Optimal tuned mass-damper-inerter (TMDI) design for seismically excited MDOF structures with model uncertainties based on reliability criteria

The tuned mass-damper-inerter (TMDI) is a recently proposed linear passive dynamic vibration absorber for the seismic protection of buildings. It couples the classical tuned mass damper (TMD) with an inerter, a two-terminal device resisting the relative acceleration of its terminals, in judicial topologies, achieving mass-amplification and higher-modes-damping effects compared to the TMD. This paper considers an optimum TMDI design framework accommodating the above effects while accounting for parametric uncertainty to the host structure properties, modeled as a linear multi degree of freedom system, and to the seismic excitation, modeled as stationary colored noise. The inerter device constant, acting as a TMD mass amplifier, is treated as a design variable, whereas performance variables sensitive to high-frequency structural response dynamics are used to account for the TMDI influence to the higher structural modes. Reliability criteria are adopted for quantifying the structural performance, expressed through the probability of occurrence of different failure modes related to the trespassing of acceptable thresholds for the adopted performance variables: floor accelerations, interstory drifts, and attached mass displacement. The design objective function is taken as a linear combination of these probabilities following current performance-based seismic design trends. Analytical and simulation-based tools are adopted for the efficient estimation of the underlying stochastic integral defining the structural performance under uncertainty. A 10-story building under stationary Kanai-Tajimi stochastic excitation is considered to illustrate the design framework for various TMDI topologies and attached mass values. It is shown that the TMDI achieves enhanced structural performance and robustness to building and excitation uncertainties compared to same mass/weight TMDs.