Design and optimization of locally resonating sonic crystals

Sonic crystals containing locally resonant structures exhibit strong sound attenuation bands at frequencies about two orders of a magnitude smaller than those predicted by Bragg´s theory. Small-size slabs can be designed from these materials, which have sound attenuation effects similar to the usual sonic crystals, but in the audible frequency range. Numerical simulations of the acoustic wave propagation in sonic crystals are performed within the framework of the local interaction simulation approach (LISA). By means of suitable imaging tools, they help to understand the underlying mechanisms. More importantly, they can be used for improving and custom tailoring their design and performance. For our simulations we have used a 13 cm slab of locally resonant sonic material and driven them at frequencies in the range from 0.3 to 6.0 kHz. Three different modes of local resonances are found in good qualitative agreement with experimental data, and their dependence on the structural parameters of the sonic crystal is analyzed. Based on these investigations we develop a simple analytical model, which is able to predict the resonance frequencies obtained by the experiments and LISA simulations.