Conditions for periodic vibrations in a symmetric n-string

• Autorzy: Claude Gauthier
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

networks of strings; wave equation; periodicity; star graphs

Kategorie tematyczne

• 35L05: Wave equation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 287-300

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Claude Gauthier

• Université de Moncton

Bibliografia

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• [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
• [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 http://dx.doi.org/10.1016/S0022-460X(02)01122-7
• [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] 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
• [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] 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
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• [12] Sagan B.E., The symmetric group, The Wadsworth & Brooks/Cole Mathematic Series, Pacific Grove, California, 1991
• [13] Sullivan D., The wave equation and periodicity, Appl. Math. Notes, 1984, 9, 1–12

Identyfikatory

DOI

10.2478/s11533-008-0017-9