In this study, the damping force algorithm called the viscous-plus-variable-friction damping force algorithm was proposed to combine advantageous features of typical viscous and friction dampers. The proposed damping force algorithm can be represented by a viscous element placed in series with a variable-friction element. As a piston velocity increases from zero, the damping force is generated by the viscous element. This is aimed to allow energy dissipation at a small velocity. When the damping force reaches a peak value of the viscous element or a preset force limit, the sliding of the variable-friction element occurs, resulting in a constant damping force. Analyses were conducted on a highway bridge subjected to the JMA Kobe ground motion record. Variable dampers were installed between a deck and a column. From the analysis, it is found that the deck displacement of the bridge with variable dampers is smaller than that with viscous dampers for almost the entire range of damping force levels, while significantly smaller than that with friction dampers for the damping force level larger than about 30% of a deck weight. The stroke requirement of variable dampers is slightly more than that of friction dampers. The ductility demand of the column with variable dampers is significantly smaller than that with friction dampers at a large damping force. Finally, a series of cyclic loading tests of a MR damper was conducted to develop the mathematical model of the MR damper for control purpose. The MR damper was controlled to exhibit the viscous-plus-variable-friction damping force. It is found that the proposed damping force algorithm can be realized by the MR damper with a good accuracy.
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