Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2014-02-26Permanent link to this record
http://hdl.handle.net/10754/552823
Metadata
Show full item recordAbstract
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.Citation
Homogenization scheme for acoustic metamaterials 2014, 89 (6) Physical Review BPublisher
American Physical Society (APS)Journal
Physical Review BAdditional Links
http://link.aps.org/doi/10.1103/PhysRevB.89.064309ae974a485f413a2113503eed53cd6c53
10.1103/PhysRevB.89.064309