Supplementary Materials for "Gear-based Metamaterials for Extraordinary Bandgap Tunability"

In this file, we further explain the bandgap equations, model parameters, and Simulation methods and simulation results. In supplementary Table 1, we list the properties of existing metamaterials with tunable bandgaps, controlled by Piezoelectric materials, Magnetorheological materials, Magnetic field, shape-morphing structures, etc. In supplementary Table 2, we show the typical bands of metamaterials with different Young's modulus of substrate material Esub. Many references for the investigation of different tunable metamaterials is also listed here.