Efficacy of Pendulum Tuned Mass Dampers in Reducing Overturning Risk of Rocking Blocks Subjected to Artificial Accelerograms

This study presents a comprehensive statistical analysis of the efficacy of pendulum tuned mass dampers (PTMD) in mitigating the overturning risk of rigid blocks subjected to artificial seismic loads. The block is modeled as a rigid parallelepiped undergoing rocking motion, with the PTMD characterized by its mass, length, and viscous damping properties, mounted on top of the block. The analysis includes the derivation of the differential equations of motion for the coupled system, which are numerically integrated. The seismic accelerograms are synthetically generated as realizations of a stationary random process characterized in the frequency domain by its power spectral density (PSD). Second-order white-noise filters are used for sample generation. A Monte Carlo simulation is performed to conduct a parametric analysis, determining the sensitivity of the PTMD parameters to seismic intensity and block slenderness. The results indicate that the efficacy of the PTMD in reducing overturning risk strongly depends on the block's slenderness and the intensity of ground motion. The TMD demonstrates robust performance for moderate ground motion and block slenderness. Although the design parameters do not exhibit systematic trends with respect to mass ratio of PTMD and block due to the inherent nonlinearity of the coupled system, stabilizing, and optimal parameter ranges can still be identified to minimize the overturning risk. Significant reduction of overturning risk can be achieved with respect to the block without PTMD.