Optimization of a viscous-elastic damper coupling two simple oscillators based on nonlinear stochastic response

Among the techniques used to control or mitigate the structural vibrations induced by dynamic input, such as wind and earthquake, the dissipative coupling is one of the most applied, especially for its ease of implementation. Indeed, for example in large urban areas, it is common to find adjacent structures where the space between the buildings becomes smaller. To optimally select the visco-elastic features of the dissipative device to be used, the paper retraces the path followed by the previous scientific works proposing new design criteria. Such criteria are based on the nonlinear stochastic response of two simple oscillators linked by a damper whose hysteretic behavior is represented by a Bouc-Wen model. A state-space formulation of the equations of motion has been adopted to facilitate the analysis of the dynamic response. At the same time, the loading is hypothesized as a zero-mean Gaussian excitation. Consequently, the nonlinear response has been approximately evaluated by the equivalent linearized standard deviations for both displacements and accelerations. Subsequently, formulations of objective functions, based on the Minimax and Total Energy of the equivalent linearized stochastic response, have been applied to determine the optimal configurations of the coupled system. The influence of both noise power amplitude and soil typology on the designed systems has been also investigated. Suggestions related to the path to achieve pre-fixed targets (as balancing of displacements and accelerations) are provided.