Negative Effective Mass and Stop Band of Nonlinear Periodic Seismic Metamaterials

The study of negative effective mass in acoustic metamaterials has received considerable attention during the last years. In this work, it is shown that a nonlinear mass-in-mass periodic system, whose unit cells are connected by means of anharmonic springs, can be equivalently represented via an anharmonic periodic chain of an effective mass-spring system. The effective mass of the nonlinear seismic metamaterial has an explicit dependence on the amplitude of the propagating mode. It is found that the stop band related to the negative effective mass is wider with respect to that of the linear case in the softening anharmonic regime and narrower in the hardening anharmonic regime. These results could pave the way towards the design and modeling of nonlinear seismic metamaterials based on the tuning of the band gap amplitude via the introduction of either hard or soft anharmonic springs.