Discrepancies between wave suppression ranges and bandgaps in the metamaterials with gradient resonators

This work investigates the wave behaviors and dynamical responses of the metamaterials with gradient resonators in which the stiffness and mass of gradient resonators vary with the same gradient factors. The dispersion relations are calculated by applying Bloch theorem and the dynamical responses of the finite lattice are obtained by numerical methods. A discrepancy between the transmission suppression ranges and bandgaps appears, which goes beyond that the bandgaps and the drops in transmission spectrum can verify each other. To explain this discrepancy, the effective mass is calculated and the Bloch modes are evaluated by the participation ratio. The results indicate that elastic waves of a frequency with discrepancy can propagate through the lattice, and the absorption of vibration energy by the gradient resonators reduces the vibrational amplitude of the main mass, thus a significant drop appears in the transmission spectrum. The metamaterial with gradient resonators helps to expand the vibration isolation beyond bandgaps.