THESIS
2014
xviii, 97 pages : illustrations ; 30 cm
Abstract
In this thesis, I 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 Green theorem
applied to the exterior domain problem, matching the surface responses
is noted to be the same as reproducing the scattering amplitud...[
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In this thesis, I 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 Green 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 six examples from three different types
of wave: elastic shear wave, acoustic pressure wave, and membrane-type
metamaterial, which is a coupling between elastic and acoustic waves. 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 muli-poles
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.
The understandings and relevant techniques of the homogenization scheme
facilitate the design of metamaterials. The acoustic metasurface is presented
as an example. We show that by covering a hard reflecting surface by a
decorated elastic membrane that is separated from the surface by a gap that
is on the order of 1 to 2 cm, one can realize robust surface resonances, each
hybridized from two membrane eigenmodes, which enable perfect impedance
matching to airborne sound. Experiment confirms a hybrid resonance at
152 Hz accompanied by a total absorption of acoustic energy. Owing to the
large displacement of the surface resonance, an acoustic to electric energy
conversion efficiency of 23% has been achieved, thereby making the system
an acoustic-electric transducer.
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