ANISOTROPIC BAND GAP IN A 2D ACOUSTIC METAMATERIAL

A two-dimensional (2D) metamaterial possessing an effective anisotropic mass is investigated. This metamaterial is a composite material in the form of an internal mass connected in two directions to the host medium. A 2D mass-in-mass lattice model is used to characterize the dynamic behavior of the metamaterial. If modeled as an effective spring-mass lattice system, the metamaterial may possess a frequency-dependent effective mass. Moreover, if an equivalent homogenous elastic continuum is used to represent the metamaterial, an anisotropic mass density may result and may assume negative values for wave frequencies that are near the local resonance frequency of the Internal mass. In fact, it was found that negative mass density occurs in the band-gap of the metamaterial. Unusual wave motion arises from the anisotropic band gap structure. In the present study, wave propagation in the representative continuum model for the metamaterial is studied in order to understand the unusual features of the dynamic behavior of the metamaterial.