Metamaterial Homogenization and Acoustic Metasurface (Vanaie testing)

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 amplitudes. We verify our scheme by applying it to six examples from three different wave-types: elastic shear waves, acoustic pressure waves, and decorated-membrane systems who is the coupling of the formal two. 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.