Abstract
Absolute phononic band gaps can be substantially improved in two-dimensional lattices by using a symmetry reduction approach. In this paper, the propagation of elastic waves in a two-dimensional hybrid triangular lattice structure consisting of stainless steel cylinders in air is investigated theoretically. The band structure is calculated with the plane wave expansion (PWE) method. The hybrid triangular Bravais lattice is formed by two kinds of triangular lattices. Different from ordinary triangular lattices, the band gap opens at low frequency (between the first and the second bands) regime because of lifting the bands degeneracy at high symmetry points of the Brillouin zone. The location and width of the band gaps can be tuned by the position of the additional rods.
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References
Yablonovitch, E., Inhibited spontaneous emission in solid state physics and electronics. Physical Review Letters, 1987, 58: 2059–2062.
John, S., Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 1987, 58: 2486–2489.
Kushwaha, M.S., Halevi, P., Martinez, G., Dobrzvnski, L. and Diafari-Rouhani, B., Theory of acoustic band structure of periodic elastic composites. Physical Review B, 1994, 49: 2313–2322.
Kushwaha, M.S. and Diafari-Rouhani, B., Sonic stop-bands for periodic arrays of metallic rods: honeycomb structure. Journal of Sound and Vibration, 1998, 218(4): 697–709.
Vasseur, J.O., Deymier, P.A., Khelif, A., Lamibn, P., Diafari-Rouhani, B., Akjouj, A., Dobrzynski, L., Fettouhi, N. and Zemmouri, J., Phononic crystal with low filling fraction and absolute acoustic band gap in the audible frequency range A theoretical and experimental study. Physical Review E, 2002, 65(056608): 1–6.
Yan, Z.Z., Wang, Y.S. and Zhang, C.Z., Wavelet method for calculating the defect states of two-dimensional phononic crystals. Acta Mechanica Solida Sinica, 2008, 21: 104–109.
Pang, Y., Liu, J.X., Wang, Y.S. and Fang, D.N., Wave propagation in piezoelectric/piezomagnetic layered periodic composites. Acta Mechanica Solida Sinica, 2008, 21: 483–490.
Maldovan, M. and Thomas, E.L., Simultaneous localization of photons and phonons in two-dimensional periodic structures. Applied Physics Letters, 2006, 88(251907): 1–3.
Vasseur, J.O., Hladky-Hennion, A.C., Djafari-Rouhani, B., Duval, F., Dubus, B., Pennec, Y. and Deymier, P.A., Waveguiding in two-dimensional piezoelectric phononic crystal plates. Journal of Applied Physics, 2007, 101(114904): 1–6.
Yang, S.X., Page, J.H., Liu, Z.Y., Cowan, M.L., Chan, C.T. and Sheng, P., Ultrasound tunneling through 3D phononic crystal. Physical Review Letters, 2002, 88(104301): 1–4. 1
Wu, T.T., Hsu, C.H. and Sun, J.H., Design of a highly magnified directional acoustic source based on the resonant cavity of two-dimensional phononic crystals. Applied Physics Letters, 2006, 89(171912): 1–3.
Sainidou, R., Stefanou, N. and Modinos, A., Widening of phononic transmission gaps via Anderson localization. Physical Review Letters, 2005, 94(205503): 1–4.
Li, Z.Y., Gu, B.Y. and Yang, G.Z., Large absolute band gap in 2D anisotropic photonic crystals. Physical Review Letters, 1998, 81: 2574–2577.
Trifonov, T., Marsal, L.F., Rodriguez, A., Pallares, J. and Alcubilla, R., Effects of symmetry reduction in two-dimensional square and triangular lattices. Physical Review B, 2004, 69(235112): 1–11.
Santoro, G., Prieto-Gonzalez, I., Gonzalez-Diaz, J.B., Martinez, L.J. and Postigo, P.A., Triangular air-hole based two-dimensional photonic crystal slabs design: A parametrical study. Optic Pure Applied, 2007, 40(3): 243–248.
Caballero, D., Sanchez-Dehesa, J., Rubio, C., Martinez-Sala, R., Sanchez-Perez, J.V., Meseguer, F. and Llinares, J., Large two-dimensional sonic band gaps. Physical Review E, 1999, 60: R6316–6319.
Martinez, L.J., Garcia-Martin, A. and Postigo, P.A., Photonic band gaps in a two-dimensional hybrid triangular-graphite lattice. Optics Express, 2004, 12: 5684–5689.
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Project supported by the National Natural Science Foundation of China (No.10632020).
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Wu, B., Wei, R., Zhao, H. et al. Phononic Band Gaps in Two-Dimensional Hybrid Triangular Lattice. Acta Mech. Solida Sin. 23, 255–259 (2010). https://doi.org/10.1016/S0894-9166(10)60028-6
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DOI: https://doi.org/10.1016/S0894-9166(10)60028-6