摘要：This paper presents an analytical study of a multistage pendulum tuned mass damper (TMD) with a long stroke. Installing TMD is a practical way of adding damping to existing high‐rise buildings against the possible long‐period and long‐duration earthquakes, because both the TMD and amount of reinforcement to the building have low weights. To verify the effectiveness of the TMD, it is necessary to evaluate the effect of the small rotational and uplifting motions when the weight vibrates with a large amplitude. To evaluate these effects, an analytical model that includes the geometric nonlinearity and uplifting motion of the multistage pendulum TMD is presented. The model is verified by a comparison of the simulation results with experimental results of a shaking table test for a multistage pendulum. The time history analysis of the multistage pendulum, modeled as an 18 degrees of freedom system installed on top of a high‐rise building, is conducted. The rolling, torsional, and uplifting motions did not significantly affect the stable transverse motion of the TMD.
