Enhancing vibration serviceability of footbridges using motion-amplified inerter absorbers

Lightweight footbridges are often governed by vibration serviceability rather than strength, since pedestrian-induced excitation may activate low-frequency vertical modes and produce acceleration levels incompatible with user comfort [1]. In this framework, the present study investigates a passive control strategy based on a motion-amplified inerter [2] absorber specifically conceived for slender beam-like pedestrian bridges. The device combines a suspended secondary mass with two elastic branches, one of which includes a damper-inerter-spring series layout, while the inerter is embedded in a rhombus-type amplification mechanism aimed at increasing the relative motion across its terminals and allowing a more versatile calibration of the device parameters. The coupled bridge-device dynamics is first formulated by starting from a continuous Euler-Bernoulli beam model subjected to pedestrian loading. Owing to the internal kinematics of the absorber, the original problem leads to a constrained differential-algebraic formulation. To enable efficient numerical treatment, the governing equations are recast into an equivalent ordinary differential system, which is then projected onto a reduced modal subspace. On this basis, an optimization problem is defined by minimizing the peak acceleration frequency response with respect to the main absorber parameters. The methodology is finally assessed on a benchmark long-span pedestrian bridge under resonant pedestrian excitation described according to the HiVoSS guidelines [3]. Numerical results show that, for the examined case study, the optimized configuration provides consistent reductions of peak acceleration over the considered pedestrian traffic classes and restores the structure to the most comfortable serviceability class even under the most demanding loading scenarios. Compared with a classical tuned mass damper with the same auxiliary mass ratio, the proposed solution yields lower resonant peaks and greater robustness to moderate shifts in the main structural frequency, confirming the potential of motion-amplified inerter-based absorbers for vibration serviceability control in flexible footbridges.