Investigation and performance assessment of tuned mass damper inerter considering structural nonlinearity and soil–structure interaction

Tuned mass damper inerters (TMDIs) have emerged as effective devices for vibration mitigation in buildings, extending the capabilities of conventional tuned mass dampers through the inclusion of inertial amplification. Nevertheless, most studies assume linear structural behavior and fixed-base conditions, limiting their applicability under realistic scenarios. This work aims to investigate the design and performance assessment of TMDIs applied to nonlinear multi-degrees of freedom structures, while explicitly accounting for soil–structure interaction (SSI). A genetic algorithm (GA) optimization framework is developed to identify the optimal TMDI parameters, which include mass ratio, damping ratio, frequency ratio, inertance, and position, based on multiple objective functions targeting displacement, acceleration and combined performance. The methodology is demonstrated on a 10-story nonlinear building base excited by a Gaussian zero mean white noise random stochastic process of different intensities. Results show that the GA-based design enhances vibration reduction compared with classical tuning approaches, especially when the structure experiences strong nonlinear behavior, particularly for combined and displacement-oriented objectives. The inclusion of SSI, modeled for soft, medium and dense soils, affects both the nonlinear response and the optimal tuning, highlighting the importance of considering soil flexibility in realistic design scenarios. The work contributes to advancing integrated methodologies for the optimal design of passive control systems in nonlinear and soil-structure-interacting buildings.