Analytical investigations have been conducted to suppress vibration of tall building structures in the presence of uncertainty in structural dynamic characteristics. Three control algorithms consisting of probabilistic optimal control, fuzzy logic control and optimal control theories are combined to control system fluctuations and severe seismic excitations. A state-space reduced order model is constructed based on dominant observable and controllable Gramians of Lyapunov equations in order to prevent the control matrix singularity and achieve computational efficiency. Both types of active and semi-active control systems are installed in the buildings to reduce the seismic response. In the case of active control systems, both an active tuned mass damper and active mass driver are installed on the top floor. In the case of semi-active systems, such as electric rheological/magnetic rheological dampers, control devices are installed in selected story units. The class of multi-objective control constraints based on minimum control efforts with respect to stochastics evaluation criteria have been defined and satisfied. The fuzzy rule base matrices and fuzzy inference systems are appropriately constructed corresponding to regular forms of optimal control laws and input-output measured data in the control sequences. The performance and robustness of both active and semi-active control systems are investigated through a series of numerical simulations of a multistory building subjected to a wide range of seismic disturbances.

Tuned mass dampers are one of the most common devices for the passive control of structures subjected to earthquakes. The structure of these dampers consists of three main parameters: mass, damping, and stiffness. Tuned mass dampers reduce the amplitude of the responses affecting on a mode. In most cases, only a single TMD (tuned mass damper) or a few dampers at several points above the building height are installed on the roof of the building, requiring considerable mass and space in some parts of the structure as overhead. It is also more important to predict the elements that will meet the required mass. In this research, the performance of multiple tuned mass dampers (MTMDs) is investigated in L- and U-shaped regular and irregular tall steel buildings with 10 and 20 floors, under the near- and far-field records. Nonlinear time history analysis is also applied to evaluate the multiple tuned mass dampers effects on the seismic responses of the structures. The SAP2000 API and MATLAB genetic algorithm are used to determine the optimal location of the MTMDs in the roof plans of the buildings. The results show the effects of multiple tuned mass dampers in reducing the seismic response of acceleration, displacement, and base shear up to 50, 40, and 40% in average, respectively. The results of determining the optimum location of MTMDs in the models indicate the importance of the symmetry of the dampers relative to the centre of mass of the building.

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In seismic codes, the force strength reduction factor is proposed to transform elastic to inelastic strength. The ductility reduction factor, R l , plays a key role on R factor if no overstrength is present. The R l is determined by SDOF systems. But the higher mode (HM) and Multi-Degreeof-Freedom (MDOF) effects need to be considered to extract the R factor. These effects are studied by proposing a v-MDOF via at least 1764 Nonlinear dynamic Analysis of 2D-frames. Also a sensitivity study has been performed on R l and a v-MDOF . Results obtained from studies conducted on the frames, indicate that HM and MDOF effects have a considerable influence on the base shear. Also the a v-MDOF is typically higher than unity both for ordinary and for near-field earthquakes and it is affected by period, span number and ductility level. These effects are remarkable for near-field motions. Finally, a simplified practical expression is proposed to estimate the a v-MDOF . Ó 2015 Faculty of Engineering, Ain Shams University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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