Conditions for periodic vibrations in a symmetric n-string

Claude Gauthier

Open Mathematics (2008)

  • Volume: 6, Issue: 2, page 287-300
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Claude Gauthier. "Conditions for periodic vibrations in a symmetric n-string." Open Mathematics 6.2 (2008): 287-300. <http://eudml.org/doc/269021>.

@article{ClaudeGauthier2008,
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.},
author = {Claude Gauthier},
journal = {Open Mathematics},
keywords = {networks of strings; wave equation; periodicity; star graphs; initial boundary value problem; small-amplitude oscillations},
language = {eng},
number = {2},
pages = {287-300},
title = {Conditions for periodic vibrations in a symmetric n-string},
url = {http://eudml.org/doc/269021},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Claude Gauthier
TI - Conditions for periodic vibrations in a symmetric n-string
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 287
EP - 300
AB - 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.
LA - eng
KW - networks of strings; wave equation; periodicity; star graphs; initial boundary value problem; small-amplitude oscillations
UR - http://eudml.org/doc/269021
ER -

References

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  7. [7] Gaudet S., Gauthier C., LeBlanc V.G., On the vibration of an N-string, J. Sound Vibration, 2000, 238, 147–169 http://dx.doi.org/10.1006/jsvi.2000.3153 
  8. [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 http://dx.doi.org/10.1016/j.jsv.2004.01.036 Zbl1236.74104
  9. [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 
  10. [10] Gnutzmann S., Smilansky U., Quantum graphs: applications to quantum chaos and universal spectral statistics, Adv. Phys., 2006, 55, 527–625 http://dx.doi.org/10.1080/00018730600908042 
  11. [11] Lagnese J.E., Leugering G., Schmidt E.J.P.G., Modeling analysis and control of dynamic elastic multi-link structures, Birkhäuser, Boston, 1994 Zbl0810.73004
  12. [12] Sagan B.E., The symmetric group, The Wadsworth & Brooks/Cole Mathematic Series, Pacific Grove, California, 1991 
  13. [13] Sullivan D., The wave equation and periodicity, Appl. Math. Notes, 1984, 9, 1–12 Zbl0547.35061

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