The Study of Phononic Crystal Band Gaps Using PC Cluster System

• Main Authors: Po-Feng Hsieh, 謝柏夆
• Other Authors: 吳政忠
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/86885694002575270193

碩士 === 國立臺灣大學 === 應用力學研究所 === 92 === In recent years, there is a rapidly growing interest in photonic crystal. The photonic crystal is a periodic arrangement structure of the dielectric materials. In photonic crystal, the electromagnetic wave with the specific frequency is forbidden throughout the periodic structure called band gap phenomena of photonic crystals. The analogy between photons and phonons suggests that band gaps would also be found in the systems comprised of two materials with different elastic properties called “phononic crystals”. Band gaps in phononic crystals may find applications in the acoustic wave filters used to prevent the acoustic waves of the specific incident angle and frequency. This thesis aims at studying the band gap phenomena of phononic crystals using Finite Difference Time Domain (FDTD) method. In this thesis, we use the FDTD method to calculate the band gap phenomena of phononic crystals. In this method, the Bloch’s theorem is used to considering the wave equation and boundary conditions of the periodic structure. From the calculations, the variations of displacements are obtained and then we can obtain the resonances of the structures using the discrete Fourier transform. Finally, the dispersion curves and the range of the band gap of the phononic crystal can be obtained and predicted accordingly. The research of the phononic crystal using FDTD method can predict the range of the band gap successfully. And the CPU time of FDTD method is much smaller than that of Plane Wave Expansion (PWE) method. The method is not only faster but also accurate in the design of the engineering devices.