Transmission properties of locally resonant sonic materials with finite slab thickness

Using multiple-scattering theory, we studied the transmission properties of a slab of composite material that have sonic band gaps due to local resonances. Thin slabs of such material have transmission properties that are apparently different from conventional band gap material. For example, there can be transmission peaks in the frequency range inside the bulk sonic band gap. If the slab thickness is changed, we found that the top of band gap shifts while the bottom of band gap, being pinned by the resonance frequency, does not. By changing the slab thickness, the "effective band gap" may be narrowed or broadened, depending on the filling fraction of the locally resonant units. In order to provide an intuitive understanding of the phenomena, we constructed a simple model to understand the phenomena by comparing its transmission and band structure with that of the locally resonant sonic materials.