Modelling of elastic metamaterials with negative mass and modulus based on translational resonance

A new elastic metamaterial model is proposed based on translational resonance to obtain simultaneously negative mass and negative modulus within specific frequency ranges, which consists of a series properly arranged stiff and soft components. Two different translational resonances exist in the proposed metamaterial representative cell. One resonance contributes directly to the negative effective modulus and the coupled effect of the two resonances can generate negative effective mass. The unique feature of the representative cell endows the model with great flexibility to generate negative effective parameters in different frequency ranges from various selections of materials and different geometrical parameters. The effect of the structural parameters of the representative cell on the frequency ranges with single negativity (negative mass or negative modulus) or double negativity (negative mass and negative modulus) has been evaluated in detail. Periodic metamaterials are formed by connecting multiple representative cells, and wave propagation in such metamaterials is studied. In the frequency ranges with single negative parameters, strong wave mitigation is observed, as expected. In the frequency ranges with double negative parameters, negative phase velocity is clearly shown. Typical examples are presented to illustrate the dynamic property of the current metamaterial. (C) 2018 Published by Elsevier Ltd.