Hierarchical metamaterial with simultaneoulsy negative mass density and Young's modulus

Abstract

In this study, we propose one-dimensional hierarchical metamaterials that have simultaneously negative mass density and Young's modulus from the perspective of effective medium. Frequency-dependent effective properties of HMMs are derived by using a dynamic homogenization theory and double negative properties are obtained at the second optical branch. Since the frequency ranges of the double negativities for hierarchical structures are significantly lower than those for periodic structures without structural hierarchy, they satisfy three necessary conditions for dynamic homogenization, which means the double negativities of HMMs are physically meaningful values. By exploring all the possible double negativities of HMMs, we check whether we can design metamaterials with opposite sign of mechanical properties in nature, ultimately aiming at a perfect transmission of wave energy