Modeling and design of non-linear seismic metamaterials - Invited talk by R. Zivieri

A model used to understand seismic metamaterials from a theoretical point of view is based on the concept of the periodic sub-wavelength resonant mass-in-mass system, see Fig. 1. Figure 1 : Sketch of the system studied. We have already proposed a continuous implementation of those type of seismic metamaterials based on the use of isochronous mechanical oscillators. However, the bandgap of this device has its centre at the resonance frequency of the atomic mass-in-mass element. A key challenge is to achieve a broad extension of the bandgap and a bandgap starting at a frequency as low as possible. Here, we focus on the possible engineering of the non-linearity of the external spring of a mass-in-mass system. In order to do that, first we define an anharmonic force exerted on the mass me resulting from a potential energy developed up to the fourth-order. Second, starting from the Lagrangian equation we obtain the dispersion relation in the presence of the anharmonic contributions. The acoustical branch of the dispersion relation is strongly downshifted with respect to that obtained in the linear case.