Wave propagation in two-dimensional elastic metastructures with triangular configuration

Abstract

A triangular configuration spring–mass model is proposed in this paper to investigate the dependence on structural parameters of elastic wave propagation in two-dimensional (2D) elastic metamaterials/metastructures (EMs). Based on the lattice dynamics, the dispersion relations of the multiple degrees of freedom (DOF) unit cell and the vibration propagation of elastic waves are derived. Moreover, the effects of the configuration angle, spring stiffness, and mass distribution on the frequency and width of bandgaps are explored. The bandgap can be widened by 31.5% or as low as 32 Hz by reasonably adjusting the stiffness and mass distribution. Finally, the asymmetric structure (Model II-1) with the most pronounced full-bandgap difference produced by scanning along two irreducible Brillouin zones (IBZs) of Γ-X-M-Γ and Γ-Y-M-Γ was selected to explore the directional bandgap properties of EM. The dispersion curves obtained by the eigenmode division method are more consistent with the attenuation ranges of the vibration transmittance and can be used to easily and comprehensively identify the bandgap properties. This research provides important clues and theoretical guidance for the design of vibration isolators, beams, plates and other renewed devices.