## 1 Introduction
The three magnets' attraction acts as a negative stiffness that opposes the conventional spring, which acts as a positive stiffness, thus, together they achieve zero or near-zero overall stiffness. Using a structural beam instead of a conventional spring as a positive stiffness part, [PERSON] [20] designed an electromagnetic vibration isolator that exhibits the HSLDS behaviour by controlling the amount of current delivered to the two electromagnets. [PERSON] et al. [21] proposed an HSLDS vibration isolator using two coaxial rings with opposite magnetization directions. This arrangement of negative stiffness magnetic spring (NSMS) along with a parallel mechanical spring can reduce the resonant frequency of the system, thus giving better isolation performance. Similarly, [PERSON] et al. [22] used the same arrangement (NSMS) with a special design of spiral flexure spring (SFS) instead of the mechanical spring. Another isolation system under the name of quasi-zero stiffness (QZS) has also been extensively investigated in the recent years, as an essential branch of the nonlinear vibration isolation systems. It exhibits a tremendous isolation performance if the system is well designed. Many studies have adopted this system using different ways of implementation to achieve what is so-called ultra-low frequency vibration isolation. [PERSON] et al. [23] deeply studied the essential characteristics of the QZS vibration isolator and the static and dynamic analysis of a simple design. The QZS vibration system merely comprises a vertical spring and two oblique springs in a pre-stressed state considering the linear and nonlinear cases. [PERSON] et al. [24] have extended the research by studying the force transmissibility of each case and comparing them with a linear system. Instead of using simple oblique springs, many other negative stiffness structures have been proposed. [PERSON] et al. [25] proposed a QZS vibration isolator consisting of a vertical linear spring and a unique negative stiffness structure using two magnets at each side with the same polarity. When the system is loaded, the linear spring is compressed, and the two magnets move closer to each other, which produces an immense repulsive force that keeps the system at an equilibrium position. [PERSON] et al. [26] used two oblique Euler buckled beams as a negative stiffness structure. Upon adding this negative structure, the two-beam' endpoints are aligned in the horizontal equilibrium state, which gives zero summation forces, thus, a vertical spring reduces the system's resonant frequency to its minimum. [PERSON] et al. [27] developed a QZS vibration isolator with unique mechanisms consisting of a fixed semi-circular cam sliding vertically on a roller that is connected to a horizontal spring by a slider. A vertical spring is connected to two adjusters that keep the system at the equilibrium position whatever the load is to achieve better isolation performance. [PERSON] et al. (2020) proposed a QZS vibration isolator using a negative structure consisting of a horizontal spring, flexures, a vertical spring, and a vertical compensator. The compensator is used to increase the linear spring's preload bearing capacity, whereas, the horizontal spring is used to apply compression force on the flexures to act as a whole as a negative structure while supporting a wide range of loads simultaneously. [PERSON] et al. (2020) designed a negative stiffness structure consisting of a sliding block connected with a horizontal spring coupled with an adjuster from one side and a bar hinged to the mass from the other side. Parallel with the negative structure, a pneumatic cylinder connected to a directional valve, where a neural network is used as a controller, a vertical spring, and a damper are selected to lower the overall stiffness and support a wide range of loads. [PERSON] et al. (2020) proposed a QZS vibration isolation system that uses scissor-like structures (SLSs), which are parts of the negative stiffness corrector along with a spring and a damper in each SLS.