Nonlinear aperiodic metamaterials with tunable electromagnetic stiffness

This research proposes and systematically investigates a current-tunable aperiodic supercell electromagnetic metamaterial beam to overcome the inherent trade-off between low-frequency and broadband vibration isolation. The design incorporates a coupled coil–magnet negative-stiffness and lever-type inertial amplification architecture, which innovatively integrates three mechanisms: inertial amplification, current-driven electromagnetic stiffness tuning, and disordered stiffness distribution. A nonlinear electromagnetic force model is derived via the filament method, revealing the synergistic effects of input current, lever ratio, and aperiodic stiffness distribution on bandgap formation and regulation. Results demonstrate that negative-stiffness tuning significantly shifts the bandgap toward lower frequencies, while the aperiodic configuration induces cascaded bandgaps, effectively mitigating the limitation of narrow low-frequency bandwidth. By combining the transfer matrix method with Galerkin discretization, a dynamic model accounting for both equivalent mass and nonlinear stiffness is established, enabling accurate analysis of dispersion relations and transmission spectra in periodic and aperiodic systems. Compared with the 22.9 Hz bandwidth of periodic metamaterial beams, the aperiodic design broadens the bandgap to 92.4 Hz, achieving nearly a fourfold enhancement. Experimental validation confirms the superior low-frequency broadband isolation performance of the aperiodic metamaterial beam under current tuning, while nonlinear time-domain simulations further demonstrate its capability to suppress chaotic vibrations and attenuate response amplitudes at specific frequencies. Overall, the proposed tunable aperiodic electromagnetic metamaterial beam, through the synergy of negative-stiffness tuning and aperiodic parameter design, provides a practical and effective solution for low-frequency broadband isolation in beam and plate structures of precision instruments.