Robust design of tuned liquid column dampers under stochastic ground motion considering fuzzy uncertanties

The tuned liquid column dampers (TLCDs) have been shown to be effective vibration control devices for flexible structures subjected to long-duration, periodic or harmonic excitations. Their potential applications for seismic protection and retrofitting were recently explored. The optimum TLCD parameters are normally obtained based on the implicit assumption that the involved variables are deterministic. However, it is well known that the efficiency of TLCDs may be jeopardized if its parameters are not properly tuned to the vibrating mode of interest, for instance as consequence of the unavoidable presence of uncertain variables. Thus, the optimization of damper parameters considering model uncertainties has attracted a great deal of interest. The robust design of TLCDs for the passive control of mechanical systems under random ground motion is investigated in the present paper by coupling random vibration analysis and credibility theory in order to take into account fuzzy uncertainties. In doing so, two antithetical objective functions are considered, and they are the expected value and the variance of an appropriate displacement-based fuzzy structural index. Specifically, this latter one is introduced to characterize the performance variability due to the existence of fuzzy uncertainties affecting, both the system and random loading parameters. A numerical study is performed to demonstrate the applicability of the developed approach.