Band Structure of Phononic Crystal Consist of Hollow Aluminum Cylinders in Different Media; Finite Element Analysis

Zafer Ozer,Mehtap Demir,Amirullah M Mamedov,Ekmel Ozbay

doi:10.1088/1757-899x/613/1/012018

Abstract

In this study, we investigated band structure of a 2D Phononic Crystal (PnC) which was consist of hollow aluminum cylinders in different media. To validate the finite element predictions, we made a square lattice PnC which has lattice constant a = 14mm, outer radius r1 = 5mm and inner radius r2 = 4mm of cylinders. In our experimental measurement, by using a signal generator software, we sent 100 Hz-20kHz sine signal for 5 seconds duration from speaker to the PnC where placed 1m away from. With the help of a microphone, we recorded the sound in front of the PnC (Pin ) and backside the PnC (Pout ). Then we were converted our recording into frequency domain by standard FFT algorithm, we calculated the Transmission Loss value according to the formula TL = 20*log10 (Pout / Pin ) and obtained the experimental Transmission Loss. After experimental validation, we conducted band structure analysis of different combination of the 2D PnC by finite element method.

Highlights

Phononic Crystals are periodic structures made of two elastic materials with different mechanical properties
Obtained acoustic band structure in Brillouin zone of the square lattice was plotted along the M–Г–X– M path for the two dimensional (2D) Phononic Crystal (PnC) as seen in fig. 3, the narrow full band observed in the dispersion curves between 13.2-13.8 kHz and a partial band between 8-14 kHz in Γ-X direction
In order to compare the band structure obtained by Finite Element Method (FEM) and the sound attenuation obtained by PnC, transmission loss was obtained numerically with finite structure seen in Fig. 2 by FEM and experimental measurement

Summary

Introduction

Phononic Crystals are periodic structures made of two elastic materials with different mechanical properties. The basic property of PnC is that mechanical (either elastic or acoustic) waves, having frequencies within a specific range, are not able to propagate within the periodic structure. This range of forbidden frequencies is called a phononic band gap. This is analogous to electrons in a crystal, where classical waves propagate in a structure with periodically modulated material parameters [1].

Published under licence by IOP Publishing Ltd

Results and discussions

Conclusions