Gradient based optimal seismic retrofitting of 3D irregular buildings using multiple tuned mass dampers

• Multi-modal optimal seismic design methodology using MTMDs in 3D irregular buildings is presented.
• The methodology enables achieving a performance-based-design.
• The gradients required are efficiently derived analytically using the adjoint analytical method.
• MTMDs overcome some of the limitations of single TMDs in seismic control.
• MTMDs can mitigate both structural and nonstructural earthquake damage.

This paper presents a formal optimization methodology for the seismic design of multiple tuned-mass-dampers (MTMDs) for the multi-modal control of 3D irregular buildings. The total weight of all TMDs is minimized while both inter-story drifts and total accelerations are constrained to allowable values so as to lead to a performance-based-design. A first order optimization method is adopted for that purpose while the gradients required are efficiently derived analytically. All constraints are first normalized by their allowable values and combined to a single constraint on their maximum value. The adjoint method is then utilized to efficiently derive its gradient. The results reveal that, with the right design, MTMDs can mitigate both structural and nonstructural earthquake damage. Hence, they can potentially present a multi-hazard strategy to mitigate both winds and earthquakes.