Wave propagation in a dual-periodic elastic metamaterial with multiple resonators

Abstract

The behaviour of elastic metamaterials is dominated by the local structure of their representative cells and their periodicity. Previous works indicated that introducing multiple resonators in the representative cells can generate better performance, such as wider band gaps. Another interesting phenomenon observed in previous studies is that elastic metamaterials featuring dual periodicity can generate asymmetric wave transmission and negative effective mass and/or modulus. However, the general property of dual-periodic metamaterials coupled with multiple local resonators are rarely explored. In the current paper, the general mechanism of implementing multiple local resonators into dual-periodic metamaterial cells is systematically studied and a new elastic metamaterial model featuring negative effective mass and/or modulus based on translational resonances is presented. In this new model, the property of the multiple local resonators and the dual-periodicity can be conveniently adjusted to achieve single negativity (negative mass or negative modulus) or double negativity (negative mass and modulus) in different frequency ranges. Due to the great flexibility of generating negative effective parameters stemming from its unique structure, the proposed elastic metamaterial can generate a broad band gap in the low frequency range with exponential wave attenuation, and the positions of the frequency ranges featuring negative phase velocity can be modified according to the desired working frequencies. To elucidate the versatility of this model, numerical validation of typical examples has been provided to demonstrate the phenomena of wave attenuation and backward wave propagation.