General band gap condition in one-dimensional resonator-based acoustic metamaterial

• An analytic condition for local resonant band gap in 1D system is presented.
• A general guide for resonant gap optimization is presented.
• The mechanism for defect state at subwavelength scale is given.

A one-dimensional model for resonator-based acoustic metamaterials is introduced. The condition for band gap in such kind of structure is obtained. According to this condition, the dispersion relation is in general a result of the scattering phase and propagating phase. The phenomenon that the band gap is less dependent on lattice structure appears only in the special system in which the coupling between the resonators and the host medium is weak enough. For strong coupled systems, the dispersion of wave can be significantly adjusted by the propagating phase. Based on the understanding, a general guide for band gap optimization is given and the mechanism for structures with the defect states at subwavelength scale is revealed.