Elastic wave propagation in a single-layered graphene sheet on two-parameter elastic foundation via nonlocal elasticity

► Elastic wave propagation in graphene sheets resting on elastic media is studied. ► Phase velocities decrease with increase of the scale coefficient. ► Phase velocities may escape and stop propagating with including small-scale effect. ► Elastic foundation plays an important role in the phase velocities. ► Elastic foundation may lead to the occurrence of cut-off frequencies.