Effective parameters and energy of acoustic metamaterials and media

Abstract

An approach is proposed to describe a general form of acoustic media, in particular, acoustic metamaterials, based on their modeling with the simplest discrete periodic structures. The parameters of the discrete models, determined from the dispersion equation, are taken as the effective parameters of the modeled media. Transfer to an effective continuous medium is achieved by uniform distribution of these parameters over the length of the periodicity cell. It is shown that all of the wave motion characteristics of the medium, including the energy characteristics, are expressed through the effective parameters thus introduced. The necessary formulas are derived. Examples are given. The proposed method is useful for designing acoustic materials with the given wave properties.