Passive coupling of adjacent structures is known to be an effective method to reduce undesirable vibrations and structural pounding effects. Past results have shown that reducing the number of dampers can considerably decrease the cost of implementation and does not significantly decrease the efficiency of the system. The main objective of this study was to find the optimal arrangement of a limited number of dampers to minimize interstorey drift. Five approaches to solving the resulting bi-level optimization problem are introduced and examined (exhaustive search, inserting dampers, inserting floors, locations of maximum relative velocity and a genetic algorithm) and the numerical efficiency of each method is examined. The results reveal that the inserting damper method is the most efficient and reliable method, particularly for tall structures. It was also found that increasing the number of dampers does not necessarily increase the efficiency of the system. In fact, increasing the number of dampers can exacerbate the dynamic response of the system.

Many theoretical and experimental studies have used heuristic methods to investigate the dynamic behaviour of the passive coupling of adjacent structures. However, few papers have used optimization techniques with guaranteed convergence in order to increase the efficiency of the passive coupling of adjacent structures. In this paper, the combined problem of optimal arrangement and mechanical properties of dampers placed between two adjacent buildings is considered. A new bi-level optimization approach is presented. The outer-loop of the approach optimizes damper configuration and is solved using the "inserting dampers" method, which was recently shown to be a very effective heuristic method. Under the assumption that the dampers have varying damper coefficients, the inner-loop finds the optimal damper coefficients by solving an n-dimensional optimization problem, where derivative information of the objective function is not available. Three different non-gradient methods are compared for solving the inner loop: a genetic algorithm (GA), the mesh adaptive direct search (MADS) algorithm, and the robust approximate gradient sampling (RAGS) algorithm. It is shown that by exploiting this new bi-level problem formulation, modern derivative free optimization techniques with guaranteed convergence (such as MADS and RAGS) can be used. The results indicate a great increase in the efficiency of the retrofitting system, as well as the existence of a threshold on the number of dampers inserted with respect to the efficiency of the retrofitting system.

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