The negative stiffness (NS) phenomenon and additional supplemental damping (AD) were proposed and investigated in recent years. Despite the bulk of literature on the base shear reduction for structures with the NS at the base or on the first story, the application of the NS and AD in the stories of a superstructure was barely studied. Considering the implementation of the NS and AD in a passive way, this paper proposes an innovative approach to optimize the NS and AD values on the different stories of civil structures. First, the formulation is derived to convert the optimization of NS and AD to the static feedback decentralized controller design problem. Then, the controller is searched by homotopy path, which leads to a local optimal solution. Finally, the procedure is validated by a 20-story benchmark structural model.
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Qu et al. (2017) studied this question.
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