Overturning resistant capacities of rocking frames with supplemental vibration control devices under pulse-type excitations

Abstract

Rocking structures are vulnerable to overturn under earthquake shaking. It is necessary to reduce the overturning probability of rocking structures. Recently, inerters were proposed to control the vibrations of rocking columns, and it was found that the structure equipped with inerter has reduced probability of overturning. However, inerter does not have capacity to dissipate energy, its control performance is believed able to be enhanced once being used in conjunction with dampers. Therefore, this paper approaches rocking structural vibration control from two directions: by applying supplemental inertia and applying supplemental damping to the structure. To this end, inerter, clutched-inerter and viscous damper are selected as control devices, and two combined scenarios are also considered, with configuration Ⅰ consisting of an inerter and a viscous damper in parallel and configuration Ⅱ consisting of a clutched-inerter and a viscous damper in parallel. The analytical models of a rocking frame with supplemental control devices in variable positions are presented and the equations of motion for each model are derived. In addition, the maximum coefficient of restitution of the rocking frame with supplemental control device is derived based on the angular momentum-impulse theorem. The effects and applicable conditions of the considered devices are evaluated by means of assessing the overturning resistances, maximum responses and fragility curves of rocking frames under different conditions. The results show that, with appropriate damping coefficient and apparent mass of the inerter, the combined configurations Ⅰ and Ⅱ provide better control effectiveness than the cases with inerter, clutched-inerter or viscous damper applied individually.