Advertisement

Acta Mechanica Solida Sinica

, Volume 23, Issue 3, pp 255–259 | Cite as

Phononic Band Gaps in Two-Dimensional Hybrid Triangular Lattice

  • Bin Wu
  • Ruiju Wei
  • Huanyu Zhao
  • Cunfu He
Article

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.

Key words

phononic crystal phononic band gap hybrid triangular lattice plane wave expansion method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Yablonovitch, E., Inhibited spontaneous emission in solid state physics and electronics. Physical Review Letters, 1987, 58: 2059–2062.CrossRefGoogle Scholar
  2. [2]
    John, S., Strong localization of photons in certain disordered dielectric superlattices. Physical Review Letters, 1987, 58: 2486–2489.CrossRefGoogle Scholar
  3. [3]
    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.CrossRefGoogle Scholar
  4. [4]
    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.CrossRefGoogle Scholar
  5. [5]
    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.Google Scholar
  6. [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.CrossRefGoogle Scholar
  7. [7]
    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.CrossRefGoogle Scholar
  8. [8]
    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.Google Scholar
  9. [9]
    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.Google Scholar
  10. [10]
    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. 1Google Scholar
  11. [11]
    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.Google Scholar
  12. [12]
    Sainidou, R., Stefanou, N. and Modinos, A., Widening of phononic transmission gaps via Anderson localization. Physical Review Letters, 2005, 94(205503): 1–4.Google Scholar
  13. [13]
    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.CrossRefGoogle Scholar
  14. [14]
    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.Google Scholar
  15. [15]
    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.Google Scholar
  16. [16]
    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.CrossRefGoogle Scholar
  17. [17]
    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.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.College of Mechanical Engineering and Applied Electronics TechnologyBeijing University of TechnologyBeijingChina
  2. 2.College of Mathematics and PhysicsShandong Jianzhu UniversityJinanChina

Personalised recommendations