Tunable bandgap characteristic of various hexagon-type elastic metamaterials for broadband vibration attenuation

Inspired by the advantages of the hexagon lattices and auxetic metamaterials, the typical two-dimensional (2D) hexagon-type elastic metamaterials (EMs), that is, the concave, the convex, and the rectangular hexagon-type EMs, are presented for investigating the dynamic behavior systematically. Firstly, the lumped mass-spring models are used to construct the band structures, and the eigenmodes are obtained by solving the eigenvalue problem of motion equations to unveil the formation mechanisms of bandgap (BG). Note that the specific dispersion branches are characterized by eigenfrequencies with the eigenmodes presenting similar vibrational forms, rather than just ranking the eigenfrequencies from low to high. Furthermore, the dependence on the main structural parameters of the lumped mass-spring models is investigated to achieve tunability of the bandgap characteristics. Then, the continuum models are also established to study the formation of bandgaps as well as the propagation of waves based on eigenmodes and transmission. The comprehensive study of the physical mechanics of the unit cells is carried out, encompassing the analysis of iso-frequency contours, deformation fields, and mesh-independent analysis. Finally, both the numerical analysis and experimental validation demonstrate the effect of vibration attenuation on in-plane elastic waves, which has the ideal great agreement with the prediction of the band structures (the values of the frequency response functions are much less than -20 dB within the ranges of BGs). This research is expected to provide valuable insight into the design of vibration isolators, beams, plates, and other devices that are being renewed.