Comparison of the sound attenuation efficiency of locally resonant materials and elastic band-gap structures

Numerical methods are applied to study the elastic wave propagation in a so-called locally resonant sonic material. The structure is a two-dimensional analog of a three-dimensional structure proposed recently, which offers interesting attenuation properties at low frequencies [K. M. Ho et al., Appl. Phys. Lett. 83, 5566 (2003)]. The present structure is based on heavy cylinders located on a square lattice, immersed in a soft polymer, and separated from each other by a rigid grid. It is demonstrated that the grid induces Fano resonances, improving the sound attenuation performances of the system compared with the mass law. The transmission characteristics of a stacking of different layers of this material are studied and compared with those of a 2D phononic crystal obtained by removing the grid. For equivalent mass and size, the latter is shown to have even better attenuation performances on a larger range of frequencies due to Bragg interference phenomena at low frequencies.