Vibrational Modes in Granular Materials

It is argued that a proper description of the vibrational properties of systems comprised of solid spheres interacting via forces exerted at their points of contact must take account of the rotational motion of the individual grains. The spectrum obtained by coupling these additional degrees of freedom to the familiar translational motion is studied in both ordered and disordered packings and, in the latter case, used to interpret data on compressional- and shear-wave speeds in systems with pressure-generated contacts.