Analytical Modeling of Acoustic Exponential Materials and Physical Mechanism of Broadband Anti-Reflection

TL;DR

This paper develops an analytical model for acoustic exponential materials, revealing their broadband anti-reflection mechanism and demonstrating ultra-low reflection in engineered micro-perforated plates across a wide frequency range.

Contribution

It introduces an analytical solution for acoustic exponential materials within transfer matrix theory, enabling accurate prediction and design of broadband anti-reflective acoustic structures.

Findings

Achieved about 0.86% reflection from 420 Hz to 10,000 Hz

Designed an acoustic dipole array mimicking exponential mass distribution

Provided a new analytical tool for gradient acoustic metamaterials

Abstract

Spatially exponential distributions of material properties are ubiquitous in many natural and engineered systems, from the vertical distribution of the atmosphere to acoustic horns and anti-reflective coatings. These media seamlessly interface different impedances, enhancing wave transmission and reducing internal reflections. This work advances traditional transfer matrix theory by integrating analytical solutions for acoustic exponential materials, which possess exponential density and/or bulk modulus, offering a more accurate predictive tool and revealing the physical mechanism of broadband anti-reflection for sound propagation in such non-uniform materials. Leveraging this method, we designed an acoustic dipole array that effectively mimics exponential mass distribution. Through experiments with precisely engineered micro-perforated plates, we demonstrate an ultra-low reflection rate of about 0.86% across a wide frequency range from 420 Hz to 10,000 Hz. Our modified transfer matrix approach underpins the design of exponential materials, and our layering strategy for stacking acoustic dipoles suggests a pathway to more functional gradient acoustic metamaterials.