Abstract
Periodic arrays of resonant scatterers can support low-frequency band gaps in addition to those associated with array periodicity. In the finite periodic arrays they correspond to frequency intervals of low transmission and lead to an improved attenuation below the first Bragg band gap. To describe low-frequency behavior, the effective medium model has been developed for the array of either thin elastic shells or composite scatterers. The latter consists of concentrically arranged hollow rigid cylinder with multiple slits (N-slit rigid cylinder) and thin elastic shell. The simplified description of the composite scatterer relies on the replacement of the N-slit cylinder by an equivalent fluid layer. Using coherent potential approximation, the analytical expressions are derived for the parameters of an effective medium. For the array of elastic shells it is demonstrated that complex density and complex compressibility become negative around n=1 resonance of the lossless shell and its axisymmetric (n=0) resonance frequencies, respectively. It is shown theoretically and confirmed in measurements that the presence of the concentric N-slit cylinder decreases the frequency of the axisymmetric resonance of the shell. The results are compared with the numerical solutions for infinite doubly periodic arrays and insertion loss data for finite arrays.
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