Passive or active control of an actual building under earthquakes using rolling rim-type TMD: A comparative study

In this study, for the first time, a novel damper -rolling rim-type tuned mass damper (rolling rim-type TMD) - is developed to passively or actively control the dynamic response of buildings under earthquakes. First, the equations of motion for multi-floor building structures with an installed rolling rim-type TMD on the top floor are established. Next, the parameters of the damper are determined based on the passive control problem by optimizing with the objective function of minimizing the vibration amplitude of the main structure. The design variables include the stiffness and damping coefficient of the damper. Additionally, the damper's performance in the active control case is also investigated by supplementing it with a control force. The linear–quadratic regulator (LQR) is used to determine the rule for the active control force. The damping effectiveness of the traditional and rolling disk-type TMDs is also compared with the proposed damper. The numerical investigations show that the proposed damper has higher efficiency in reducing the main structure's dynamic responses and has a smaller displacement than the remaining dampers. Furthermore, it also demonstrates stability when the structure is subjected to different earthquakes and robustness when the stiffness of the structure changes. The advantages of the proposed damper in terms of damping effectiveness and operational space highlight its potential for application in structures under dynamic loads.