Acoustic Metamaterials Applied on Circular Interfaces

A number of planar-interface types of acoustic metamaterials (PAMs), including tapered labyrinthine structures and porous materials, have been proposed based on the generalized Snell's law. Circular-interface types of acoustic metamaterials (CAMs), however, have not been studied extensively. These can find applications on aero-engine intakes and aircraft fuselages. In this study, CAMs are studied analytically and numerically. An analytical expression of the sound refraction through the CAMs is derived based on the principle of stationary phase. In the numerical study, several fibrous metal foams with various parameters that generate a periodical linear phase gradient on the transmitted interface, are applied on circular interfaces. Results indicate that two parameters, which are the angular distance over a period of CAMs and the ratio between the radius of a circular interface and the incident wavelength, are determining factors in the excitation of high-order wave modes in the scattered sound pressure field. The high-order wave modes will disappear in the refracted sound pressure field when these two parameters are at critical values. The analytical expression is derived based on the assumption that the distance between two incident sound wave paths is infinitesimal. The assumption leads to the differences between the critical values given by analytical predictions and numerical simulations, which can be significantly reduced with the increase of ratios between the radius of a circular interface and the incident wavelength. This study offers a technical method in extending the industrial applicability of acoustic metamaterials from a planar interface to a circular interface. Copyright © (2018) by International Institute of Acoustics & Vibration. All rights reserved.