Focusing by Gradient-index Sonic Crystals and Dispersion Characteristics with Elliptic Rods

• Main Authors: Chi Lin, 林奇
• Other Authors: 宋家驥
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/53466857492500281670

碩士 === 國立臺灣大學 === 工程科學及海洋工程學研究所 === 101 === Similar to photonic crystals, sonic crystals (SC) is a periodic array composed of scatters embedded in a host material. Here we study the dispersion characteristics of 2D sonic crystal with circular and elliptic rods first, including band gap, partial band gap and directional propagation, and then the gradient-index sonic crystals. The use of plane wave expansion method is to obtain the band structure. We compare the propagation characteristics analyzed by the equifrequecy surfaces with the simulation results by finite element method. The refractive indexes for various filling fractions, materials or frequencies of a sonic crystals are all different. By the concept of gradient-index in optics, we designed a two-dimensional gradient-index (GRIN) sonic crystals to control the propagations of acoustic waves. The GRIN SC was composed of square array steel cylinders in the background of air. The refractive index is obtained by plane wave expansion method, and the wave propagation is simulated by finite-element method. Altering the rotation angles of the elliptic rods in 2D SC to make various refractive indexes and the refractive index distribution is designed as hyperbolic secant function. The results and discussions for different layers and gradient coefficient demonstrate the GRIN SC lens focusing behavior of acoustic wave. It is anticipated that this study may be applied in 3D acoustic assembled devices or in ultrasonic devices.