Retrieving effective acoustic impedance and refractive index for size mismatch samples

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 first considered the air gap as a separate domain and modeled the problem as a bilayer metamaterial inside a duct. Then, we established theoretically that when the dimensions of an acoustic metamaterial are known, the effective properties may be derived by solving a set of eight linear equations. Finally, we assessed the proposed technique using numerical simulation data. The proposed method is shown to calculate the effective refractive index and impedance with an error of less than 1%. This method provides an efficient approach to analyze the effective properties of acoustic metamaterials of different sizes.