Optimum design of tuned mass damper with pinched hysteresis under nonstationary stochastic seismic ground motion

The optimum design of a recent tuned mass damper with pinched hysteresis (TMD-PH) for seismic protection of structures is here investigated. The considered device consists of mixed NiTiNOL-steel wire ropes undergoing combined tension-flexure cycles. Previous studies demonstrated that concurrent interwire friction and phase transformation of the shape memory material exhibited by these composite wire ropes generate a peculiar pinched hysteretic behavior, which can be well described by means of a modified Bouc–Wen model. A stochastic-based optimum design methodology is here proposed for such TMD-PH, which is tailored to determine the best design parameters for the seismic protection of general structural systems. The seismic ground motion is modeled as a filtered nonstationary random process whereas the inherent pinched hysteresis of the device is dealt with via the stochastic linearization technique. The expressions of the linearization coefficients are obtained ad hoc and the optimum design of the TMD-PH is formulated as box-constrained single-objective optimization problem. Three objective function formulations are considered to reflect alternative design philosophies, namely, displacement-, acceleration- and energy-based design strategies. Unlike most literature studies addressing the optimum design of vibration absorbers via finite difference-based numerical schemes or non-gradient-based metaheuristic methods, the search for the optimal parameters of the TMD-PH is here performed by means of an iterative semi-analytical gradient-based numerical technique in which the derivatives for the covariance matrix of the system response are calculated analytically. A comprehensive numerical campaign is finally presented. First, a parametric study is carried out to evaluate the effects of the protected system characteristics and those of the seismic ground motion duration on the optimal parameters and performance of the device under consideration. The performance of the TMD-PH optimized according to the proposed methodology is also assessed in the context of a practical case study which makes use of synthetic and natural seismic ground motion records.