Robust Design of Tuned Mass Damper Systems for Seismic Protection of Multistory Buildings

In this paper, a method is proposed for the robust design of tuned mass damper (TMD) systems for seismic protection of multistory buildings. The seismic excitation is a random ground motion acceleration modeled by a stationary filtered white noise process. The protected building consists of a generic multi-degree-of-freedom (MDOF) structure, represented by its modes of vibration and linear mass dampers. The design properties of the TMD system are mass, frequency and damping ratio of the TMD units, along with their location within the structure, considered as fixed at its base. Uncertainties in the properties of both the building and the input seismic excitation are explicitly accounted for in the robust design of the TMD system. In particular, the uncertain parameters considered are stiffness and damping of the structure, and frequency and damping properties of the Kanai-Tajimi model used for representing the surface ground filter of the white noise process acting at the bedrock. The response quantity chosen to be representative of the seismic demand in the building is the interstory drift ratio. Its variation to the uncertainties is treated with the direct perturbation method, by applying a mixed-order approach. Robustness in the design of the TMD properties is formulated as a multiobjective optimization problem, in which both mean and standard deviation of the building response, produced by the considered uncertain parameters, are minimized. The weighted sum method is applied for transforming the multiple objective into an aggregated scalar objective function and then solving the minimization problem. The proposed design procedure is implemented on an illustrative example, consisting of a multistory building protected with a TMD system made from two units that have to be tuned with the first-and second-mode period of the structure, respectively. Parametric analyses on protected systems characterized by different properties are carried out, and the significance of the effects produced by the variation of such properties on the optimum design of the TMD system is shown. Differences between a robust design with the proposed procedure and a more conventional one that does not account for uncertainties in the system properties are finally evaluated