Elastic metamaterials with negative bands

Abstract

The unusual properties of a metamaterial come from special resonances supported by its resonating structure units. Guided by a previously developed effective medium theory, which links the resonances of the microstructures and the unusual properties, two types of elastic metamaterials in two dimensions were designed with different resonant structures in their building blocks that exhibit multiple negative dispersion bands with special characteristics. The first type possesses negative mass density and negative shear modulus simultaneously over a large frequency regime, which leads to a negative band for shear waves only. Mode conversion takes place at the interface of the metamaterial and the common solids. The second type is able to produce negative effective moduli in different frequency regimes within a large frequency regime of negative effective mass density. This results in a super anisotropic negative band and a negative band that only compressional is allowed. All of these unusual properties are demonstrated by simulations. This work was supported by Hong Kong RGC Grant No. 605008, HKUST604207 and KAUST start-up package.