Benchmark Analysis of a Helmholtz Resonator for Estimating Acoustic Metamaterial Properties

Abstract

Acoustic metamaterial gets significant attention due to possibility in control, direct and manipulate sound waves. Various metamaterial models have been proposed mostly for air medium, however applicable to water medium for cloaking purpose. Control of the various forms of sound waves is possible with a negative refractive index material, mostly accomplished through bulk modulus and density of the material. However, in case of acoustic metamaterial, the shapes and structures play vital role in accomplishing the same. Present research focuses in analysing the most known acoustic structure, Helmholtz resonator, to estimate the metamaterial properties such as effective mass density and effective bulk modulus. The transfer matrix of Helmholtz resonator is used to extract the scattering matrix, which is subsequently used to estimate the effective bulk modulus and effective mass density. Next, a finite element analysis (FEA) has been carried out using two-load boundary condition to estimate the transfer matrix, validated against experimental results. In a similar manner, the effective mass density and effective bulk modulus have been extracted and validated against analytical results. Moreover, two Helmholtz resonators separated with a known duct have been analysed to evaluate the applicability of transfer matrix method in estimating acoustic metamaterial properties. All analytical results have been validated against numerical results for air medium.