Inerter-enhanced locally resonant metamaterial for seismic-induced vibration control

Locally resonant metamaterials (LRMs) have attracted significant attention in recent years for seismic-induced vibration control due to their unique ability to generate frequency bandgaps that inhibit the propagation of elastic waves. However, achieving a bandgap in the low-frequency range remains a persistent challenge. Although the authors’ previous studies have shown that negative stiffness mechanisms can effectively lower bandgap frequencies, the practical application of static negative stiffness springs is often hindered by fabrication complexities and inherent system instability. This study investigates an Inerter-enhanced Locally Resonant Metamaterial (I-LRM) tailored to achieve stable, low-frequency vibration suppression. Unlike most previous approaches that primarily utilize the inertial amplification effect, the proposed I-LRM leverages the inerter’s frequency-dependent negative stiffness mechanism to ensure both high performance and structural stability. Analytical models for both infinite and finite structures are derived to characterize the dispersion relations and transmission spectra. A comprehensive energy flow analysis is conducted to demonstrate the energy distribution of a finite-cell system. Numerical investigations are then conducted to evaluate its dynamic performance. The results demonstrate that the I-LRM can effectively generate a low-frequency bandgap, although with a narrower bandwidth than the conventional LRM. Despite this trade-off, the proposed configuration significantly enhances engineering feasibility by avoiding the need for very low connecting stiffness and/or excessive additional mass, providing a physically realizable approach for low-frequency vibration control.