This article proposes an optimization-based-methodology for designing multiple active mass dampers (AMDs) in tall buildings in multihazard environments. A realistic cost of the AMD system is formulated as the objective-function, and the multihazard Life-Cycle-Cost (LCC) that represents the long-term hazard-related losses, is selected as the main performance-constraint. This allows joining winds and earthquakes in a single decision parameter. Additional constraints limit the dampers forces and strokes. To ensure stability of the actively controlled building, the LQR algorithm is nested within the formal optimization problem. In addition, for the first time in the context of AMDs, their masses are considered as design variables, emerging directly as an optimization output. As the LQR control law is not aimed at optimizing costs and LCC, the lower triangular matrices related to the LQR weighting matrices are used as additional design variables. Thus, their values converge throughout the optimization to optimize the formulated cost function while satisfying the constraints. As this strategy produces large-scale problems, an efficient gradient-based algorithm is developed, using the adjoint sensitivity analysis method. The framework is applied to several examples for a benchmark-building, providing consistent results. One example demonstrates that AMDs can offer similar performance to its passive TMDs counterpart, requiring a mass 40% lower.

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