On the behavior of acoustic/elastic metamaterials with anisotropic mass density

The effect of anisotropic mass density in acoustic/elastic metamaterials on wave propagation is presented in this research. The use of microstructures to achieve anisotropic physical properties in metamaterials is an intensive field of study. In this work, a two-dimensional (2D) ‘mass-in-mass’-spring lattice system is utilized to achieve anisotropic effective mass density in two orthogonal principal directions.In each direction, the effective mass density is frequency-dependent and can be “effectively negative” if it falls within the frequency bandgap region. A 2D numerical continuum model,based on a recently developed cantilever-in-mass model, is further presented and examined to study how wave input angles affect 2D wave propagation. Results show that wave attenuation is dependent on both input frequency and wave input angle in a 2D metamaterial. This study demonstrates a case whereby wave attenuation is achieved,by selecting wave input frequency in the bandgap region to enact “negative effective mass density”. This study also illustrates another case when wave attenuation is obtained for positive anisotropic mass density. This behavior is achieved by directing wave propagation to transverse direction at a specific input wave angle of 60°. Both numerical calculations of mass-spring lattice model and continuum cantilever-in-mass model show good agreement.