Bandgap regulations of longitudinal wave for a nonlinear metastructure isolator with high-static-low-dynamic stiffness

Linear structures are inherently difficult to exhibit mechanical properties with high-static-low-dynamic stiffness (HSLDS), which means that linear isolators with these structures struggle to have both high-quality load-bearing capacity and low-frequency isolation ability at the same time. To address this issue, we have designed a high-load-capacity local resonance (LR) nonlinear metastructure isolator for low-frequency vibration isolation of target objects. We reveal the regulation mechanism of longitudinal wave attenuation in such metastructures and conduct comparative study by finite element method (FEM) and experiments for a 3D printed prototype metastructure. The results show that in specific excitation frequencies, the LR nonlinear metastructure with a cantilever beam oscillator having a natural frequency of 11.7 Hz triggers a LR mechanism. Under the action of the nonlinear isolator, the vibration transmissibility is as low as 10 % at the center frequency of the bandgap under the base excitation. Furthermore, the dispersion equation of such nonlinear metastructures is derived, and through the analysis of the regulation of bandgaps, the variation trend of the transmissibility of nonlinear metastructure isolators is effectively predicted. The calculation method and design idea of this metastructure isolators provide a new approach for vibration isolation.