Wave propagation of 2D elastic metamaterial with rotating squares and hinges

Auxetic metamaterials have attracted widespread attention because of their untraditional physical properties and practical application values. In this paper, we focus on an elastic auxetic metamaterial composed of hinged rotating rigid squares. Theoretical analysis based on a mass-spring system is adopted to investigate the wave propagation behavior and vibration characteristic of the elastic metamaterial (EM). The motion equations are derived based on a discrete rigid-squares hinged model. The dispersion curves and eigenmodes under two configurations are studied based on Bloch's theorem with linear assumption. Moreover, the evolution process of the bandgap with the change of configuration parameter is revealed systematically and the transmission of the finite periodic hinged squares are explored under harmonic excitation. The results show that with proper parameter configuration, the considered EM structure can exhibit a complete bandgap. The formation mecha-nism of the bandgap is translational and rotational mode resonance. Moreover, the expressions of bandgap boundary frequencies with parameters are analytically derived, which provides explicit guidance for the adjustment of the bandgap characteristics and the parameter design of the structure. Furthermore, the harmonic transmission analysis validates the wave attenuation predicted by the bandgap. The structure can convert part of the energy into rotational energy, thereby obtaining a better vibration control capability. This work provides significant guidance for the design of elastic metamaterials with potential applications of vibration control.