Abstract
For damped acoustic metamaterials, a discrete model is proposed in the form of a periodic structure with cells of the simplest type. The effective parameters of the model are determined by criteria based on the equality of dispersion of waves. The general properties of the model are studied. An example of one negative type of metamaterials is presented. The model is useful for analyzing wave properties and creating metamaterials with given acoustic properties.
Similar content being viewed by others
References
A. N. Norris and M. R. Haberman, J. Acoust. Soc. Am. 132, Part 2. Special issue on acoustic metamaterials, 2783 (2012).
R. V. Craster and S. Guenneau, Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking (Springer-Verlag, Dortrecht, 2013).
Yu. I. Bobrovnitskii, K. D. Morozov, and T. M. Tomilina, Acoust. Phys. 56, 127 (2010).
A. Climente, D. Torrent, and J. Sanchez-Dehesa, Appl. Phys. Lett. 100, 144103 (2012).
M. I. Hussein and M. J. Frazier, J. Sound Vibr. 332, 4767 (2013).
Yu. I. Bobrovnitskii, Acoust. Phys. 60, 134 (2014).
Yu. I. Bobrovnitskii, Acoust. Phys. 61, 255 (2015).
F. R. Gantmakher, Matrix Theory (Nauka, Moscow, 1966).
L. Brillouin and M. Parodi, Propagation des Ondes dans les Milieux Périodiques? (Masson–Dunod, 1956; InLit, Moscow, 1959).
Yu. I. Bobrovnitskii, Acoust. Phys. 57, 442 (2011).
M. A. Isakovich, General Acoustics, Cp. 12 (Nauka, Moscow, 1973).
V. V. Tyutekin and R. N. Viktorova, Acoust. Phys. 44, 275 (1998).
R. W. Cottle, Linear Algebra and its Appl. 8, 189 (1974).
D. J. Ewins, Modal Testing Theory: Practice and Applications (Res. Studies, Baldock, UK, 2000).
H. Lamb, Proc. London Math. Soc., Ser. 2 1, 473 (1904).
D. Inman, in Encyclopedia of Vibration Ed. by S. Brown, (Academic, San Diego, CA, 2002). Vol. 1, pp. 335–342.
A. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, 1944; NKTP SSSR, Moscow, 1935).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © Yu.I. Bobrovnitskii, T.M. Tomilina, M.M. Laktionova, 2016, published in Akusticheskii Zhurnal, 2016, Vol. 62, No. 1, pp. 3–9.
Rights and permissions
About this article
Cite this article
Bobrovnitskii, Y.I., Tomilina, T.M. & Laktionova, M.M. A discrete model of damped acoustic metamaterials. Acoust. Phys. 62, 1–7 (2016). https://doi.org/10.1134/S1063771016010012
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063771016010012