Tuning of a Viscous Inerter Damper: How to Achieve Resonant Damping Without a Damper Resonance

Inerter dampers are effectively employed to mitigate and dampen structural vibrations in slender or high-rise buildings. The simple viscous inerter damper, with a viscous dashpot placed in series with an inerter, is designed to create resonant vibration damping, although the damper itself is without an internal resonance. The apparent resonant behavior is instead obtained by increasing the damper inertance until the two lowest modes of the considered building model interact, whereafter the viscous coefficient is adjusted until the desired response mitigation is achieved. The present modal interaction tuning requires that the reduced-order single-mode dynamic model of the building includes both inertia and flexibility from the (other) modes otherwise discarded by the model reduction. While the inertia correction adjusts the modal mass of the inerter damper, the corresponding flexibility introduces the apparent damper stiffness that creates the desired damper resonance. Thus, the accurate representation of other modes is essential for the design and resonant tuning of the simple viscous inerter damper. The resonant damper performance by the non-resonant viscous inerter damper is illustrated by a numerical example with a 20-story building model, for which the desired resonant modal interaction requires an inertance of almost ten times the entire translational building mass.