Skip to main content
SpringerLink
Log in

Vibration of a vertical axially moving string or chain under the influence of gravity

  • Note
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The vertical axially moving string with non-negligible weight is solved for the first time. Using an efficient initial value method, the natural frequencies are determined for various axial speeds and string densities. Nonexistence of standing waves is explained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Watson, G.N.: A Treatise on the Theory of Bessel Functions. Cambridge University Press, Cambridge (1958)

    Google Scholar 

  2. Johnson, H.L.: The existence of a periodic solution of a vibrating hanging string. SIAM J. Appl. Math. 16, 1048–1058 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  3. Triantafyllou, M.S., Triantafyllou, G.S.: The paradox of the hanging string: an explanation using singular perturbations. J. Sound Vib. 148, 343–351 (1991)

    Article  MathSciNet  Google Scholar 

  4. Sujith, R.I., Hodges, D.H.: Exact solution for the free vibration of a hanging cord with tip mass. J. Sound Vib. 179, 359–361 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  5. Deschaine, J.S., Suits, B.H.: The hanging cord with a real tip mass. Eur. J. Phys. 29, 1211–1222 (2008)

    Article  Google Scholar 

  6. Wang, C.Y.: Vibration of a hanging tapered string with or without a tip mass. Eur. J. Phys. 32, L29–L34 (2011)

    Article  MATH  Google Scholar 

  7. Verbin, Y.: Boundary conditions and modes of the vertically hanging chain. Eur. J. Phys. 36, 015005 (2015)

    Article  MATH  Google Scholar 

  8. Huang, T., Dareing, D.W.: Frequencies of a hanging chain. J. Acoust. Soc. Am. 45, 1046–1049 (1969)

    Article  Google Scholar 

  9. Chen, L.Q.: Analysis and control of transverse vibrations of axially moving strings. Appl. Mech. Rev. 58, 91–116 (2005)

    Article  Google Scholar 

  10. Sack, R.A.: Transverse oscillations in traveling strings. Br. J. Appl. Phys. 5, 224–226 (1954)

    Article  Google Scholar 

  11. Nelson, H.M.: Transverse vibration of a moving strip. J. Sound Vib. 65, 381–389 (1979)

    Article  MATH  Google Scholar 

  12. Bruner, R.F.: Traveling, vibrating strings. Am. J. Phys. 59, 564–565 (1991)

    Article  Google Scholar 

  13. Mote, C.D.: A study of band saw vibrations. J. Frankl. Inst. 279, 430–444 (1965)

    Article  Google Scholar 

  14. Abrate, S.: Vibrations of belts and belt drives. Mech. Mach. Theory 27, 645–659 (1992)

    Article  Google Scholar 

  15. Rao, S.S.: Vibration of Continuous Systems. Wiley, New York (2007)

    Google Scholar 

  16. Barasch, S., Chen, Y.: Vibration of a rotating disk. J. Appl. Mech. 39, 1143–1144 (1972)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA

    C. Y. Wang

Authors
  1. C. Y. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C. Y. Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, C.Y. Vibration of a vertical axially moving string or chain under the influence of gravity. Acta Mech 228, 357–362 (2017). https://doi.org/10.1007/s00707-016-1703-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-016-1703-5

Search

Navigation