Optimal design of a rhombus-configured improved-inerter vibration absorber (IIVA) for mitigating human-induced vibrations in footbridges

This paper investigates the optimal design and performance of an Improved Inerter Vibration Absorber (IIVA) for mitigating human-induced vibrations in slender footbridges. The proposed device integrates an inerter within a rhombus-shaped mechanism that amplifies the effective inertance while maintaining limited physical mass. The absorber consists of a secondary mass connected to the structure through a series arrangement of spring, inerter, and viscous damper, with a parallel spring. Compared to previous studies, this configuration, by exploiting the rhombus mechanism, enhances design flexibility and provides greater virtual inertial effect with smaller inertance, which is advantageous for integration within the limited depth typically available in bridge decks. An analytical framework of the coupled footbridge-IIVA system is developed as differential-algebraic equations and reformulated into ordinary differential equations. An optimization procedure, based on a reduced-order modal model, is formulated to minimize the peak acceleration frequency response of the footbridge, in compliance with vibration serviceability requirements. Finally, the effectiveness of the proposed IIVA is assessed through numerical simulations on a continuous beam model of a benchmark footbridge under pedestrian-induced loading modeled according to the HiVoSS guidelines. The results show that the amplification mechanism enables more efficient use of the inerter, allowing a reduction of the required inertance without increasing the physical stiffness and damping of the device. Compared to conventional tuned mass dampers with the same auxiliary mass, the proposed IIVA provides superior vibration mitigation performance and restores acceptable comfort levels under dense pedestrian traffic. Moreover, it exhibits improved robustness with respect to moderate variations in the structural frequency and damping ratio, highlighting its potential as a compact passive solution for vibration serviceability enhancement in lightweight footbridges.