Anisotropic mass density by two-dimensional acoustic metamaterials

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.Torrent Martí, D.; Sánchez-Dehesa Moreno-Cid, J. (2008). Anisotropic mass density by two-dimensional acoustic metamaterials. New Journal of Physics. 10. doi:10.1088/1367-2630/10/2/02300410Sánchez-Pérez, J. V., Caballero, D., Mártinez-Sala, R., Rubio, C., Sánchez-Dehesa, J., Meseguer, F., … Gálvez, F. (1998). 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