Adaptive Stiffness Structures with Dampers: Seismic and Wind Response Reduction Using Passive Negative Stiffness and Inerter Systems

High-rise structures and large-span bridges have low vibration frequencies and low intrinsic damping and hence are subjected to multimode vibrations under environmental excitation. Supplementing damping is a viable means to suppress such vibrations. The amount of supplemental damping is nevertheless limited as the damping devices in practice can only be attached to the structure at positions while the displacements or relative displacements in vibrations are small. Introducing negative stiffness, passively by negative stiffness devices (NSDs) or inerters, at the damping device positions is an effective damping enhancement approach. This study focuses on the multimode damping effects of dampers enhanced by NSDs and inerters for flexible structures, with emphasis on the frequency-independence (NSDs)/dependence (inerters) of the introduced negative stiffness. Tall buildings/bridges with outrigger systems incorporating NSDs (NSDOs) and inerters (IDOs) are taken as examples for demonstration of the multimode response mitigation performance. First, the principle of equal modal damping is applied for tuning IDOs to achieve maximal damping for a target mode. Then, an equivalent NSDO is determined to achieve the same level of damping of the target mode. Subsequently, multimode damping ratios for the first several modes are compared for the building respectively with the tuned IDOs and the equivalent NSDOs. The results show that the IDOs when tuned to a particular mode (e.g., the second mode) have almost no effect on the damping of a lower mode (first mode)—as compared to what can be achieved by conventional damped outriggers (CDOs). IDOs tend to lock the relative motion between the outrigger and the perimeter columns in higher structural modes because of their frequency dependence. However, NSDOs achieve comparable damping enhancement for all modes as compared to CDOs because of their frequency independence. It is also found that for a higher mode it might be preferable to use IDOs with small inertance to achieve a target level of damping that requires a large absolute negative stiffness value, although NSDs can be enhanced by adding levers to achieve large negative stiffness values as demonstrated recently by the first author. The findings have also been confirmed by numerical analyses of a typical building under seismic and wind loading. Practical and implementable NSD with rate-independent damping is developed based on the classical Maxwell—Weichert model to help mitigate vibrations in several modes, which is the subject of a future study.