Robust reliability-based design of seismically excited tuned mass-damper-inerter (TMDI) equipped MDOF structures with uncertain properties

This paper considers a reliability-based approach for the optimal design of the tuned mass-damper-inerter (TMDI) in linear building frames with uncertain structural properties subject to seismic excitations defined as stationary colored random processes with uncertain parameters. The TMDI is a recently introduced generalization of the classical linear passive tuned mass-damper (TMD) comprising an additional mass attached to the primary structure whose oscillations are to be suppressed via a linear spring and dashpot in parallel. The TMDI benefits from the mass amplification property, the so-called inertance, of an inerter device that links the additional mass to a different floor from the one it is attached to which improves the vibration suppression capabilities of the TMD. Herein, the structural seismic performance is quantified through the probability of occurrence of different failure modes, related to the floor acceleration, the inter-storey drifts, and the attached mass displacement exceeding acceptable thresholds. The overall design objective is taken as a linear combination of these probabilities whereas the TMDI linear spring constant , viscous damping constant , and inertance properties are taken as the design variables. The parametric structural and excitation uncertainty is efficiently addressed through a two-stage approach combining a Taylor series approximation and Monte Carlo simulation. Numerical data for a 10-storey shear frame structure equipped with a TMDI with different values of attached mass and arranged in 8 different topologies are furnished indicating the enhanced performance of the TMDI over the classical TMD for relatively small attached masses. The reported numerical results evidence that the performance of optimally designed TMDIs is less affected by the parametric uncertainties as the total inertia TMDI properties (attached mass and inertance) increases, indicating that the inclusion of the inerter leads to more robust passive vibration control