  The existence of surface elastic waves at a mechanically free surface of
granular phononic crystals is studied. The granular phononic crystals are made
of spherical particles distributed periodically on a simple cubic lattice. It
is assumed that the particles are interacting by means of normal, shear and
bending contact rigidities. First, Rayleigh-type surface acoustic waves, where
the displacement of the particles takes place in the sagittal plane while the
particles possess one rotational and two translational degrees of freedom, are
analyzed. Second, shear-horizontal-type waves, where the displacement of the
particles is normal to the sagittal plane while the particles possess one
translational and two rotational degrees of freedom are studied. The existence
of zero-group velocity surface acoustic waves of Rayleigh-type is theoretically
predicted and interpreted. A comparison with surface waves predicted by the
Cosserat theory is performed, and its limitations are established.
