Reliability-based design optimization of tuned mass-damper-inerter for mitigating structural vibration

Abstract

The tuned mass-damper-inerter (TMDI), comprising mass blocks, springs, dampers, and two-terminal inertial elements, has garnered significant attention as an advanced iteration of the tuned mass damper (TMD) in recent years. However, previous studies of TMDI's design are primarily conducted according to the theoretical formulas based on deterministic analysis assuming harmonic excitations or stochastic analysis assuming Gaussian white noise type excitations. This treatment falls short of capturing the non-stationary and non-Gaussian characteristics exhibited by engineering excitations and thus cannot ensure the safety of controlled structure. A few studies considering non-stationary excitations and based on reliability metrics, in conjunction with stochastic simulation methods, often confront excessive computational overhead. Aiming at such a challenge, the reliability-based design optimization (RBDO) of TMDI system, combining the probability density evolution method (PDEM) and genetic algorithm (GA), for mitigating structural vibration under non-stationary excitations is performed in this study. For the purposes of illustration, a single-degree-of-freedom system attached the TMDI and subjected to stochastic ground motions is studied. Considering the cases of different levels of inertance-to-mass ratios, the RBDO of the TMDI is carried out. The solutions by the theoretical formulas and by the variance-based design optimization are compared to verify the superiority of the proposed method. For assessing the seismic mitigation performance of the optimized TMDI system, probability density evolution analysis of structure-TMDI system with three levels of inertance-to-mass ratios is performed. Comparison between the RBDO of TMDI and that of TMD under consistent mass ratio is further addressed. Numerical results reveal the technical advantages of TMDI in a probabilistic sense, i.e., high vibration mitigation performance, considerable mass reduction, and less stroke demand.