Retrieving Effective Acoustic Impedance and Refractive Index for Size Mismatch Samples

TL;DR

This paper introduces an analytical method to accurately determine the effective acoustic properties of size-mismatched metamaterials using measured transmission and reflection data, validated by numerical simulations.

Contribution

It presents a novel analytical solution for extracting effective acoustic impedance and refractive index in size-mismatched metamaterials, solving a set of linear equations with high accuracy.

Findings

Achieves below 1% error in property estimation

Validates method with numerical simulations

Provides an efficient approach for size-mismatched acoustic metamaterials

Abstract

In this paper, we have presented an analytical solution to extract the effective properties of acoustic metamaterials from the measured complex transmission and reflection coefficients when the metamaterial and impedance tube have different sizes. We have first modeled this problem as a bilayer metamaterial located inside a duct and treated the air gap as a separate domain. Then we have mathematically proved that the effective properties of acoustic metamaterial can be obtained by solving a set of eight linear equations when the dimensions are known. Finally, we have evaluated the proposed method with results from numerical simulations. It is shown that the proposed method can calculate the effective refractive index and impedance with an error of below 1\%. This method provides an efficient approach to analyzing the effective properties of acoustic metamaterials of various sizes.