article · Journal of Vibration and Control
A series-parallel inerter system incorporating negative stiffness has been developed for passive vibration control in single-degree-of-freedom structures subjected to base excitation. Stability conditions and boundaries were established using the Routh-Hurwitz criterion, while optimal tuning parameters were derived using fixed-point theory. The performance of this configuration was evaluated against both a standard series-parallel inerter system and a traditional tuned mass damper across harmonic, transient, and white noise excitations. The proposed system achieved superior suppression bandwidths and lower peak vibration amplitudes compared to the alternative devices. Under base acceleration, it delivered substantial reductions in peak amplitude and bandwidth gains over the tuned mass damper, with even greater improvements observed under displacement excitation. Additionally, the system demonstrated significantly shorter stabilisation times during transient events and better performance under random white noise excitation when using a small inertance mass ratio.
Uncontrolled vibrations caused by earthquakes or ground motion can severely damage buildings and mechanical systems. By combining negative stiffness with an inerter mechanism, this design dramatically improves passive vibration control without requiring external power. These findings offer engineers an effective mathematical framework to reduce structural motion and shorten recovery times during dynamic disruptions.
This research could support the development of advanced passive vibration isolators for civil structures and mechanical machinery exposed to seismic or base-induced vibrations. Structural and mechanical engineers are the primary prospective users. As the abstract describes theoretical modelling, stability boundaries, and numerical comparisons for an idealised single-degree-of-freedom system, the technology represents early-stage conceptual research that requires physical prototyping and experimental testing before commercial deployment.
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This study proposes a series–parallel inerter system with negative stiffness for the passive vibration control of an undamped single–degree–of–freedom system under base excitation. The necessary and sufficient conditions for stability of series-parallel inerter system with negative stiffness are established by Routh–Hurwitz criterion, and the stability boundary is obtained. The tuning parameters of the series-parallel inerter system with negative stiffness are determined through fixed point theory, and a comparison between the vibration mitigation performance of series-parallel inerter system with negative stiffness, series–parallel inerter system (without negative stiffness), and tuned mass damper is presented considering both harmonic excitation, transient excitation, and random (white noise) excitation. The results of this study demonstrate that under base harmonic excitation, series-parallel inerter system with negative stiffness outperforms the series–parallel inerter system and tuned mass damper in terms of suppression bandwidth and reducing the peak vibration amplitude of the primary mass. In the case of base acceleration–excited primary structure, more than 49.84% and 67.53% improvement can be obtained from series-parallel inerter system with negative stiffness as compared with tuned mass damper in terms of suppression bandwidth and reducing the peak vibration amplitude, respectively. Whereas in the case of base displacement–excited primary structure, more than 78% and 80% improvement can be obtained from series-parallel inerter system with negative stiffness, respectively, following the same criteria. A slightly lower improvement has been obtained from series-parallel inerter system with negative stiffness as compared with series–parallel inerter system, which justified the superiority of series–parallel inerter system compared to tuned mass damper. The transient response investigation showed that series-parallel inerter system with negative stiffness outperforms the series–parallel inerter system and tuned mass damper in terms of much shorter stabilization times and lower peak amplitude of the primary mass. Finally, the further comparison among these devices (series-parallel inerter system with negative stiffness, series–parallel inerter system, and tuned mass damper) under white noise excitation also shows that series-parallel inerter system with negative stiffness is superior to series–parallel inerter system and tuned mass damper for a small inertance mass ratio. This result could provide a theoretical basis for the design of inerter-based isolators with negative stiffness.
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DOI: 10.1177/1077546320985335
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