Bandgap merging and widening of elastic metamaterial with heterogeneous resonator

Much effort has been devoted to exploring broad bandgap in low frequency with limited mass by various structural designs of elastic metamaterials (EMs). In this paper, a heterogeneous resonator configuration in 1-D dissipative lattice mass system without additional increase of mass and coupling complexity is presented to generate multiple bandgaps. Special attention is focused on the effect of parameters control to merge the multiple bandgaps, and the analytical expression of parameters setting is obtained for broad bandgap merging. Specifically, the merging of all bandgaps in EMs with two heterogeneous resonators achieves 30% lower and 135% wider bandgap than that of classical local resonance (LR) EMs with the same mass ratio and stiffness ratio, while the merging of three LR bandgaps in EMs with three heterogeneous resonators is 20% lower and 63% wider. The relative movements of masses in the unit cell at different frequencies are depicted to reveal the working mechanism. The effect of damping factor on broadening vibration attenuation regime is studied. Finally, the vibration transmission properties of finite system with heterogeneous resonators, mass graded resonators and mass detuning resonators are compared to ensure the broad vibration attenuation range. This work could be beneficial for the design of vibration attenuation application in industry.