Abstract
We show that specially designed two-dimensional arrangements of full elastic cylinders embedded in a nonviscous fluid or gas define (in the homogenization limit) a new class of acoustic metamaterials characterized by a dynamical effective mass density that is anisotropic. Here, analytic expressions for the dynamical mass density and the effective sound velocity tensors are derived in the long wavelength limit. Both show an explicit dependence on the lattice filling fraction, the elastic properties of cylinders relative to the background, their positions in the unit cell, and their multiple scattering interactions. Several examples of these metamaterials are reported and discussed.
Highlights
Whose properties can be tailored by changing the positions of the scatterers in the unit cell and/or their material constituents
The method is based on the properties of SC in the homogenization limit
It was shown that 2D arrays of cylinders ordered in lattices with symmetries other than the square and hexagonal symmetry behave in the range of large wavelengths as effective acoustic metamaterials having acoustic parameters that are anisotropic
Summary
An anisotropic acoustic medium can be characterized by its anisotropic mass density tensor, ρi j , and the scalar bulk modulus, B [21]. From equation (1b) the wave equation for the acoustic pressure is obtained: i,k ρk−i 1. Its insertion in equation (4) gives: ρx−x1 cos θ + ρy−y1sin θ + (ρx−y1 + ρy−x1) sin θ cos θ k2. The speed of sound, c = ω/k, is c2(θ ) = B[ρx−x1 cos θ + ρy−y1 sin θ + (ρx−y1 + ρy−x1) sin θ cos θ ],. This is the well-known Wood’s law [22] generalized to the case of an anisotropic medium. Consider a cluster of N parallel cylinders with arbitrary transversal section located at Rα
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