Skip to main content
SpringerLink
Log in

Conditions for periodic vibrations in a symmetric n-string

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

A symmetric N-string is a network of N ≥ 2 sections of string tied together at one common mobile extremity. In their equilibrium position, the sections of string form N angles of 2π/N at their junction point. Considering the initial and boundary value problem for small-amplitude oscillations perpendicular to the plane of the N-string at rest, we obtain conditions under which the solution will be periodic with an integral period.

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

Similar content being viewed by others

References

  1. Ali Mehmeti F., Nonlinear Wave in Networks, Mathematical Research 80, Akademie-Verlag, Berlin, 1994

    Google Scholar 

  2. Berkolaiko G., Keating J.P., Two-point spectral correlation for star graphs, J. Phys. A, 1999, 32, 7827–7841

    Article  MathSciNet  MATH  Google Scholar 

  3. Cattaneo C., Fontana L., D’Alembert formula on finite one-dimensional networks, J. Math. Anal. Appl., 2003, 284, 403–424

    Article  MathSciNet  MATH  Google Scholar 

  4. Dáger R., Zuazua E., Controllability of star-shaped networks of strings, C. R. Acad. Sci. Paris Ser.I Math., 2001, 332, 621–626

    MathSciNet  MATH  Google Scholar 

  5. Dáger R., Zuazua E., Controllability of tree-shaped networks of vibrating strings, C. R. Acad. Sci. Paris Ser.I Math., 2001, 332, 1087–1092

    MathSciNet  MATH  Google Scholar 

  6. Gaudet S., Gauthier C., A numerical model for the 3-D non-linear vibrations of an N-string, J. Sound Vibration, 2003, 263, 269–284

    Article  Google Scholar 

  7. Gaudet S., Gauthier C., LeBlanc V.G., On the vibration of an N-string, J. Sound Vibration, 2000, 238, 147–169

    Article  Google Scholar 

  8. Gaudet S., Gauthier C., Léger L., Walker C., The vibration of a real 3-string: the timbre of the tritare, J. Sound Vibration, 2005, 281, 219–234

    Article  Google Scholar 

  9. Gauthier C., The amplification of non-linear travelling waves through a tree of 3-strings, Nuovo Cimento Soc. Ital. Fis. B, 2004, 119, 361–369

    MathSciNet  Google Scholar 

  10. Gnutzmann S., Smilansky U., Quantum graphs: applications to quantum chaos and universal spectral statistics, Adv. Phys., 2006, 55, 527–625

    Article  Google Scholar 

  11. Lagnese J.E., Leugering G., Schmidt E.J.P.G., Modeling analysis and control of dynamic elastic multi-link structures, Birkhäuser, Boston, 1994

    MATH  Google Scholar 

  12. Sagan B.E., The symmetric group, The Wadsworth & Brooks/Cole Mathematic Series, Pacific Grove, California, 1991

    Google Scholar 

  13. Sullivan D., The wave equation and periodicity, Appl. Math. Notes, 1984, 9, 1–12

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Université de Moncton, Moncton, N.B., Canada, E1A 3E9

    Claude Gauthier

Authors
  1. Claude Gauthier
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claude Gauthier.

About this article

Cite this article

Gauthier, C. Conditions for periodic vibrations in a symmetric n-string. centr.eur.j.math. 6, 287–300 (2008). https://doi.org/10.2478/s11533-008-0017-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11533-008-0017-9

MSC

Keywords

Search

Navigation