Resonant Modes of One-Dimensional Metamaterial Containing Helmholtz Resonators with Point Defect

Dongbao Gao,Kaifeng Han,Xuanjun Liu,Xinwu Zeng

doi:10.4236/jmp.2017.810102

Abstract

The metamaterial constructed by Helmholtz resonators (HR) has low-frequency acoustic forbidden bands and possesses negative mass density and effective bulk modulus at particular frequencies. The resonant modes in one-dimensional HR structure with point defect were studied using finite element method (FEM). The results show that the acoustic energy is localized between the resonant HR and the opening in the local-resonant-type gap. There is a high pressure area around the defect resonator at the frequency of defect mode. In the Bragg type gap, the energy mainly distributes in the waveguide with harmonic attenuation due to the multi-scattering. Phase opposition demonstrates the existence of negative dynamic mass density. Local negative parameter is observed in the pass band due to the defect mode. Based on further investigation of the acoustic intensity and phase distributions in the resonators corresponding to two different forbidden bands, only one local resonant mode is verified, which is different from the three-component local resonant phononics. This work will be useful for understanding the mechanisms of acoustic forbidden bands and negative parameters in the HR metamaterial, and of help for designing new functional acoustic devices.

Highlights

IntroductionWith the increasing research on phononic crystals and acoustic metamaterials, the structure based on Helmholtz resonators (HR) has been reconsidered for its property of sound forbidden [3]-[8]
To study the resonant modes in the metamaterial constructed by Helmholtz resonators with point defect is useful for understanding the mechanisms of acoustic band gaps and negative parameters
The distributions of acoustic intensity and phase for 1D Helmholtz resonators (HR) structure with point defect were analyzed basing on 3D finite element method (FEM)

Summary

Introduction

With the increasing research on phononic crystals and acoustic metamaterials, the structure based on HRs has been reconsidered for its property of sound forbidden [3]-[8]. A localized mode is that, at a particular frequency, the linear free oscillations are trapped around the defect resonators and decay exponentially away from them [7] In this case, the acoustic energy can be captured by the point defect or limited directionally transmitting along the line defect and area defect. Since the complex geometry is simplified in former theoretical methods which are unable to investigate the detailed field distribution in the structure, an accurate approach must be introduced to analyze the resonant modes property of the HR metamaterial. Local resonant modes were investigated for different forbidden gaps

Model and Verification of the Method

Simulation Based on FEM

Conclusions