Abstract
Sonic crystals are scatterers arranged periodically in a homogeneous fluid medium, for which sound does not transmit through the crystal in certain frequency bands known as stop bands. Acoustic wave transmission through a two-dimensional sonic crystal composed of a finite array of scatterers is investigated. Two types of scatterers are considered: sound-hard cylinders and C-shaped locally resonant scatterers. An analytical method is devised to solve the corresponding multiple scattering problems. The method combines an integral equation technique for the single scatterer with an enhanced multipole method using domain decomposition into slabs. A numerical approach using commercial software is also considered for validation and is based on the finite element method. Simulations of sound transmission through an array of 5 by 51 scatterers show remarkably good agreement with the corresponding infinite system. For an array comprising locally resonant scatterers, an approximate band gap around the resonator natural frequency is observed in addition to the band gap due to the overall periodicity of the finite sonic crystal.
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