Elastic analogue of graphene: Dirac cones and edge states in the propagation of flexural waves in thin plates

An elastic analogue of graphene is presented. It consists in a honeycomb arrangement of spring-mass resonators attached to a thin elastic plate. It is shown that the band structure for the propagation of flexural waves of the resulting system presents Dirac points. Also, it is shown that finite “slabs” of this honeycomb arrangement can be used as waveguides due to the presence of “edge states”, a special type of guided states that does not appear in the dispersion relation of the infinite system. Finally, multiple scattering simulations of finite clusters of resonators are shown supporting the theory.