###### Abstract  
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 \(H_{2}\) 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 (TIDI)) 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. t 10 July 20  
Many scholars have performed various studies on lever dampers, and the results show that they have good control performance. [PERSON] et al. [24] conducted the pioneering work regarding the lever-type damper. A so-called dynamic anti-resonance vibration isolator (DAVI) was introduced into the base-isolation system and achieved excellent control performance. Since then, the lever-type damper has attracted a great attention. It is interesting to point out that the DAVI was initially utilized in the field of helicopter research to prevent undesirable vibrations of the cabin caused by the engine vibration. [PERSON] et al. [20] conceived three new types of lever-type DAVIs (different combinations of the lever and the conventional spring and dashpot). It was shown that the lever mechanism can enhance the performance of the conventional vibration isolation system. [PERSON] et al. [25; 26] introduced this lever mechanism into an X-shape structure for achieving broadband isolation system. [PERSON] et al. [27] conceived a novel lever-type based on a nonlinear damper, which incorporated the nonlinear energy sink with the lever mechanism. It was theoretically demonstrated that the lever mechanism can improve the damping performance of the original nonlinear energy sink. Similar work has been conducted by [PERSON] et al. [28], who embedded a lever into a bistable nonlinear energy sink, whose results indicated that the lever can improve energy harvesting performance. For further improvement of the lever-type dampers, an additional lever or even multiple levers may be an effective solution. [PERSON] et al. [29] developed two lever-type vibration isolators given the practical arrangement configuration, and it was shown that a smaller damping is more beneficial for achieving broadband isolation. In their following study [30], more complicated two levers vibration isolators are proposed; the results showed that such design can achieve a lower band frequency. [PERSON] et al. [31; 32; 33; 34] included a lever into the eddy current-based dampers, which significantly enhanced the original damper performance. In addition to the foundation vibration isolation system, the lever mechanism also has a good application prospect in the field of the dynamic vibration absorber (DVA). [PERSON] et al. [35] conceived novel lever-type devices called the lever-arm tuned mass damper inerter (LTMDI), where an inerter was implemented to enhance the lever-type performance. [PERSON] et al.