Nonlinear dispersion properties and tunable vibration suppression in metamaterial beam with inertial amplification

Compressional-torsional coupling local resonators demonstrate prominent advantages in low-frequency vibration control through inertial amplification effects, yet their inherent narrow-band characteristics critically constrain engineering application potential. To address this limitation, this study proposes a novel compressional-torsional coupling local resonator incorporating nonlinear stiffness. Theoretical investigations reveal that the introduced nonlinear stiffness effectively extends the bandgap range of conventional linear resonators. The dynamic characteristics of the nonlinear resonator are systematically investigated using the harmonic balance method, while the excitation-amplitude-dependent bandgap properties are further elucidated through multi-scale method. A nonlinear compressional-torsional coupling local resonator prototype was designed and fabricated by implementing magnetically induced nonlinear stiffness. Experimental results verify the tunable bandgap characteristics in the nonlinear compressional-torsional coupling metamaterial beam. Furthermore, the in-situ tunability of the developed resonator was experimentally investigated. By adjusting the magnetic pole spacing, a resonance frequency shift of up to 122.9% was achieved. This work provides a highly promising solution for low-frequency broadband vibration control.