Phononic crystals are composite materials made of periodic distributions of inclusions embedded in a matrix. Due to their periodic structure, these materials may exhibit, under certain conditions, absolute acoustic band gaps i.e. forbidden bands that are independent of the direction of propagation of the incident elastic wave. In the first part, we present some examples of two-dimensional bulk phononic crystals i.e. two dimensional arrays of inclusions assumed of infinite extent along the third spatial direction. We show that the existence and bandwidth of the gaps depend strongly on the nature of the constituent materials (solid or fluid), the contrast between the physical characteristics (density and elastic constants) of the inclusions and the matrix, the geometry of the array of inclusions, the inclusion shape and the filling factor. The second part is devoted to some possible applications of these composite materials. In particular, we show that defect modes (cavities, wave guides, stubs...) inserted inside the 2D periodic structure may lead to the possibility of manipulating the propagation of sound, very selective frequency filters and efficient devices for wavelength demultiplexing. We present also the possibility of devising sonic insulators for frequencies of the order of the kHz with relatively small thicknesses of the phononic crystal sample. Finally we report on the vibration modes of a 2D plate, i.e. a phononic crystal of finite thickness along the axis of the inclusions. We show the possibility of absolute band gaps in the band structure of the plate, either free or deposited on a substrate. We discuss the surface and guided modes which may occur in such a band gap. This should open new perspectives in the field of high-frequency radiofrequency devices.

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