Rocking Dynamics and Control of Rigid Blocks Using Rotary Tuned Mass Dampers

Rocking of rigid blocks is a motion pattern of many nonstructural components. This paper investigates the rocking control of rigid blocks with rotary tuned mass damper (RTMD). A 2‐DOF analysis model is proposed for the RTMD‐controlled rocking system, and the rocking motion equations are established by the Lagrangian method. The free rocking responses of the RTMD‐controlled system are analytically solved, which is further verified in comparison with the numerical simulation. The RTMD is capable of involving positive modal stiffness in the rocking system due to the torsional stiffness. The tuning stiffness and damping of RTMD are key parameters for vibration control. The roles of RTMD tuning parameters and inertia ratio are investigated through analyses of free rocking responses and overturning accelerations. In conclusion, the design period of RTMD corresponding to the fastest decay of free rocking motion and the maximum increase in overturning acceleration is essentially the same, and the RTMD design period can be quickly obtained through analytical solutions of free rocking response. Undamped RTMDs can significantly improve the maximum overturning acceleration, while increasing damping further enhances this improvement, more notably under high‐frequency excitation. In addition, RTMDs contribute mainly to reducing the occurrence of overturning with impact.