The elastic band structures of two-dimensional phononic crystal plates are computed with the help of a super-cell plane wave expansion (PWE) method. These band structures strongly differ from the infinite 2D phononic crystal dispersion curves. In particular, these band structures exhibit surface modes and guided modes. The influence of the constituent materials, of the plate thickness and of the geometry of the array on the band structure is investigated. We focus more specifically on determining the thicknesses of the plate for which absolute forbidden bands exist. Namely, we show that absolute forbidden bands occur in the band structure if the thickness of the plate is of the same order of magnitude as the periodicity of the array of inclusions.

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