Locally resonant metamaterials with shape-memory alloy springs

Locally resonant metamaterials offer bandgap formation for wavelengths much longer than the lattice size, en- abling low-frequency and wideband vibration attenuation. Acoustic/elastic metamaterials made from resonating components usually do not exhibit reconfigurable and adaptive characteristics since the bandgap frequency range (i.e. target frequency and bandwidth combination) is fixed for a given mass ratio and stiffness of the resonators. In this work, we explore locally resonant metamaterials that exploit shape-memory alloy springs in an effort to develop adaptive metamaterials that can exhibit tunable bandgap properties. An analytical model for locally res- onant metastructures (i.e. metamaterials with specific boundary conditions) is combined with a shape-memory spring model of the resonator springs to investigate and exploit the potential of temperature-induced phase transformations and stress-induced hysteretic behavior of the springs. Various case studies are presented for this new class of smart metamaterials and metastructures.