# Modeling of the resonance of an acoustic wave in a torus

Jérôme Adou^{[1]}; Adama Coulibaly^{[1]}; Narcisse Dakouri^{[1]}

- [1] UFR de Mathématiques et Informatique Université de Cocody Abidjan 22 BP 582 Abidjan 22 CÔTE D’IVOIRE

Annales mathématiques Blaise Pascal (2013)

- Volume: 20, Issue: 2, page 377-390
- ISSN: 1259-1734

## Access Full Article

top## Abstract

top## How to cite

topAdou, Jérôme, Coulibaly, Adama, and Dakouri, Narcisse. "Modeling of the resonance of an acoustic wave in a torus." Annales mathématiques Blaise Pascal 20.2 (2013): 377-390. <http://eudml.org/doc/275641>.

@article{Adou2013,

abstract = {A pneumatic tyre in rotating motion with a constant angular velocity $\Omega $ is assimilated to a torus whose generating circle has a radius $R$. The contact of the tyre with the ground is schematized as an ellipse with semi-major axis $a$. When $(\Omega R/C_\{0\})\ll 1$ and $(a/R)\ll 1$ (where $C_\{0\}$ is the velocity of the sound), we show that at the rapid time scale $R/C_\{0\}$, the air motion within a torus periodically excited on its surface generates an acoustic wave $h$. A study of this acoustic wave is conducted and shows that the mode associated to $p=0$ leads to resonance. In resonance the acoustic wave $h$ moves quadratically in time and also decreases asymptotically faster when the mean pressure in the domain is low.},

affiliation = {UFR de Mathématiques et Informatique Université de Cocody Abidjan 22 BP 582 Abidjan 22 CÔTE D’IVOIRE; UFR de Mathématiques et Informatique Université de Cocody Abidjan 22 BP 582 Abidjan 22 CÔTE D’IVOIRE; UFR de Mathématiques et Informatique Université de Cocody Abidjan 22 BP 582 Abidjan 22 CÔTE D’IVOIRE},

author = {Adou, Jérôme, Coulibaly, Adama, Dakouri, Narcisse},

journal = {Annales mathématiques Blaise Pascal},

keywords = {Acoustic waves; pneumatic; Resonance; Air; Torus; Numerical Modeling; acoustic waves; resonance; air; torus; numerical modeling},

language = {eng},

month = {7},

number = {2},

pages = {377-390},

publisher = {Annales mathématiques Blaise Pascal},

title = {Modeling of the resonance of an acoustic wave in a torus},

url = {http://eudml.org/doc/275641},

volume = {20},

year = {2013},

}

TY - JOUR

AU - Adou, Jérôme

AU - Coulibaly, Adama

AU - Dakouri, Narcisse

TI - Modeling of the resonance of an acoustic wave in a torus

JO - Annales mathématiques Blaise Pascal

DA - 2013/7//

PB - Annales mathématiques Blaise Pascal

VL - 20

IS - 2

SP - 377

EP - 390

AB - A pneumatic tyre in rotating motion with a constant angular velocity $\Omega $ is assimilated to a torus whose generating circle has a radius $R$. The contact of the tyre with the ground is schematized as an ellipse with semi-major axis $a$. When $(\Omega R/C_{0})\ll 1$ and $(a/R)\ll 1$ (where $C_{0}$ is the velocity of the sound), we show that at the rapid time scale $R/C_{0}$, the air motion within a torus periodically excited on its surface generates an acoustic wave $h$. A study of this acoustic wave is conducted and shows that the mode associated to $p=0$ leads to resonance. In resonance the acoustic wave $h$ moves quadratically in time and also decreases asymptotically faster when the mean pressure in the domain is low.

LA - eng

KW - Acoustic waves; pneumatic; Resonance; Air; Torus; Numerical Modeling; acoustic waves; resonance; air; torus; numerical modeling

UR - http://eudml.org/doc/275641

ER -

## References

top- J. Adou, Etude de la résonance du mode géostrophique dans un tore, C. R. Acad. Sci. Paris 327 (1999), 1391-1396 Zbl0981.76102
- J. Adou, Modelling of a resonant inertial oscillation within a torus, Arch. of Applied Mech. 71 (2001), 695-702 Zbl1002.76098
- J. Adou, Sur l’origine aérodynamique du danger de sous-gonflage des pneumatiques, Entropie 234 (2001), 54-60
- J.-P. Guiraud, R. Zeytounian, Evolution des ondes acoustiques sur une longue période: le concept d’écoulement incompressible avec densité fonction du temps, C. R. Acad. Sci. Paris (1980), 75-77 MR618100
- C. Gulpin, Manuel de calcul numérique appliqué, (2000), EDP sciences Zbl0958.65005

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.