Particle-damping-enhanced inertial amplification metamaterials for low and broadband vibration attenuation

The inertial amplification effect in compressional-torsional coupling resonators provides an effective route for low-frequency vibration attenuation. However, compared with conventional local resonators with the same bandgap starting frequency, such resonators usually exhibit a narrower attenuation bandwidth. To alleviate this limitation, this paper proposes a particle-damping-enhanced multi-bandgap inertial amplification metamaterial beam. By exciting its different vibration modes, the designed single resonator system successfully opens up two flexural wave bandgaps. Particle damping is further introduced as a passive nonlinear bandwidth-compensation strategy. The results show that particle damping broadens the attenuation regions associated with the two resonant modes and promotes their partial merging, with the merged attenuation-region width exceeding 200% of the total width of the original attenuation regions. Beyond merging and widening the attenuation regions, the particle damping also effectively suppresses resonance peaks outside the bandgaps. The proposed metamaterial is investigated through theoretical analysis, the spectral element method, numerical simulations, and experiments. Moreover, by experimentally identifying the amplitude-dependent equivalent parameters of the particle-damped resonator, the regulation mechanism of particle damping on the shift, broadening, and merging of the attenuation regions is revealed. This work demonstrates the potential of particle damping for overcoming the bandwidth limitation of compressional-torsional coupling local resonators and provides a feasible strategy for broadband low-frequency vibration attenuation in local resonance metamaterials.