Abstract
The dispersion curves of bulk acoustic waves in systems of circular holes made in an isotropic elastic material are calculated by the finite-element method for the cases of the square and hexagonal symmetries of the hole arrangement. The presence of total band gaps for acoustic waves is demonstrated, and the presence of inverse quasi-transverse first-order modes is revealed. For the hexagonally symmetric system of holes, total band gaps are found in the region of higher-order modes. For waves with a purely shear polarization, the imaginary part of the wave number in the first band gap is calculated.
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References
E. Yablonovitch, T. J. Gmitter, and K. M. Leung, Phys. Rev. Lett. 67, 2295 (1991).
M. S. Kushwaha, P. Halevi, G. Martinez, et al., Phys. Rev. B 49, 2313 (1994).
V. N. Bogomolov, L. S. Parfen’eva, I. A. Smirnov, et al., Fiz. Tverd. Tela 44, 175 (2002) [Phys. Solid State 44, 181 (2002)].
Y. Tanaka, Y. Tomoyasu, and S. Tamura, Phys. Rev. B 62, 7387 (2000).
M. Wilm, A. Khelif, S. Ballandras, et al., Phys. Rev. E 67, 065602 (2003).
T. T. Wu, Z. C. Hsu, and Z. G. Huang, Phys. Rev. B 71, 064303 (2005).
J. H. Sun and T. T. Wu, in Proceedings of the IEEE Ultrasonics Symposium, 2005, p. 73.
J. C. Hsu and T. T. Wu, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53, 1169 (2006).
A. R. Bagkhai-Vadzhi, V. P. Plesskiĭ, and A. V. Simonyan, Akust. Zh. 38, 806 (1993) [Acoust. Phys. 38, 442 (1993)].
V. I. Grigor’evskiĭ and Yu. V. Gulyaev, Akust. Zh. 46, 474 (2000) [Acoust. Phys. 46, 405 (2000)].
O. V. Ivanov, S. A. Nikitov, and Yu. V. Gulyaev, Usp. Fiz. Nauk 176, 175 (2006) [Phys. Usp. 49, 167 (2006)].
P. Silvester and R. Ferrari, Finite Elements for Electrical Engineers (Cambridge Univ. Press, New York, 1983; Mir, Moscow, 1986).
S. M. Balabaev and N. F. Ivina, Akust. Zh. 42, 172 (1996) [Acoust. Phys. 42, 149 (1996)].
V. L. Bonch-Bruevich and S. G. Kalashnikov, Physics of Semiconductors (Nauka, Moscow, 1977) [in Russian].
C. Qiu, X. Zhang, and Z. Liu, Phys. Rev. B 71, 054302-1 (2005).
C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, Phys. Rev. B 65, 201104-1 (2002).
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Original Russian Text © A.V. Grigor’evskiĭ, V.I. Grigor’evskiĭ, S.A. Nikitov, 2008, published in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 3, pp. 341–346.
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Grigor’evskiĭ, A.V., Grigor’evskiĭ, V.I. & Nikitov, S.A. Dispersion curves of bulk acoustic waves in an elastic body with a two-dimensional periodic structure of circular holes. Acoust. Phys. 54, 289–293 (2008). https://doi.org/10.1134/S1063771008030019
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DOI: https://doi.org/10.1134/S1063771008030019