TY - JOUR
T1 - Homogenization scheme for acoustic metamaterials
AU - Yang, Min
AU - Ma, Guancong
AU - Wu, Ying
AU - Yang, Zhiyu
AU - Sheng, Ping
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2014/2/26
Y1 - 2014/2/26
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/552823
UR - http://link.aps.org/doi/10.1103/PhysRevB.89.064309
UR - http://www.scopus.com/inward/record.url?scp=84897696251&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.89.064309
DO - 10.1103/PhysRevB.89.064309
M3 - Article
SN - 1098-0121
VL - 89
JO - Physical Review B
JF - Physical Review B
IS - 6
ER -