thus is unstabilized). In addition, 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 an external excitation.

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References

  1. S. Kaczmarczyk, The passage through resonance in a catenary-vertical cable hoisting system with slowly varying length, Journal of Sound and Vibration, 208(2) (1997) 243–269.

    Article  Google Scholar 

  2. S. Kaczmarczyk and W. Ostachowicz, Transient vibration phenomena in deep mine hoisting cables part 1: Mathematical model, Journal of Sound and Vibration, 262 (2003) 219–244.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  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, Engineering Mechanics, 25(12) (2008) 202–207.

    Google Scholar 

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

    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, Journal of Applied Mechanics, 69 (2002) 83–87.

    Article  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, Journal of Vibration and Acoustics, 148(1) (1991) 154–159.

    Google Scholar 

  9. Y. Terumichi, M. Ohtsuka, M. Yoshizawa, Y. Fukawa, Y. Tsujioka, Nonstationary vibrations of a string with timevarying length and a mass-spring system attached at the lower end, Nonlinear Dynamics, 12 (1997) 39–55.

    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, Journal of Sound and Vibration, 206(3) (1997) 399–423.

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Y. H. Zhang and S. Agrawal, Coupled vibrations of a varying length flexible cable transporter system with arbitrary axial velocity, Proceedings of the 2004 American Control Conference, Boston, 5455–5460.

  13. W. D. Zhu and Y. Chen, Theoretical and experimental investigation of elevator cable dynamics and control, Journal of Vibration and Acoustics, 128 (2006) 66–78.

    Article  Google Scholar 

  14. J. Y. Choi, K. S. Hong and K. J. Yang, Exponential stabilization of an axially moving tensioned strip by passive damping and boundary control, Journal of Vibration and Control, 10(5) (2004) 661–682.

    Article  MATH  MathSciNet  Google Scholar 

  15. Q. C. Nguyen and K. S. Hong, Transverse vibration control of axially moving membranes by regulation of axial velocity, IEEE Transactions on Control Systems Technology, 20(4) (2012) 1124–1131.

    Article  MathSciNet  Google Scholar 

  16. Q. H. Ngo, K. S. Hong and I. H. Jung, Adaptive control of an axially moving system, Journal of Mechanical Science and Technology, 23 (2009) 3071–3078.

    Article  Google Scholar 

  17. Y. H. Zhang, Longitudinal vibration modeling and control a flexible transporter system with arbitrarily varying cable lengths, Journal of Vibration and Control, 11 (2005) 431–456.

    Article  MATH  MathSciNet  Google Scholar 

  18. P. Zhang, C. M. Zhu and L. J. Zhang, Analyses of longitudinal vibration and energetic on flexible hoisting systems with arbitrarily varying length, Journal of Shanghai Jiao-Tong University, 42(3) (2008) 481–488.

    Google Scholar 

  19. A. Kumaniecka and J. Niziol, Dynamic stability of a rope with slow variability of the parameters, Journal of Sound and Vibration, 178(2) (1994) 211–226.

    Article  Google Scholar 

  20. W. D. Zhu and J. Ni, Energetics and stability of translating media with an arbitrarily varying length, Journal of Vibration and Acoustics, 122(7) (2000) 295–304.

    Article  Google Scholar 

  21. M. Stylianou and B. Tabarrok, Finite element analysis of an axially moving beam, part II: stability analysis, Journal of Sound and Vibration, 178(4) (1994) 455–481.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, 200240, China

    Ji-hu Bao, Peng Zhang & Chang-Ming Zhu

  2. School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, 200072, China

    Wei Sun

Authors
  1. Ji-hu Bao
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  2. Peng Zhang
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  3. Chang-Ming Zhu
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  4. Wei Sun
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Corresponding author

Correspondence to Peng Zhang.

Additional information

Recommended by Editor Yeon June Kang

Ji-Hu Bao received his M.S. degree in the Institute of Automotive Engineering from Shanghai Jiaotong University, China. He is currently a Ph.D. candidate in Mechanical Engineering at Shanghai Jiaotong University. His main research interests include dynamic modeling, vibration analysis and control of elevator system, and strength analysis of machinery.

Peng Zhang received his Ph.D. in Mechanical Engineering, Shanghai Jiaotong University, China. He is currently an assistant professor in Mechanical Engineering, Shanghai Jiaotong University. His main research interests include system dynamics analysis, computer modeling and simulation of complex systems, and energy saving technology of the elevator.

Chang-Ming Zhu is a Professor in the School of Mechanical Engineering, Shanghai Jiaotong University, China. His main research interests include the logistics equipment system dynamics, measurement, control and intelligence of electromechanical systems.

Wei Sun is an Assistant Professor in the School of Mechatronic Engineering and Automation, Shanghai University, China. His main research interests are in the areas of control, fatigue life-span and classification strategy.

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Bao, Jh., Zhang, P., Zhu, CM. et al. Transverse vibration of flexible hoisting rope with time-varying length. J Mech Sci Technol 28, 457–466 (2014). https://doi.org/10.1007/s12206-013-1110-y

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  • DOI: https://doi.org/10.1007/s12206-013-1110-y

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