Wave propagation in an elastic metamaterial with anisotropic effective mass

The effect of anisotropic mass density on wave propagation in acoustic/elastic meta materials is presented in this research. The use of microstructures to achieve mass anisotropy in metamaterials is an intensive field of study. In this work, a numerical continuum model, based on a recently developed cantilever-in-mass model, is proposed. Mass anisotropy in this model is derived based on analytical calculations of a two-dimensional (2D) 'mass-in-mass'-spring lattice system. The mass-spring lattice is able to portray anisotropic effective mass density in two orthogonal principal directions. Effective mass density along each direction is frequency-dependent. A strong "effective mass anisotropy" is accomplished within the frequency band gap or just below the frequency range of negative effective mass. The proposed mass-cantilever continuum model is used to examine 213 wave propagation. Results show that wave attenuation in a metamaterial with 2D anisotropic mass density is dependent on both input frequency and wave input angle. This study demonstrates a case whereby wave attenuation is achieved by selecting wave input frequency in the band gap region to enact "negative effective mass density", thereby mitigating wave propagation. In this case, the most efficient attenuation performance is achieved at an input wave angle of 0 degrees. This study also illustrates another case whereby wave attenuation is obtained by mass anisotropy at a frequency just below the local resonance frequency. Wave attenuation is achieved by redirecting wave propagation along the transverse direction, particularly prominent at an input wave angle of 70 degrees. Both numerical calculations of mass-spring lattice model and continuum cantilever-in-mass model show excellent agreement with each other. (C) 2019 Elsevier B.V. All rights reserved.