한국음향학회지 (The Journal of the Acoustical Society of Korea)

  • 제34권5호
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  • Pages.335-342
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  • 2015
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  • 1225-4428(pISSN)
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  • 2287-3775(eISSN)
한국음향학회 (The Acoustical Society of Korea)
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수중에서 정방형 격자를 갖는 2차원 포노닉 크리스탈의 음향 밴드 구조

Acoustic Band Structures in Two-dimensional Phononic Crystals with a Square Lattice in Water

  • 투고 : 2015.06.17
  • 심사 : 2015.08.17
  • 발행 : 2015.09.30
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초록

포노닉 크리스탈이란 기저물질 내에 주기적으로 배열된 산란체로 구성된 복합물질로서 포노닉 크리스탈에 입사된 음파가 특정 주파수 대역에서 차단되는 현상인 밴드 갭이라는 중요한 특성을 갖는다. 본 연구에서는 수중에서 산란체로서 1 mm의 직경을 갖는 원기둥 형태의 스테인리스 스틸 막대가 1.5 mm의 격자상수를 가지며 정방형으로 배열된 2차원 포노닉 크리스탈의 음향 밴드 구조를 이론 및 실험적으로 고찰하였다. 2차원 포노닉 크리스탈의 밴드 구조를 예측하기 위해 유한요소법을 이용하여 첫째 브릴루앙 영역의 ${\Gamma}X$ 방향에 대해 주파수와 파동벡터에 대한 분산관계를 계산하였다. 초음파가 입사되는 방향과 수직한 스테인리스 스틸 막대 층의 개수를 1, 3, 5, 7, 9개로 변화시켜가며 투과계수 및 반사계수를 측정하였다. 계산된 분산관계로부터 2 MHz 이하의 주파수 대역에서 5개의 밴드 갭이 존재하는 것으로 예측되었으며, 첫째 밴드 갭은 0.5 MHz를 중심으로 나타났다. 투과계수 및 반사계수로부터 실험적으로 확인된 밴드 갭은 분산관계로부터 예측된 밴드 갭과 잘 일치하는 것으로 나타났다.

Phononic crystals are composite materials consisting of a periodic arrangement of scattering inclusions in a host material. One of the most important properties of phononic crystals is the existence of band gaps, i.e., ranges of frequencies at which acoustic waves cannot propagate through the structure. The present study aims to investigate theoretically and experimentally the acoustic band structures in two-dimensional (2D) phononic crystals consisting of periodic square arrays of stainless steel solid cylinders with a diameter of 1 mm and a lattice constant of 1.5 mm in water. The theoretical dispersion relation that depicts the relationship between the frequency and the wave vector was calculated along the ${\Gamma}X$ direction of the first Brillouin zone using the finite element method to predict the band structures in the 2D phononic crystals. The transmission and the reflection coefficients were measured in the 2D phononic crystals with 1, 3, 5, 7, and 9 layers of stainless steel cylinders stacked in the perpendicular direction to propagation at normal incidence. The theoretical dispersion relation exhibited five band gaps at frequencies below 2 MHz, the first gap appearing around a frequency of 0.5 MHz. The location and the width of the band gaps experimentally observed in the transmission and the reflection coefficients appeared to coincide well with those determined from the theoretical dispersion relation.

키워드

참고문헌

  1. W. Cai and V. Shalaev, Optical metamaterials; fundamentals and application (Springer, New York, 2010), pp. 1-10.
  2. M.-H. Lu, L. Feng, and Y.-F. Chen, "Phononic crystals and acoustic metamaterials," Materials Today 12, 34-42 (2009).
  3. R. H. Olsson. III and I. El-Kady, "Microfabricated phononic crystal devices and application," Meas. Sci. Technol. 20, 012002 (2009). https://doi.org/10.1088/0957-0233/20/1/012002
  4. R. Gonzalo. P. Maagt, and M. Sorolla, "Enhanced patchantenna performance by suppressing surface waves using photonic-bandgap substrates," IEEE Trans. Microwave Theory Tech. 47, 2131-2138 (1999). https://doi.org/10.1109/22.798009
  5. J. H. Park and J. K. Cho, "Numerical analysis of magnetooptic performance of one-dimensional magneto-photonic crystal," J. Korean Magn. Soc. 10, 99-105 (2000).
  6. J. H. Page, A. Sukhovich, S. Yang, M. L. Cowan, F. Van Der Biest, A. Tourin, M. Fink, Z. Liu, C. T. Chan, and P. Sheng, "Phononic crystals," Phys. Stat. Sol. 241, 3454-3462 (2004). https://doi.org/10.1002/pssb.200405363
  7. Y. Pennec, J. O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, and P. A. Deymier, "Two dimensional Phononic crystals: Examples and applications," Surf. Sci. Rep. 65, 229-291 (2010). https://doi.org/10.1016/j.surfrep.2010.08.002
  8. M. Oudich, M. Senesi, M. Badreddine Assouar, M. Ruzenne, J.-H. Sun, B. Vincent, Z. Hou, and T.-T. Wu, "Experimental evidence of locally resonant sonic band gap in two-dimensional phononic crystal stubbed plates," Phys. Rev. B 84, 165136 (2011). https://doi.org/10.1103/PhysRevB.84.165136
  9. G. W. C. Kaye and T. H. Laby, Tables of physical and chemical constants and some mathematical functions (Longman, London, 1995), pp. 1-10.
  10. C. Kittel, Introduction to solid state physics (Wiley, New York, 2005), pp. 33-34.
  11. D. P. Elford, L. Chalmers, F. V. Kusmartsev, and G. M. Swallowe, "Matryoshka locally resonant sonic crystal," J. Acoust. Soc. Am. 130, 2746-2755 (2011). https://doi.org/10.1121/1.3643818
  12. M. Hirsekorn, P. P. Delsanto, N. K. Batra, and P. Matic, "Modelling and simulation of acoustic wave propagation in locally resonant sonic materials," Ultrasonics 42, 231-235 (2004). https://doi.org/10.1016/j.ultras.2004.01.014
  13. D. Zhao, Y. Ye, S. Xu, X. Zhu, and L. Yi, "Broadband and wide-angle negative reflection at a phononic crystal boundary," Appl. Phys Lett. 104, 043503 (2014). https://doi.org/10.1063/1.4863691
  14. A. Khelif, B. Djafari-Rouhani, J. O. Vasseur, and P. A. Deymier, "Transmission and dispersion relations of perfect and defect-containing waveguide structures in phononic band gap materials," Phys. Rev. B 68, 024302 (2003).
  15. A. Sukhovich, L. Jing, and J. H. Page, "Negative refraction and focusing of ultrasound in two-dimensional phononic crystals," Phys. Rev. B 77, 014301 (2008).
  16. J. H. Oh, H. M. Seung, and Y. Y. Kim, "A truly hyperbolic elastic metamaterial lens," Appl. Phys Lett. 104, 073503 (2014). https://doi.org/10.1063/1.4865907
  17. Z. Chen, B. Guo, Y. Yang, and C. Cheng, "Metamaterials-based enhanced energy harvesting: A review," Physica B 438, 1-8 (2014). https://doi.org/10.1016/j.physb.2013.12.040
  18. C. Jo and I.-K. Oh, "A revisit to imperfect acoustic cloak of multi-layered shell structures considering sound speed and impedances matching," J. Sound Vib. 333, 4637-4652 (2014). https://doi.org/10.1016/j.jsv.2014.05.001