Abstract The dynamic responses of the buildings and the optimum parameters of tuned mass damper inerter (TMDI) may change significantly when soil-structure interaction (SSI) is considered. Thus, it is necessary to consider the effect of the SSI in the optimization of TMDI. The study aims at proposing a methodology for optimization of TMDI parameters in reducing maximum structural responses of a high-rise building under earthquake considering the SSI effects. The equations of motion for time-domain analysis are derived for obtaining seismic-induced vibrations of a multi-story shear building with TMDI when the SSI is considered. An improved particle swarm optimization (IPSO) is used to obtain the optimum parameters. The aim of the optimization is to reduce the amplitude of the acceleration transfer function (ATF). The effectiveness of the optimally designed TMDI is assessed for twelve earthquake records with different frequency contents. The effect of the different mass ratios (μ), inertance ratios (β) and support conditions on control performance of the TMDI are investigated in detail. Numerical results proved that the SSI effect and the inertance ratio have a significant impact on the optimal design and effectiveness of the TMDI. From the seismic analysis results, it is seen that the controlled displacement response usually increases with the increase in the inertia ratio for both the fixed and flexible foundation, and a lower seismic response is obtained in the building controlled by TMD compared with the TMDI with different inertance ratios.
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