Abstract
Acoustic metamaterials (AMM) composed of dynamic subwavelength heterogeneities in a host fluid may generate an overall response that can be represented with dynamic effective parameters such as negative dynamic density or compressibility. Dynamic parameters imply that highly variable effective wavelengths exist even in the long wavelength limit where k0a << 1, with k0 representing the wavenumber in the host and a the descriptive size of the heterogeneity. The variability in effective wavelength is the result of strong frequency dispersion, often accompanied by nonlocal and spatial dispersion effects that complicate efforts to correctly homogenize the medium. This work presents a three-dimensional, source-driven, non-local homogenization scheme for a periodic AMM composed of a host fluid containing dynamic heterogeneities. The resulting constitutive relations couple macroscopic volume-strain and momentum fields and are analogous to the Willis relations of elastodynamics and bianisotropy in electromagnetism. The model accounts for first-order spatial dispersion effects in the long wavelength limit and reveals the origins of coupled field response. One dimensional examples of AMM will be used to demonstrate the homogenization procedure and the effects of spatial dispersion. [Work supported by ONR.]
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