Nonlocal homogenisation scheme for lossless and anisotropic metafluids and phononic crystals

Abstract

We present a systematic homogenisation approach to describe macroscopic dynamics of generic periodic acoustic materials composed of a rigid structure filled with a lossless fluid. This approach takes temporal dispersion as well as spatial dispersion effects into account, and can characterise, in a general manner, the oblique propagation and anisotropic effects. The theory is formulated such that all effects are encoded in, only, the effective frequency and wavevector dependent density, which can be calculated through a source-driven problem. Also, we demonstrate that the theory can homogenise materials even in frequency band gaps, including those that correspond to local-resonance phenomena or to Bragg scattering.We present a systematic homogenisation approach to describe macroscopic dynamics of generic periodic acoustic materials composed of a rigid structure filled with a lossless fluid. This approach takes temporal dispersion as well as spatial dispersion effects into account, and can characterise, in a general manner, the oblique propagation and anisotropic effects. The theory is formulated such that all effects are encoded in, only, the effective frequency and wavevector dependent density, which can be calculated through a source-driven problem. Also, we demonstrate that the theory can homogenise materials even in frequency band gaps, including those that correspond to local-resonance phenomena or to Bragg scattering.