Different types of tuned mass dampers (TMD) have been applied to reduce wind and seismic induces vibrations in buildings. We analyze a pendulum tuned mass damper (PTMD) to reduce vibrations of structures that exhibit elastoplastic behavior subjected to ground motion excitation. Using a simple dynamic model of the primary structure with and without the PTMD and a random process description of the ground acceleration, the performance improvement of the structure is assessed using statistical linearization. The Liapunov equation is used to estimate the mean-square response in the stationary condition of the random process and optimize PTMD parameters. The optimum values of the PTMD frequency and damping ratio are defined as PTMD design values for a specific maximum seismic intensity design criterion. The results show that: (1) The values of the PTMD effectiveness criterion and the optimal design values of the frequency ratio are higher when the damping ratio of the primary structure decreases. (2) The performance of the optimized PTMD is higher when the structure exhibits a linear hysteresis loop (low seismic intensity). (3) The optimized PTMD controls the development of structural plasticity reducing vulnerability. (4) There is a strong dependence of the optimum PTMD parameters on the dynamic soil properties of the building foundation. (5) The PTMD performance improves as its mass increases. The optimum frequency ratio decreases, and the damping ratio increases as the mass of the pendulum increases. The PTMD designed and optimized with the proposed methodology reduces vibrations, controls the development of plasticity, and protects the primary structure, particularly in low and medium-intensity earthquakes.
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