Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T20:02:07.400Z Has data issue: false hasContentIssue false
  • English
  • Français

Approximate theory of acoustic waveguide of metamaterials

Published online by Cambridge University Press:  12 April 2011

CHIANG C. MEI  and
YING-HUNG LIU
CHIANG C. MEI*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
YING-HUNG LIU
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We theoretically examine the propagation of sound in a waveguide bounded by a metamaterial formed by an array of small Helmholtz resonators. The field equation is shown to be similar to that governing sound in a bubbly liquid. The effects of dissipation on the wave dispersion are examined. In particular, it is shown that the energy in a monochromatic wave train is not transported by the real part of the complex group velocity unless dissipation is absent. We further derived the envelope equation and show that in a one-dimensional waveguide, energy is transported forward despite the backward motion of the envelope peak.

JFM classification

Acoustics: Acoustics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 203 - 220
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985 Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273.CrossRefGoogle Scholar
Cheng, Y., Xu, J. Y. & Liu, X. J. 2008 One-dimensional structured ultrasonic metamaterial with simultaneously negative dynamic density and modulus. Phy. Rev. B 77, 045134. 1–9.CrossRefGoogle Scholar
Chester, W. 1964 Resonant oscillations in closed tubes. J. Fluid Mech. 18, 44–64.CrossRefGoogle Scholar
Fang, N., Xu, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C. & Zhang, X. 2006 Ultrasonic metamaterials with negative modulus. Nature Mater. 5, 452–456.CrossRefGoogle ScholarPubMed
Garrett, C. G. & McCumber, D. E. 1970 Propagation of a Gaussian light pulse through an anomalous dispersive medium. Phys. Rev. A 1 (3), 305–313.CrossRefGoogle Scholar
McDonald, K. T. 2001 Negative group velocity. Am J. Phys. 69 (5), 607–614.CrossRefGoogle Scholar
Mei, C. C. 1989 Applied Dynamics of Ocean Surface Waves. World Scientific.Google Scholar
Pendry, J. R. 2004 Negative refraction. Contemp. Phys. 45 (3), 191–202.CrossRefGoogle Scholar
Sugimoto, N. 1992 Propagation of nonlinear acoustic waves in a tunnel with an array of Helmholtz resonators. J. Fluid Mech. 244, 55–76.CrossRefGoogle Scholar
Sugimoto, N. 2000 Mass, momentum and energy transfer by the propagation of acoustic solitary waves. J. Acoust. Soc. Am. 107 (5), 2398–2405.CrossRefGoogle ScholarPubMed
Sugimoto, N. & Horioka, T. 1995 Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators. J. Acoust. Soc. Am. 97 (3), 1446–1459.CrossRefGoogle Scholar
Zhang, S., Xin, L. & Fang, N. 2009 Focussing ultrasound with an acoustic metamaterial network. Phys. Rev. Lett. 102, 194301–194304.CrossRefGoogle Scholar