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 miti-gation 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). Structural nonlinearity is modeled through a Bouc-Wen hysteretic law at each story. A genetic algorithm optimization framework is developed to design the optimal TMDI parameters, which include the mass ratio, inertance ratio, frequency ratio, damping ratio, and device location along the structure. The optimization is based on the definition of an objective function in terms of structural displacements and it is conducted by adopting as seismic input a Gaussian zero mean white noise random stochastic process at given intensity under fixed base conditions. The methodology is demonstrated on a literature benchmark 10-story nonlinear building. Results show that the GA-based design is able to provide structural vibration reduction even when the structure experiences moderate nonlinear behavior. When considering the inclusion of SSI, modeled for dense, medium and soft soils, it is shown that it 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.