Quasi-full bandgap generating mechanism by coupling negative stiffness and inertial amplification

Abstract

Current research on mechanical metastructures cannot achieve extremely wide and low bandgaps because of engineering constraints, such as size, stability, and weight. To isolate vibration in both ultralow and middle-high frequency ranges, we propose a new bandgap merging mechanism that coordinates the Bragg and locally resonant bandgaps to form a quasi-full bandgap, starting from zero frequency. In the proposed mechanism, negative stiffness and inertial amplification are introduced to overcome the mass and stiffness limitations, allowing us to tune the lower boundary of the locally resonant bandgap and the cut-off frequency of the Bragg bandgap. The quasi-full bandgap can be achieved analytically by determining certain parameter conditions. Here, the dispersion curves become two horizontal lines independent of the wave vectors with frequencies always zero and another constant. A damping mechanism is introduced to lower the resonance peak below 0 dB for full-band vibration attenuation. To prove the bandgap tunability at large wave amplitude, the nonlinear dispersion relation of the proposed metastructure is solved with the Harmonic Balance Method. Numerical simulations and experiments are also conducted to confirm the results. In general, the proposed bandgap merging mechanism may provide a route for controlling time-varying, ultralow, and wide-frequency vibrations.