Homogenization scheme for acoustic metamaterials

Min Yang, Guancong Ma, Ying Wu, Zhiyu Yang, Ping Sheng

Research output: Contribution to journalArticlepeer-review

78 Scopus citations

Abstract

We present a homogenization scheme for acoustic metamaterials that is based on reproducing the lowest orders of scattering amplitudes from a finite volume of metamaterials. This approach is noted to differ significantly from that of coherent potential approximation, which is based on adjusting the effective-medium parameters to minimize scatterings in the long-wavelength limit. With the aid of metamaterials’ eigenstates, the effective parameters, such as mass density and elastic modulus can be obtained by matching the surface responses of a metamaterial's structural unit cell with a piece of homogenized material. From the Green's theorem applied to the exterior domain problem, matching the surface responses is noted to be the same as reproducing the scattering amplitudes. We verify our scheme by applying it to three different examples: a layered lattice, a two-dimensional hexagonal lattice, and a decorated-membrane system. It is shown that the predicted characteristics and wave fields agree almost exactly with numerical simulations and experiments and the scheme's validity is constrained by the number of dominant surface multipoles instead of the usual long-wavelength assumption. In particular, the validity extends to the full band in one dimension and to regimes near the boundaries of the Brillouin zone in two dimensions.
Original languageEnglish (US)
JournalPhysical Review B
Volume89
Issue number6
DOIs
StatePublished - Feb 26 2014

Fingerprint

Dive into the research topics of 'Homogenization scheme for acoustic metamaterials'. Together they form a unique fingerprint.

Cite this