SUMMARY
Locally resonant (LR) elastic/acoustic metastructures exhibit bandgaps at wavelengths much longer than the lattice size, enabling low-frequency vibration/noise attenuation. Most investigations in this domain have considered nominally identical linear resonators that are regularly, or periodically, placed with in the structure. In these cases, the LR bandgap depends on the natural frequency of the resonators, and the bandwidth is limited by the added inertia, which is to be minimized in most applications. In this work, the LR metastructure concept is expanded in two directions: one includes nonlinearity, and specifically considers bistable attachments; the other one considers aperiodicity through resonators in quasiperiodic arrangements. First, numerical and experimental results show the amplitude-dependent enhancement of the attenuation bandwidth in LR metastructures via bistable attachments, and demonstrate that the vibration attenuation band offered by nonlinear inter-well oscillations is substantially wider than the linear LR bandgap.Next, the dynamic behavior and topological properties of LR mechanical metastructures hosting quasiperiodic distributions of resonators are investigated. Quasiperiodic placement of resonators introduces additional bandgaps that are topologically non-trivial and host protected edge-localized modes. The findings suggest the application of quasiperiodic placement of resonators as an effective way to achieve vibration attenuation over multiple frequency bands and to control the vibration localization at frequencies determined by the placements of the resonators. The proposed work includes the investigation of 2D concepts as well as electromechanical implementation of these concepts.