Tunable Topological Mechanical Metamaterials Through Local-Resonance-Induced Effective Stiffness

Localized edge-states have been extensively explored inside Bragg-scattering-based bandgaps, like in the prototypical 1D stiffness dimer (mapped from the Su-Schrieffer-Heeger or SSH model). Limitations of such bandgaps in the low-frequency regimes, such as requiring large impractical length scales of lattice periodicity, extend to the edge-states hosted within them. While local-resonance-based bandgaps have been used widely in various low-frequency studies, edge-states within them are relatively unexplored. The key challenge involves a lack of band inversion phenomena that typically produces non-trivial edge-states, since locally resonant bandgaps can't be closed. We propose a novel chain, by adding a hidden source of strain to the intracell couplings of an SSH system using local resonators, that addresses this challenge. Interplay between the two types of bandgaps in this system, which we call the effective stiffness dimer, produces a non-trivial locally resonant bandgap. We further demonstrate extreme localization and two kinds of edge-state profiles, corresponding to positive and negative parameter frequency domains, with high tunability.