Reliability-based design of tuned mass-damper-inerter (TMDI) equipped multi-storey frame buildings under seismic excitation

The reliability based optimal design is considered of tuned mass-damper-inerter (TMDI) equipped linear building frames subject to seismic excitations modeled as stationary colored random processes. The TMDI is a recently introduced generalization of the classical linear tuned mass-damper (TMD) benefitting from the mass amplification property, the so-called inertance, of the inerter device to enhance the vibration suppression capabilities of the TMD. The frequency, damping ratio, and inertance TMDI properties are treated as design variables to minimize out-crossing rates of prespecified thresholds for building floor accelerations, inter-storey drifts, and TMDI mass displacement. Numerical data pertaining to a 10-storey frame structure equipped with a TMDI arranged in 12 different topologies are furnished indicating the enhanced performance of the TMDI over the classical TMD especially for relatively small additional attached mass