On the dynamic behaviour of discrete metamaterials: From attenuation to energy localization

Metamaterials are generally known for their waves attenuation capabilities. This behaviour, which is related to the microstructure composing these materials, can be due to a Bragg-type scattering mechanism or to local resonances. The objective here is to exploit the two phenomena for generating a system able to localize the energy carried by propagating elastic (or acoustic) waves. To this purpose, we employ a 1D lattice composed of a chain of mass-in-mass particles, connected by elastic springs. The lattice contains an internal defect that causes the energy localization. This configuration allows for a completely analytical description of the problem. Eventually, an extensive discussion on the interaction between the two attenuation mechanisms is also given.