We investigate theoretically the band structure of a phononic crystal of finite thickness constituted by a periodical array of cylindrical dots deposited on a thin plate of a homogeneous material. We show that this structure can display a low frequency gap, as compared to the acoustic wavelengths in the constituent materials. The opening of this gap requires an appropriate choice of the geometrical parameters. The gap persists for various combinations of the materials constituting the plate and the dots. Besides, the band structure can exhibit one or more higher gaps whose number increases with the height of the cylinders.
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