###### Abstract  
Conventional base isolation (BI) techniques require a great reduction in the fundamental frequency of the system in order to mitigate the structural dynamic responses due to earthquake excitations. However, the resulting base displacements are large and can cause utility connection problems, rendering BI inadequate for retrofitting. This paper proposes a vibration control system (VCS) that can be used as a supplement to the conventional BI to increase the effective damping, and thus reduce the required base displacements. A novel passive negative stiffness (NS)-based vibration absorber, based on the KDamper, is implemented in parallel to a BI. The design of the VCS follows a constrained optimization approach that accounts for geometrical and manufacturing limitations. The NS is realized with a realistic displacement-dependent mechanism that generates controlled NS. The VCS is designed for various soil-types in order to determine its effectiveness and soil-structure-interaction (SSI) effects are accounted with respect to the soil-type. The earthquake excitation input is selected according to the ECS by generating a database of artificial accelerograms for each ground type. Finally, the VCS is compared to a conventional BI, and based on the numerical results obtained, the VCS is an effective alternative to BI and a possible retrofitting option. b 2021 2021 5 July 202  
and placed where the absolute motion of the system is the largest, which for the building structure is at the top [5; 6]. TMDs have also been implemented in the bases of structures as a supplement to BI [7; 8; 9; 10], as the maximum relative displacements occur at the base level. The placement of the TMD in the base of structures does not result in an increase in the total load of the superstructure. TMDs are known to be effective and reliable, however, their usage encounters significant disadvantages. The TMD properties can be significantly altered by environmental or other external parameters affecting the TMD tuning, and as a result, deteriorate its performance [11]. The essential limitation of the TMD is that in order to achieve significant vibration absorption, the additional oscillating masses need to be high. This fact renders the implementation and realization of TMDs rather difficult. An indirect approach to increase the effective inertia of the added mass of the TMD in BI systems, is the combination of a conventional BI system with an inerter or a Tuned Inerter Damper (TID) [12; 13; 14; 15]. The inerter is a two-terminal device, that aims to increase the overall effective inertia of the structure, without increasing its actual mass [16]. The overall dynamic behavior of the structure is indeed improved, however, marginally superior to that of a high mass TMD. The effectiveness of this system is limited and comparable to a highly damped base isolation system due to the saturation effects observed. In the last years, the concept of negative stiffness has been introduced in seismic isolation. True negative stiffness is defined as a force that assists the motion instead of opposing it, as in the case of a positive stiffness spring. Negative stiffness devices significantly reduce the stiffness of the isolator and consequently reduce the natural frequency of the system even at almost zero levels, as in [PERSON] et al. [17], being thus called \"Quazi Zero Stiffness\" (QZS) oscillators. Among others, QZS oscillators find numerous applications in seismic isolation [18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. The QZS oscillators are designs of an essentially non-linear stiffness, combining a positive spring in parallel with a non-linear spring, which exhibits a negative stiffness region under nominal load. In this way, QZS oscillators combine a high static stiffness, capable of maintaining the structural load, with a low dynamic stiffness, enabling a low isolation frequency. However, QZS oscillators offer a low damping capacity.