## 1 Introduction
The inerter element itself has the function of inertia regulation, and the physical mass of the structure is basically unchanged when the inertia of the structure is changed. The DVA with the inerter has the characteristics of low natural frequency, large load bearing, and superior vibration reduction effect. In addition, the role of the inerter is to optimize the system quality, so as to achieve vibration reduction effect, which was applied in different structural types [19; 20; 21; 22; 23]. The influence of the inerter depends significantly on the terminal locations. [PERSON] et al. [23] found that the performance of nonlinear energy sink inerter strongly depended on the inerter locations. [PERSON] et al. [24] discussed the effect of additional damping and an inerter on the dynamical behavior of the system and compared the vibration reduction effects caused by added damping and inerter. [PERSON] et al. [25] proposed a novel inerter-based three-element-type DVA and investigated its suppression effect. Furthermore, some scholars considered introducing both negative stiffness and inerter devices to enhance the vibration reduction effect [15; 26; 27; 28]. [PERSON] et al. [26] proposed a novel inerter-based DVA with negative stiffness and determined the best working range of inerter. In terms of the arrangement of the inerter, damper, and spring, [PERSON] et al. [27] designed a series of tuned mass dampers with negative stiffness and analyzed the vibration reduction performance of tuned mass dampers under different excitation. When the system is subjected to harmonic excitation, the H\({}_{\infty}\) optimization criterion is usually used for parameter optimization. [PERSON] et al. [28] proposed a tuned inerter damper with negative stiffness device and performed H\({}_{\infty}\) optimization and numerical analysis for different degree-of-freedom structures. [PERSON] et al. [29] put forward an improved inertia-based vibration absorber by inserting the inerter into a rhombus truss structure. [PERSON] et al. [30] investigated two tuned mass damper with inertertopologies. [PERSON] et al. [31] introduced inerter into a nonlinear energy sink and discussed the advantages of inertial nonlinear energy sink. Lever mechanism can improve the effective quality of the systems. [PERSON] [32] introduced the lever element and designed a new vibration isolator. [PERSON] et al. [33] proposed a lever-type multiple tuned mass dampers and used it to suppress bridge vibration, which showed stronger robustness. [PERSON] et al. [34] proposed the lever-type vibration isolation system with the X-shaped structure, which had excellent vibration isolation performance. [PERSON] et al. [35] designed a lever-type nonlinear energy sink. Under the proper pivot location, the absorption performance was superior to the traditional nonlinear energy sink. [PERSON] et al. [36] introduced the lever-type nonlinear energy sink to a fluid-conveying pipe coupled system and found that the lever-type nonlinear energy sink could reduce the resonance response amplitude by 91.33%. In the meantime, it was found in the literature [37; 38; 39; 40] that some scholars worked on the performance of the DVA by introducing lever and other devices simultaneously. [PERSON] et al. [37] introduced eddy current damping into a lever isolator. [PERSON] et al. [38] studied a novel DVA with grounded stiffness and lever component and concluded that the control effect of the presented DVA with positive grounded stiffness was better. [PERSON] et al. [39; 40] designed two different types of DVA that simultaneously contained a lever, inerter, and grounded stiffness, and it was found that the system would be unstable if the inerter was inappropriate. Furthermore, the performance of the vibration absorber could be further improved by adding variable negative stiffness [41], a metamaterial component [42], or a distributed arrangement [43; 44].