Acoustic Properties of Fluidlike Metamaterials Based on Sonic Crystals

Abstract

A homogenization method is used to get the effective parameters of two-dimensional clusters of solid cylinders embedded in a non viscous fluid or gas. The full elasticity is employed to describe the properties of cylinders. Asymptotic relations are derived and employed to formulate a method of homogenization based on the scattering properties of the cluster. Exact formulas for the effective parameters (i.e., effective sound velocity and effective density) are obtained as a function of the location of each cylinder, its physical parameters, and the embedded medium. Results of several solid-fluid composites will be reported. Also, phase-diagrams of fluid-like metamaterials based on sonic crystal will be analyzed. It is concluded that the method provides a tool to design acoustic metamaterials with prefixed refractive properties. The long wavelength behavior (homogenization) of two dimensional sonic crystals (periodic arrangements of two dimensional sound scatters) has been widely studied in the last years [1–9] due to its possible use as refractive acoustic devices. In a previous paper [2] the authors develop a theory to obtain the effective acoustic parameters of a cluster of fluid cylinder embedded in a non viscous fluid or gas, both for ordered and disordered case. The application of this theory to solid cylinder-fluid medium is only possible when the cylinder is rigid, that is, the sound does not propagates inside the cylinder. When it happens, elasticity must be taken into account, and a solid cylinder, in principle, cannot be considered a fluid cylinder with similar parameters. Here, the theory will be completed for the case of an elastic cylinder, and it will be discussed under what conditions an elastic cylinder can be considered a fluid cylinder, and which ones are the acoustic parameters of this fluid cylinder. It will be shown also that the effective parameters of clusters of elastic cylinders can lead to an effective medium with an effective speed of sound both higher and lower than that of the surrounding medium, and a phase diagram to analyze and predict this behavior will be given. Finally, a method to obtain a relative acoustic impedance equal to one (zero surface reflectance) will be discussed, and also a phase diagram to obtain it will be given.