Acoustic Waves in an Elastic Channel near the Free Surface of Granular Media

Abstract

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.