# Shared Tuned Mass Dampers for Mitigation of Seismic Pounding
## 1 Introduction  
Seismic bounding refers to the collision of adjacent structures during earthquakes. When closely spaced structures vibrate out of phase, they might bound against each other. Pounding can cause local damage at the contact region. In addition, the impact generates short-duration acceleration pulse that can adversely affect the bounding buildings and their contents (see, for example, [PERSON] [1], and references therein). Such effects have been documented during past earthquakes. [PERSON] et al. [2] and [PERSON] et al. [3] provide very good reviews of seismic bounding and refer to many studies describing bounding observed during past earthquakes. Various methods of modeling bounding and computation of structural response have been discussed in the literature (see, for example, [PERSON], [4]). Pounding can be avoided if adjacent buildings are adequately separated, but there is large uncertainty in just how much separation is adequate. Architectural and financial factors often dictate separation distance between buildings in metropolitan areas where land is expensive and scarce. Mitigation of seismic bounding is, therefore, an important structural engineering problem. One approach is to reduce the consequences of bounding, while the other is to reduce probabilities of bounding. Collision shear walls have been found to be effective in reducing the consequences of bounding ([PERSON] and [PERSON], [5]). Elastic gap devices (see, for example, [PERSON], [6]), have been shown to be effective in mitigating damage caused by bounding. Several solutions for reducing probabilities of bounding between adjacent structures have been proposed in the literature. These solutions range from connecting adjacent buildings with springs and viscous/viscoelastic dashpots ([PERSON] and [PERSON], [7]; [PERSON] et al., [8; 9]; [PERSON] and [PERSON], [10; 11]; and [PERSON], [12]). Friction dampers and viscous fluid dampers have also been proposed for mitigation of bounding risk (see, for example, [PERSON] et al., [13] and [PERSON] and [PERSON], [14]). Active, semi-active, and fuzzy control using magneto-rheological dampers have also been shown to be effective for seismic bounding mitigation (see, for example, [PERSON] et al., [15]; [PERSON] and [PERSON], [16]). Pounding risk may be reduced by controlling the vibrations of adjacent structures. Tuned mass dampers (TMDs) for vibration control have been extensively studied in the literature (see, for example, [PERSON] and [PERSON], [17] or the review by [PERSON] and [PERSON], [18]). The risk of bounding in base-isolated buildings is higher due to large displacements concentrated at the isolation level ([PERSON] and [PERSON], [19]). Controlling displacement demands on base-isolated structures has been investigated using different strategies in the literature. These strategies include the use of tuned liquid column dampers [20], and tuned mass dampers located at different locations of the host buildings [20; 21; 22; 23]. Coupling of base isolation system with tuned mass damper inerter systems is reported in [PERSON] and [PERSON] [24], [PERSON] et al. [25] and [PERSON] et al. [26]. Other strategies for displacement control of base-isolated buildings include the use of gap dampers [27]. While several studies on active and semi-active dampers for bounding mitigation are available in the literature, very few have tested passive TMDs for this purpose. The only work we are aware of in this regard is that of [PERSON] et al. [28]. The idea was extended to semi-active TMD by [PERSON] [29]. [PERSON] et al. [28] presented the concept of a shared TMD to reduce vibrations and seismic bounding between adjacent buildings. Their optimal solution is to connect the TMD mass with a spring to one of the buildings and with a dashpot to the other building. If effective, this device could be advantageous due to its simplicity and low cost compared to active control schemes.