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Etude théorique et expérimentale de la propagation acoustique dans les cristaux phononiques granulaires tridimensionnels

Abstract : A periodic, ordered and noncohesive structure of monodisperse spherical beads forms a granular phononic crystal. This work is devoted to the propagation of an acoustic wave within this kind of structure. During the propagation of an acoustic wave through a granular crystal, the properties of the phononic crystals (dispersion due to the geometrical periodicity) are combined with the properties of wave propagation in granular media (nonlinearities, rotational degrees of freedom). In this thesis, the dispersion relation of the bulk modes propagating in a hexagonal close-packed structure are theoretically derived. The structure is modeled by a mass-spring structure. The contact interactions between two beads (considered as rigid masses) are modeled by two springs obeying the Hertz-Mindlin theory, with one stiffness for the normal interactions and one for the transverse interactions. In the first part, the spectrum of bulk modes is determined in the case where the transverse interactions are neglected. The dispersion relations of the translational modes propagating within the crystals are derived. In the second part, the transverses rigidities are taken into account. The existence of the transverse interaction associated with the nonzero distance between the centers of the beads and the contact points requires to take into account the rotational degrees of freedom of each individual bead. In the description of continuum elastic media, the rotational degres of freedom are included in the generalized theory of elasticity which is also known as the Cosserat or micropolar theory. Experimental observations in granular materials of the modes predicted by the Cosserat theory (rotational modes and coupled rotational-translational modes) have not been reported before. After the theoretical investigations in a peculiar direction of propagation, the experimental observation of coupled rotational-translational modes in this direction is reported, and constitute a convincing evidence of the phenomena predicted by the Cosserat theory for the granular media. Finally, in this work, we also demonstrated the asymmetry of the classical nonlinear acoustic effect of self-demodulation relative to the direction of the acoustic wave propagation in noncohesive granular crystal under gravity.
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Submitted on : Tuesday, January 8, 2013 - 4:23:15 PM
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Aurélien Merkel. Etude théorique et expérimentale de la propagation acoustique dans les cristaux phononiques granulaires tridimensionnels. Acoustique [physics.class-ph]. Université du Maine, 2010. Français. ⟨tel-00771282⟩

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