Performance and stability analysis of active elastic metamaterials with a tunable double negative response

Metamaterials can possess material parameters which do not exist in conventional materials. Consequently metamaterials provide a novel way to control wave propagation within a structure. These characteristics are achieved by designing a material with a particular sub-wavelength structure which leads to negative constitutive parameters in the long wavelength limit. For elastic materials these parameters are the density and modulus. In a previous study, a theoretical design for a novel active elastic metamaterial (AEM) was proposed. In this material control forces are applied to an array of resonant units in order to achieve a simultaneously negative effective density and modulus over a prescribed frequency band. This design potentially overcomes some of the restrictions imposed by previous passive designs. In this paper a new design of AEM is proposed which compensates for actuator dynamics and provides a basis for practical implementation. This design is shown to have a stable response with a tunable double negative frequency band.