# Experimental Study of Vibration Isolation Characteristics of a Geometric Anti-Spring Isolator
## 1 Introduction  
For a linear passive vibration isolation system, the vibration isolation performance is effective only when the frequency of external disturbance is more than \(\sqrt{2}\) times the natural frequency. In order to attenuate vibration in the low-frequency band, one must reduce the stiffness of the linear vibration isolation system. However, reduction of the stiffness will diminish load bearing capacity of linear vertical vibration isolation system, resulting in undesirable excess deflection and over-stress of spring material. Finally, the linear vibration isolation system will fail to work well. In order to settle this problem, nonlinear vibration isolation systems attract great interests, because they exhibit the typical characteristics of high static stiffness and low dynamic stiffness (HSDS), which are very different from the invariant stiffness characteristic of linear vibration isolation system [1]. At the static equilibrium point, nonlinear vibration isolation systems can not only provide sufficiently large static stiffness to reduce static deflection, but also offer very small dynamic stiffness to obtain good low-frequency vibration isolation performance. So far, nonlinear vibration isolation systems are mainly realized by integrating negative stiffness structures with linear positive stiffness springs. There are several methods to achieve negative stiffness characteristics. Inclined spring negative stiffness structure is the most studied one in the literature. [PERSON] et al. [2; 3; 4] firstly reported a quasi-zero-stiffness system in which two inclined springs connected in parallel with one vertical spring. Typically, this system outperforms the linear system provided that the system parameters are chosen appropriately. Based on this work, [PERSON] [5] put forward design guidelines for the quasi-zero-stiffness isolator and solved the performance limit of this isolator. To further improve vibration isolation effectiveness of the vehicle seat, the quasi-zero-stiffness vibration isolation model was developed [6; 7], and it is experimentally confirmed that the proposed system offers a larger isolation frequency range and a higher attenuation rate than that of the linear system. After that, various methods were conducted to develop the quasi-zero-stiffness vibration isolator, and the effects of various loads and archetypal dynamical model of this quasi-zero stiffness isolator were discussed in the literature [8; 9]. Moreover, a quasi-zero stiffness isolator using Euler buckled beams as negative stiffness corrector was reported and the results showed that introducing the negative stiffness was an effective way to lower the resonance frequency even with the stiffness and load imperfections [10; 11]. Although quasi-zero stiffness vibration isolation systems (QZS-VIS) are potentially advantageous in many practical applications, QZS-VIS have many disadvantages, such as the easiness to lose stability, low loading capability and potential bifurcation effect at equilibrium [3; 5; 11; 12]. Utilizing permanent magnets and electromagnets to produce negative stiffness is another method for the negative stiffness characteristics [13; 14; 15; 16]. [PERSON] et al. [17] presented the geometric nonlinear magnetic vibration isolation devices with the quasi-zero-stiffness characteristic. In comparison to the corresponding linear system, the vibration isolation range of the proposed system can be largely extended to the lower frequency domain. [PERSON] et al. [18] employed a pair of coaxial ring permanent magnets installed in parallel with the mechanical spring to reduce the resonance frequency of the linear isolator, and the proposed quasi-zero-stiffness isolator can really outperform a linear isolator. [PERSON] et al. [19] designed a novel six degrees of freedom vibration isolator system utilizing magnetic levitation, which realized inherent quasi-zero stiffness in the vertical direction, and zero stiffness in other five degrees of freedoms.