| In this thesis, I present a homogenization scheme for acoustic metamaterialsthat is based on reproducing the lowest orders of scattering amplitudesfrom a finite volume of metamaterials. This approach is noted to differsignificantly from that of coherent potential approximation, which is basedon adjusting the effective medium parameters to minimize scatterings inthe long wavelength limit. With the aid of metamaterials' eigenstates,the effective parameters such as mass density and elastic modulus can beobtained by matching the surface responses of a metamaterial's structuralunit cell with a piece of homogenized material. From Green theoremapplied to the exterior domain problem, matching the surface responsesis noted to be the same as reproducing the scattering amplitudes. Weverify our scheme by applying it to six examples from three different typesof wave: elastic shear wave, acoustic pressure wave, and membrane-typemetamaterial, which is a coupling between elastic and acoustic waves. Itis shown that the predicted characteristics and wave fields agree almostexactly with numerical simulations and experiments, and the scheme'svalidity is constrained by the number of dominant surface muli-polesinstead of the usual long wavelength assumption. In particular, thevalidity extends to the full band in one dimension and to regimes near theboundaries of the Brillouin zone in two dimensions.;The understandings and relevant techniques of the homogenization schemefacilitate the design of metamaterials. The acoustic metasurface is presentedas an example. We show that by covering a hard reflecting surface by adecorated elastic membrane that is separated from the surface by a gap thatis on the order of 1 to 2 cm, one can realize robust surface resonances, eachhybridized from two membrane eigenmodes, which enable perfect impedancematching to airborne sound. Experiment confirms a hybrid resonance at152 Hz accompanied by a total absorption of acoustic energy. Owing to thelarge displacement of the surface resonance, an acoustic to electric energyconversion efficiency of 23% has been achieved, thereby making the systeman acoustic-electric transducer. |
