# Shared Tuned Mass Dampers for Mitigation of Seismic Pounding
## 3 Numerical Study
### Effectiveness of STMDs  
Based on the results and arguments presented above, the stiff solution cannot be considered as a shared TMD. However, we can define a shared TMD in such a way that it is tuned to the frequency  
Figure 6: Peak roof displacements, device stroke, and the minimum separation distance between two buildings connected by an STMD. The optimal solution presented in [PERSON] [28] is shown with red dots. The results correspond to El Centro ground motion. of building A, for example. This solution would correspond to the frequency ratio in the vicinity of 1. An optimal STMD in this context would correspond to the one that minimizes the cost function \(J\) in the vicinity of resonance with building A. The example presented above shows that this STMD marginally reduces the bounding distance for the El Centro ground motion. To test if this observation can be generalized to different ground motions and quantify the effectiveness in reducing bounding distance, we use several ground motion records for dynamic analysis of the system. The ground motion records are taken from the European Strong Motion Database [31]. The database contains 462 ground motion records from 110 earthquakes recorded in Europe and the Middle East. The ground motions are obtained from earthquakes with a moment magnitude of 4.2 to 7.6. The range of epicentral distance is 1 to 558 km, and that of peak ground acceleration (PGA) is 0.9% to 91% of acceleration due to gravity. The strong motion duration, defined as the interval covering 5-95% of Arias Intensity is in the range of 1.2 s to 139 s. Response spectra and duration of these ground motions have been presented in [PERSON] and Sigbjorsson [32; 33]. More details about this database can be found in [PERSON] et al. [34]. Optimal parameters of the STMD are estimated by minimizing the cost function using a genetic algorithm. Population size is taken as 50 and the initial population follows uniform distribution in the specified bounds. Elite count is set to 5% of the population. Crossover fraction is set to 0.8 and migration fraction is set to 0.2. The selection criterion is stochastic uniform and mutation are Gaussian. The 'ga' function in Matlab(tm) with default options was used to implement the algorithm. Different scenarios are simulated: (i) both the buildings are uncontrolled; (ii) TMD is used in building A only, the parameters of the TMD are optimized based on [PERSON]'s (1997) equations; (iii) the STMD is connected with a spring to building A, and a dashpot to building B. These cases are denoted hereafter as UC (uncontrolled), AC (building A controlled), and SC (controlled with STMD), respectively. In all cases, the TMD mass is taken as 1% of the mass of building A. Peak roof displacement of building A and bounding distance corresponding to the 462 earthquake ground motions are presented in Figure 7. The response of the uncontrolled and controlled structures are plotted on the abscissa and ordinate, respectively. The diagonal lines in the figure correspond to the equal response of uncontrolled and controlled structures. The results show that the TMDs result in reduction of peak roof displacement of building A in almost all the ground motions. When the displacement of the uncontrolled structure is small, the response reduction obtained by the TMD is not very significant. However, as the ground motions get more demanding, the effectiveness of the TMDs is higher. For the most severe case (that producing the highest response of the uncontrolled structure), the TMD reduces the response by about 50%. However, it is interesting to note that when the TMD is shared with building B, its effectiveness in controlling the response of building A remains almost unchanged for all the ground motions considered in this study. This shows that sharing the TMD with building B does not reduce its effectiveness. The shared TMD is not effective in controlling the response of building B. Neither does it provide any advantage in reducing the bounding distance between the two buildings.