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2015 Vol.34, Issue 5
Acoustic Band Structures in Two-dimensional Phononic Crystals with a Square Lattice in Water

수중에서 정방형 격자를 갖는 2차원 포노닉 크리스탈의 음향 밴드 구조

Yoon Mi Kim1
,
Kang Il Lee1*
,
Hwi Suk Kang2
,
Suk Wang Yoon2
김 윤미1
,
이 강일1*
,
강 휘석2
,
윤 석왕2
1Department of Physics, Kangwon National University
1강원대학교 물리학과
2성균관대학교 물리학과
*교신저자. *Corresponding Author. 
30 September 2015. pp. 335-342
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Abstract

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 ΓX 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.

Keywords
Acoustic metamaterial
Phononic crystal
Band gap
Transmission coefficient
Reflection coefficient

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 ΓX 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.

키워드
음향 메타물질
포노닉 크리스탈
밴드 갭
투과계수
반사계수
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Information
  • Publisher :The Acoustical Society of Korea
  • Publisher(Ko) :한국음향학회
  • Journal Title :The Journal of the Acoustical Society of Korea
  • Journal Title(Ko) :한국음향학회지
  • Volume : 34
  • No :5
  • Pages :335-342
  • Received Date : 2015-06-17
  • Revised Date : 2015-07-27
  • Accepted Date : 2015-08-17
  • DOI :https://doi.org/10.7776/ASK.2015.34.5.335
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