Tunable Bandgaps in Locally Resonant Shape Memory Alloy Metastructures

Abstract

Research in metamaterials first originated from efforts to use engineered structures, rather than intrinsic material properties, to control electromagnetic waves. This idea has since expanded into almost every area involving wave and transport phenomena. Bandgaps created in metamaterials due to local resonance or Bragg scattering offer interesting alternatives to existing vibration control, wave guiding and filtering technologies. The tunability of these bandgaps, i.e.the increase/decrease in bandwidth as well as the shift in frequency range, is of considerable interest in advancing the applications of these novel materials/structures for real-time control. Recent research efforts have sought to exploit kinematic and material nonlinearities to induce additional flexibility to existing metamaterial designs. In addition to offering an alternative mechanism to tune bandgaps, nonlinear metamaterials demonstrate non-reciprocity in wave propagation as well as the creation of multiple bandgaps through sub-harmonic and super-harmonic generation. This thesis will focus on results from numerical simulations that demonstrate the tunability of bandgaps in metamaterials possessing the pseudo-elastic type material nonlinearity commonly exhibited by shape memory alloys (SMAs). As a case study, the tunability of the bandgap formed in an acoustic metamaterial beam with embedded SMA resonators will be demonstrated. The thesis will include a computational framework to derive the governing equations of motion for the periodic unit cell of the acoustic metamaterial beam. A separate computational framework will be established to treat the nonlinearity demonstrated by the SMA resonator and to predict its effect on the resulting bandgap. In addition to demonstrating the tunability of bandgaps in acoustic metamaterial structures, the thesis will also focus on both computational and experimental efforts to create multiple bandgaps in finite acoustic metamaterial structures.