Stochastic Optimization and Sensitivity Analysis of the Combined Negative Stiffness Damped Outrigger and Conventional Damped Outrigger Systems Subjected to Nonstationary Seismic Excitation

Abstract

In recent years, various kinds of damped outrigger systems, particularly with the negative stiffness devices, have been shown to effectively suppress excessive vibration induced by earthquake and wind. To gain insight into such systems, this paper proposes a stochastic optimization method to investigate optimal configurations of combined negative stiffness damped outriggers (NSDOs) and conventional damped outriggers (CDOs) subjected to nonstationary stochastic seismic excitation. The simplified analysis model of various combinations of damped outriggers is developed, and the state-space representation of outrigger systems is then formulated. The nonstationary seismic excitation is modeled as a uniformly modulated stationary Gaussian process with a time-modulating function following Clough–Penzien spectrum, and combining equations of motions of outrigger systems and seismic excitation gives rise to the augmented state-space representation of structure-damper-excitation and subsequently the differential Lyapunov equation. The optimal designs of damped outriggers are defined via the solution of the differential Lyapunov equation. The multiobjective optimization with Pareto optimal fronts is adopted to deal with conflicting objectives between harmful interstory drift and floor absolute acceleration. The sensitivity of negative stiffness devices on optimal objectives is also investigated. The optimal designs are further examined under real typical and near-fault earthquake records. The results demonstrate the efficacy of the proposed method and provide insight into the systems subjected to nonstationary seismic excitation. While the purely NSDO systems could have better performance with adequate negative stiffness devices, the proposed combined NSDO and CDO systems prove to be more effective with limited negative stiffness devices and thus provide more design flexibilities tailored to different application situations.