Determination of effective properties and effective thickness of resonant acoustic metamaterial

Abstract

Multiple scattering in periodic structures with strong modulation of elastic constants leads to phononic band structures. According to the Bragg’s theory, the spatial modulation of the periodic structure must be of the same order as the wavelength of considered elastic waves. A resonant acoustic metamaterial’s respective wavelength is about two orders of magnitude larger than the lattice constant. Each unit cell consists of a locally resonant structural unit in contrast to simple acoustic scatterers in phononic crystals. In this report, we will address the design of locally resonant sonic materials. These materials may offer dynamic effective negative material properties around resonance frequency. Locally resonant sonic crystals, such as an array of Helmholtz resonators and cylinders or spheres coated with acoustically soft material, were analyzed in the literature. However, existing literature lacks a systematic study of the dependence of effective properties for a finite slab of these metamaterials both on the geometry and the properties of its constituent materials. In this report, we present a method for obtaining effective properties and effective thickness of a slab of acoustic metamaterial. The dependence of effective acoustic properties of a metamaterial on the geometrical and acoustic properties of constituent materials will be discussed.