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 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 that can be solved analytically to understand the phenome...[ Read more ]

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 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 that can be solved analytically to understand the phenomena by comparing its transmission and band structure with that of the locally resonant sonic materials. We have found a simple explanation to the transmission properties of locally resonant sonic materials.