# The Role of a Simple Inerter in Seismic Base Isolation
## 1 Introduction  
Inerter-based dampers have recently seen tremendous growth in popularity for controlling structural vibration [1]. An inerter is used for mass augmentation effects, and its resisting force is predicted to be proportional to the relative acceleration between ends [2]. A tuned mass damper inerter (TMDI) simulates a conventional tuned mass damper (TMD) with an inerter. Additionally, it is referred to as a tuned inerter damper (TID) when the TMD mass is replaced with the inerter. The performance of base-isolated structures with TMDI fixed to the isolation floor under both real and stochastic earthquake excitation was examined [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. It was demonstrated that the TMDI reduces the response of base-isolated structures equipped with linear as well as non-linear isolators. An enhanced performance of the optimal TMDI was further observed when it was placed on the upper floors of the isolated structure or used in tandem [14; 15]. Recently, it has also been demonstrated experimentally that it is possible to achieve reasonable results in the response of base-isolated structures augmented with TMDI by using a simplified linear dissipative model instead of a nonlinear model with friction and gear backlash [16; 17]. The efficiency and optimum TID parameters for the base-isolated structure when considering the stochastic model of earthquake excitation are also illustrated [18; 19; 20; 21; 22; 23]. To reduce the seismic response and vibration isolation in the base-isolated structures, a geometrically nonlinear TID arrangement is also being investigated for multidirectional isolation [24]. The use of multiple TMDs to control the seismic response of base-isolated buildings has recently been studied [25; 26]. In seismic base isolation, the supplemental fluid inerter damper (FID) and electromagneticinertial mass damper (EIMD) represent novel applications, with the FID incorporating fluid inerter technology and the EIMD integrating electromagnetic inertial mass principles to enhance seismic resilience. The performance of the base-isolated structures with FID has been investigated by various researchers and has shown that these are effective in seismic response control [27; 28; 29; 30; 31; 32; 33; 34]. Lately, there has been a showcase of the dynamic characteristics of electromagnetic inertial mass dampers (EIMDs) and the identification of optimal parameters to effectively control the structural response of base-isolated structures [35; 36]. The review above suggests that the researchers are very interested in using inerter-based supplemental devices for base-isolated structures. The period of base-isolated structures is usually quite long, and the tuning effects of TMDI, TID, or TMD may not be achieved during the strong motion duration of the earthquake excitation. However, there is still a reduction in the response of the isolated structure, which is primarily due to the added damping and stiffness (ADAS) of the above devices and not because of the tuning effects [37]. The tuned damper-type devices are relatively less effective for the system with higher damping than the corresponding systems with lower damping [38]. It implies that for base-isolated buildings generally equipped with heavy damping, the supplemental tuned mass-type damper devices may not be very effective. Further, in the FID and EIMD, the inerter works in tandem with the fluid damper (FD) and electromagnetic damper (ED), and it's unclear whether the inerter or the FD and ED provide beneficial effects in response reduction. It may be possible that a single FD or ED can achieve similar or even better beneficial effects. As a result, it will be interesting to investigate the controlling effects of the inerter by examining the seismic response of base-isolated structures with FID or EIMD. This is proposed to be achieved by comparing the response of isolated structures with FID or EIMD with the corresponding response without inerter in the FID or EIMD devices.