H2 Optimization of a New Type of Tuned Lever Inerter-like Mass Damper (TLIMD) for Attenuating Structure Vibrations

The lever or the lever-type mechanism can achieve an inertia amplification effect by appropriately calibrating its structural configuration, and it is also proven to be one of the most cost-effective solution for the inerter realization compared with other mechanical devices. Benefitting from this property, the present paper adopted a new type of tuned lever inerter-like mass damper (TLIMD) for attenuating stochastic load-induced structure dynamic responses. A set of closed-form formulae for the TLIMD optimal parameters are developed by the use of H2 norm optimization criterion, wherein the structure’s inherent damping is explicitly accounted for. It is theoretically demonstrated that the TLIMD optimal parameters are mainly dominated by three critical parameters, i.e., the damper mass ratio, the lever length ratio (known as the inertia amplification ratio) and also the host structural damping. The proposed formulae for the TLIMD optimization are validated through the seismic analysis, where two classic inerter-based dampers (i.e., the tuned mass damper inerter (TMDI) and the tuned inerter damper (TID)) optimized by the numerical technique are included in the discussion. It is found that the TLIMD has a superior advantage in reducing the structure responses and also exhibits stronger robustness for the detuning condition than the classic inerter-based dampers. Furthermore, the increase in the damper mass ratio and the lever length ratio can be beneficial for enhancing its performance.