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We present the proposal and the theoretical characterization of the elastic analog of the so called photonic black-hole. The structure has a cylindrical symmetry and consists of two parts, a shell that bends the flexural waves and a core where the energy concentrates. The shell behaves like a gradient index lens and the variation of the refractive index has been obtained by changing the thickness of the plate. The simulations based on a multiple scattering algorithm demonstrate the broadband and omnidirectional properties of the structure.

Metamaterial shells based on radially dependent anisotropic parameters are analyzed in view of achieving different types of applications. The theoretical proposal is reviewed together with some possible applications of these resonant structures. Position sensors, energy harvesters or wireless energy transfer systems are briefly presented.

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.