On the dynamic behaviour of a two-dimensional elastic metamaterial system

A two-dimensional mechanical system with local resonators is proposed as an elastic metamaterial model that exhibits both negative mass and negative modulus under specific frequencies. The proposed representative cell, which consists of a series of properly arranged local elements, can generate controllable translational and rotational resonance. By adjusting the local property of the element negative mass and negative modulus can be achieved independently. The dynamic behaviour of the developed metamaterial system under different loading frequencies is studied in detail and the effective mass and effective elastic modulus under different loading frequencies are evaluated. Examples of harmonic elastic waves in this two-dimensional metamaterial system are studied to illustrate the effect of the generated negative mass and/or modulus on wave propagation.