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                <title xml:lang="en">Validation of shift cell approach for the modelling of acoustic properties of porous materials embedding periodic inclusions</title>
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              <p>The design based on periodic elements can be a powerful strategy for the achievement of lightweight sound packages and can represent a useful solution for manufacturing aspects. The inclusion of vibroacoustic design rules, at early stage of the product development, is a feasible and interesting research target; in fact, the use of porous media with periodic inclusions canimprove the dynamic filtering effects thus offering several possibilities of applications in the engineering fields where both weight and space, as well as vibroacoustic integrity and comfort, still represent critical issues. Indeed, although porous materials are commonly used for vibroacoustic applications, they suffer from a lack of absorption at low frequencies. This difficulty is usually overcome by a multi-layering approach. However, while reducing the impedance mismatch at the air-material interface, the efficiency of such devices relies on the allowable thickness. A more efficient way to enhance the low frequency performances of sound packages consists in embedding periodic inclusions in a porous layer. If the radius of these periodic inclusions is comparable with the acoustic wavelength, then an increase of the acoustical performances can be observed since the excitation of additional acoustic modes helps in dissipating more acoustic energy. Therefore, even if this procedure still relies on the dimension of the inclusions, it can provide an acoustical performance improvement, which is way more efficient than just increasing the thickness. This paper starts with the description of the shift cell technique, which allows the description of the propagation of all existing waves from the description of the unit cell. The shift cell technique provides a reformulation of Floquet-Bloch periodic conditions and its major advantage is that it allows the implementation of any frequency dependence and damping in the problem: this is a new advantage when computing the dispersion curves of a porous material modelled as an equivalent fluid. The second part of this work shows the improvements of acoustic properties (in terms of transmission loss) that are obtained due to the periodic nature of the system and some qualitative considerations. The test case herein presented involves a square unit cell of porous material with a circular inclusion, for which the results are quite encouraging and promising.</p>
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