Band-gap flexible design and metadamping mechanism of inerter-enhanced viscously damped metamaterial

Abstract Elastic metamaterials equipped with locally resonant components exhibit low-frequency band-gap characteristics that serve wave propagation control and vibration suppression. However, although locally resonant metamaterials generate band-gaps at frequencies far lower than those of Bragg-scattering metamaterials, their vibration control capacity remains constrained by the requirement of heavy resonators and the inherently narrow stop-band range. This study explores an inerter-enhanced viscously damped metamaterial (IeVDM) integrating baseline-type and locally resonant inerters to realize coordinated adjustment of band-gap center, band-gap width, and metadamping performance. The mechanical model is established with two inerter configurations, from which the dispersion relation and complex eigenfrequencies are derived to quantify band-gap characteristics and equivalent damping properties. The wave propagation mechanism with special concern on the inertance distribution on spatial attenuation and temporal decay is systematically investigated, revealing its governing role in coordinating band-gap downshifting, band-gap width expanding, and metadamping adjusting. A band-gap and metadamping capacity-oriented design strategy is formulated for IeVDM with recommended parameter selection criteria and an easy-to-utilize performance curve to achieve target performance under constrained total inertance. The results show that the IeVDM achieves a substantially lowered band-gap center while maintaining adequate width and metadamping, benefitting from the coordinated inertance allocation between baseline and locally resonant inerters. The proposed design strategy effectively balances band-gap metrics and attenuation capacity, reduces the inertance demand relative to single-inerter designs, and enhances the practicality of low-frequency vibration suppression for engineering applications.