Propagation d'ondes acoustiques guidées dans les milieux granulaires

Abstract : In granular media, owing to the inter-grain contact geometry, the elastic moduli show a non-linear pressure dependence. In a granular medium under gravity with a free surface, the pressure increases with the depth. As a result, only surface waves can propagate. We show theoreticaly that this system is an index gradient waveguide. in wich sagittal and transverse waves propagate. They split in discrete and infinite series of modes fo which we have calculated the dispersion relations. Their celerity increases weakly with their index as n1/6, making difficult the interpretration of measurements. For finite depth, a geometrical waveguide is superimposed to the last.The altered modes show a cut-off frequency. Experimentally, emitting gaussian wavepackets in a channel (geometrical waveguide) allowed to isolate the fundamental surface mode and to plot its dispersion relation. The exponent of its scaling law validates the meanfield standpoint and refute the hypothesis of an isostatic situation in the vicinity of the free surface. However, the shear modulus is abnormally weak. A gravity driven granular flow in smooth silo generates a spontaneous sound emission. We show experimentally and theoretically that it results from a convective instability for which the friction lead to amplification and frequency selection. Its growth leads to shockwaves. We think that this instability could explain dune's booming or dynamic earthquake triggering.
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Lenaïc Bonneau. Propagation d'ondes acoustiques guidées dans les milieux granulaires. Acoustique [physics.class-ph]. Université Paris-Diderot - Paris VII, 2009. Français. ⟨pastel-00559001⟩

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