Double Negative Elastic Metamaterial Design Through Electrical-Mechanical Circuit Analogies

Previous studies into solid elastic metamaterials which have a simultaneously negative effective bulk modulus and density have proposed designs for materials with relatively narrow bandwidths, because of the reliance on resonators to provide the dispersive material properties. Some of the proposed novel applications for metamaterials, such as invisibility cloaks and sub-wavelength lenses, generally require materials with inherently larger bandwidths for practical exploitation. In this paper, a well-known electromagnetic metamaterial design is used together with the electrical-mechanical circuit analogies to propose a simultaneously double negative elastic metamaterial design which does not suffer from the narrow bandwidth constraints of previous designs. An interesting consequence of the proposed design is that it has an effective wavelength which asymptotically goes to infinity with frequency.