Elastic waves propagating in graphene nanoribbons were studied using both continuum modeling and molecular dynamics simulations. The Mindlin's plate model was employed to model the propagation of interior waves of graphene, and a continuum beam model was proposed to model the propagation of edge waves in graphene. The molecular dynamics results demonstrated that the interior longitudinal and transverse wave speeds of graphene are about 18,450 m/s and 5640 m/s, respectively, in good agreement with the Mindlin's plate model. The molecular dynamics simulations also revealed the existence of elastic edge waves, which may be described by the proposed continuum beam model.

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