Elastic wave propagation and bandgaps mechanism of two-dimensional windmill-like elastic metamaterials

Abstract

Inspired by the advantages of the grille structures, an innovative two-dimensional (2D) windmill-like elastic metamaterials (EMs) based on multiple resonators is presented for obtaining ultrawide bandgaps at a relatively low frequency. The dispersion relations and the mechanism of bandgap formation are investigated using an analytical model of windmill-like EMs. Moreover, the low-frequency bandgap between the optical and acoustic dispersion curves of windmill-like EMs with a single local resonator has been independently determined analytically. Afterward, the band structures of windmill-like EMs with different numbers of local resonators and symmetry and the same total mass are compared. By applying the finite element method, continuous symmetrical and chiral windmill-like EMs are established and analyzed based on the analytical results. The introduction of the antisymmetric chiral structure results in a 23.08% reduction in the frequency of the first bandgap compared to symmetric windmill-like EM.A further study is conducted on the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission spectra. Both the numerical analysis and experimental validation of finite periodic lattices demonstrate the effect of vibration attenuation on longitudinal elastic waves. This research provides important clues and theoretical guidance for the design of vibration isolators, beams, plates, and other renewed devices.