Abstract
SUMMARY A random packing of like elastic spheres is taken as a model of a densely packed granular medium and a method is presented for calculating the dispersion relations for waves travelling through such a medium. To avoid the possible separation of individual grains the medium is first subjected to a hydrostatic confining pressure. Two particular cases are considered and these correspond to when the spheres are infinitely rough and when they are perfectly smooth. In the latter case, two waves propagate and these correspond to the usual longitudinal and shear waves of isotropic elasticity. In the former cases, two additional waves exist and these are, in the main, due to relative rotations of the individual grains. In all cases, the waves exist only with certain ranges of values of the frequency.
Published Version
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