Local resonant acoustic band gaps in two-dimensional square-arranged Helmholtz resonators array

In this paper, by taking the acoustic property of a two-dimensional squarely arranged Helmholtz resonator array for example, we point out that there exist two kinds of couplings in the local resonance phononic crystal, which are the coupling between the resonator and background and the coupling among the resonators, respectively. The first coupling effect can be changed by changing the quality factor of the resonator. A local-resonant type of band gap can be converted into a Bragg-scattering type continually when this kind of coupling becomes larger and larger. The second one, which is based on the overlapping of the near filed around the resonators, can be enhanced by reducing the distance between the nearest resonators. As a result, a wider band gap, but a smaller penetration depth of the wave, can be obtained.