Acoustic waves in an elastic channel near the free surface of granular media.
A theoretical description of a natural acoustical waveguide existing in unconsolidated granular materials due to a gravity-induced stiffness gradient is proposed. The analytical theory for the acoustic modes propagating in the medium with a power-law type inhomogeneity uses some original solutions of the Helmholtz equation that have not been derived before either in classical or in quantum mechanics. The dispersion relations and a physical mechanism of localization for these modes indicate their essential difference both from the Rayleigh surface acoustic waves and the waveguide modes in homogeneous plates.
Gusev
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Laboratoire de Physique de l'Etat Condensé UMR-CNRS 6087, Université du Maine, Avenue Olivier Messiaen, 72085 Le Mans cedex 9, France.
Aleshin
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Tournat
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