On the mechanism of inerter in changing dynamic characteristics of mass-spring chain system

In this study, the influence of inerters on the dynamic characteristics of mass-spring chain systems is systematically investigated through both theoretical analysis and numerical simulations. Specifically, the effects of the inerter coefficient on the natural frequencies, mode shape vectors, and frequency response functions (FRFs) are examined. A novel concept, termed the critical inerter coefficient, is introduced to identify a threshold beyond which the dynamic behavior of a vibration system undergoes fundamental change. At this critical value, both the mode shapes and FRFs exhibit significant deviations from those observed in conventional mass-spring chain systems. Moreover, by introducing a new pole-cancellation mechanism, resonance peaks in the FRFs can be effectively eliminated, leading to essential modifications in the dynamic response. The simulation results further reveal that the combined action of dampers and inerters gives rise to frequency response behaviors that are qualitatively different from those in systems employing traditional damping mechanisms. In particular, not only is the resonance peak suppressed, but distinctive dips or bulges emerge in the FRFs near the natural frequency. Building on these findings, the analysis is extended to an n -degree-of-freedom ( n -DOF) mass-spring chain system incorporating inerters. A theoretical criterion for determining the critical inerter coefficients is derived, providing analytical insights into the influence of inerters on the natural frequencies, mode shape vectors, and FRFs of n -DOF systems. The theoretical predictions are corroborated through numerical simulations, which also uncover the intricate interaction mechanisms between damping and inerters in these systems. This work advances the understanding of how inerters modify the dynamic behavior of vibration systems and offers a theoretical framework for their utilization in structural vibration control and mitigation strategies.