Abstract
An approach is proposed to describe a general form of acoustic media, in particular, acoustic metamaterials, based on their modeling with the simplest discrete periodic structures. The parameters of the discrete models, determined from the dispersion equation, are taken as the effective parameters of the modeled media. Transfer to an effective continuous medium is achieved by uniform distribution of these parameters over the length of the periodicity cell. It is shown that all of the wave motion characteristics of the medium, including the energy characteristics, are expressed through the effective parameters thus introduced. The necessary formulas are derived. Examples are given. The proposed method is useful for designing acoustic materials with the given wave properties.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. S. Bakhvalov and G. P. Panasenko, Averaging of Processes in Periodical Structures (Nauka, Moscow, 1984) [in Russian].
Topics in the Mathematical Modeling of Composite Materials, Ed. by A. V. Cherkaev and R. Kohn (Birkhauser-Verlag, Basel, 1997).
S. Nemat-Nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials (Elsevier, Amsterdam, 1999).
Special Issue on Acoustic Metamaterials, J. Acoust. Soc. Am. 132, Part 2, 2783 (2012).
V. A. Burov, V. B. Voloshinov, K. V. Dmitriev, and N. V. Polikarpova, Phys.-Usp. 54, 1165 (2011).
N. Fang, S. Zhang, and L. Yin, Phys. Rev. Lett. 102, 194301 (2009).
S. H. Lee, C. M. Park, Y. M. Seo, Z. G. Wang, and C. K. Kim, Reverse Doppler Effect of Sound, vol. 2, arXiv: 0901.2772 (2009).
J. Li, L. Fok, X. Yin, G. Bartal, and X. Zhang, Nat. Mater. 8, 931 (2009).
J. B. Pendri and J. Li, New J. Phys. 10, 115032 (2008).
D. Torrent and J. Sanchez-Dehesa, New J. Phys. 9, 323 (2007).
Yu. I. Bobrovnitskii, K. D. Morozov, and T. M. Tomilina, Acoust. Phys. 56, 127 (2010).
Yu. I. Bobrovnitskii, M. D. Genkin, V. P. Maslov, and A. V. Rimskii-Korsakov, Wave Propagation in Constructions from Thin Rods and Plates (Nauka, Moscow, 1974) [in Russian].
F. R. Gantmakher, Theory of Matrices (Nauka, Moscow, 1966) [in Russian].
L. Brillouin and M. Parodi, Wave Propagation in Periodical Structures (Dover, New York, 1953; Inostrannaya Literatura, Moscow, 1959).
Yu. I. Bobrovnitskii, Acoust. Phys. 58, 30 (2012).
Yu. I. Bobrovnitskii, Acoust. Phys. 59, 1 (2013).
R. W. Cottle, Linear Algebra and Its Applications 8, 189 (1974).
Yu. I. Bobrovnitskii, Acoust. Phys. 57, 442 (2011).
H. Lamb, Proc. London Math. Soc., Ser. 2 1, 473 (1904).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.I. Bobrovnitskii, 2014, published in Akusticheskii Zhurnal, 2014, Vol. 60, No. 2, pp. 137–144.
Rights and permissions
About this article
Cite this article
Bobrovnitskii, Y.I. Effective parameters and energy of acoustic metamaterials and media. Acoust. Phys. 60, 134–141 (2014). https://doi.org/10.1134/S1063771014020018
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063771014020018