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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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Numerical investigation of acoustic solitons; pp. 304–310

(Full article in PDF format) doi: 10.3176/proc.2015.3.15


Authors

Bruno Lombard, Jean-François Mercier, Olivier Richoux

Abstract

Acoustic solitons can be obtained by considering the propagation of large amplitude sound waves across a set of Helmholtz resonators. The model proposed by Sugimoto and his coauthors has been validated experimentally in previous works. Here we examine some of its theoretical properties: low-frequency regime, balance of energy, stability. We propose also numerical experiments illustrating typical features of solitary waves.

Keywords

nonlinear acoustics, solitary waves, fractional derivatives.

References

1. Engelbrecht , J. , Fridman , V. , and Pelinovski , E. Nonlinear Evolution Equations. Longman , Harlow , 1988.

2. LeVeque , R. J. and Yong , D. H. Solitary waves in layered nonlinear media. SIAM J. Appl. Math. , 2003 , 63 , 1539–1560.
http://dx.doi.org/10.1137/S0036139902408151

3. Lombard , B. and Mercier , J. F. Numerical modeling of nonlinear acoustic waves in a tube with Helmholtz resonators. J. Comput. Phys. , 2014 , 259 , 421–443.
http://dx.doi.org/10.1016/j.jcp.2013.11.036

4. Matignon , D. An introduction to fractional calculus. In Scaling , Fractals and Wavelets (Abry , P. , Goncalves , P. , and Lévy Véhel , J. , eds). ISTE-Wiley , 2008 , 237–273.

5. Richoux , O. , Lombard , B. , and Mercier , J. F. Generation of acoustic solitary waves in a lattice of Helmholtz resonators. Wave Motion , 2015 , 56 , 85–99.
http://dx.doi.org/10.1016/j.wavemoti.2015.02.005

6. Sugimoto , N. Propagation of nonlinear acoustic waves in a tunnel with an array of Helmholtz resonators. J. Fluid. Mech. , 1992 , 244 , 55–78.
http://dx.doi.org/10.1017/S0022112092002969

7. Sugimoto , N. , Masuda , M. , Yamashita , K. , and Horimoto , H. Verification of acoustic solitary waves. J. Fluid. Mech. , 2004 , 504 , 271–299.
http://dx.doi.org/10.1017/S0022112004008109

 
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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December