Investigation on negative hybrid-resonant bands of elastic metamaterials by revised effective medium theory

In this paper, a revised effective medium theory is presented to investigate negative dispersion bands which are formed by the hybridization effect of multiple resonances. The negative hybrid-resonant bands are selective for propagation of compressional or shear waves. With a simplified model, a new negative dispersion band is firstly achieved by combinations of negative transverse modulus and negative mass density, thus three negative dispersion bands are formed by hybridization effect of a monopolar or quadrupolar resonance and a dipolar resonance. Secondly, transmission spectrums are also performed to demonstrate the negative behaviors of three hybrid resonant bands and illustrate their unusual transmission properties. Moreover, a revised effective medium theory based on numerical simulation is derived to obtain four effective parameters of the elastic metamaterials along two wave vectors when the long wavelength limitation is not fully satisfied, which perfectly explain the unusual transmissions of negative dispersion bands. Finally, the physical mechanisms of negative parameters are systematically investigated by three typical deformation states. The work has guiding significances for designing the elastic metamaterials structures with negative hybrid-resonant bands.