Dynamic behaviour of a metamaterial system with negative mass and modulus

Different models of metamaterials have been developed to generate negative mass and/or negative modulus. The resulting mass and modulus in existing works, however, cannot be independently controlled. The current study presents a new representative cell of elastic metamaterials in an effort to provide a comprehensive model for generating negative mass and/or negative modulus. The current model consists of a series of properly arranged rigid bodies and linear springs. By introducing both translational and rotational motions in the representative cell, negative mass and negative modulus can be obtained in a controlled manner. The mechanisms and conditions under which negative mass and/or negative modulus can be achieved are studied in detail. Numerical examples indicate that by varying the design of the representative cell, different properties of the material system can be reliably generated, i.e., double negative (mass and modulus) or single negative (mass or modulus). The dynamic behaviour of the developed material system under different loading frequencies is evaluated and the longitudinal elastic wave propagation in such metamaterials is studied.