Optimization of the local resonant sonic material by tuning the shape of the resonator

The resonator shape dependence of the first resonance frequency (RF) and the normalized gap width of a layer local resonant sonic crystal was studied. The unit block of the local resonant sonic material, the three component resonator, extended from spherical symmetry to azimuthal symmetry. Both the least square collocation method and the Lagrange multiplier method were introduced to study the more complicated system. Based on numerical calculation, it was found that both the first RF and the normalized gap width can be optimized by adjusting the shape of the core or cavity of the resonator under certain conditions. The approach can be extended to more general cases.