# Experimental Study of Vibration Isolation Characteristics of a Geometric Anti-Spring Isolator
## 1 Introduction
The negative stiffness structures that originated from the permanent magnets and electromagnets were very effective. However, they were quite thermally sensitive and may induce unwanted couplings to external electromagnetic fields. In addition, there are many other novel designs for quasi-zero-stiffness vibration isolation systems reported, such as sliding beam structure [20], composite bi-stable plate [21], scissor-like structured platform [22], and super elastic shape memory alloy bars [23]. However, because of structural complexity or unknown structural stability or environmental dependence, much deep-in research work still needs to be done, with the objective of further industrial application. The geometrical anti-spring structure was first proposed by [PERSON] [24] and [PERSON] [25] for the purpose of seismic attenuation. It was successfully applied in optical table prototype designed for advanced LIGO (Laser Interferometer Gravitational wave Observatory) [26] and external injection bench of the Advanced Virgo gravitational wave detector [27; 28]. Due to its nonlinear characteristics of high static low dynamic stiffness, the geometric anti-spring structure would be a perfect candidate for the design of low-frequency vibration isolation system. In contrast to other designs for the nonlinear isolator, the advantages of geometric anti-spring isolator include structurality simple and compactness, space saving and insensitive to temperatures or external electromagnetic fields, and so on. However, expect for the seismic attenuation in gravitational wave observatory, the geometric anti-spring isolator has not been applied in any other vibration reduction application. And the detailed nonlinear stiffness characteristic of the geometric anti-spring structure have not been intensively investigated. The effect of load and stiffness imperfection on the performance of this nonlinear isolation structure has not been discussed, which is very important for its further application in the field of vehicles, ships, and other precision equipment, especially for the situation under the excitation of low frequency (several Hz) and large amplitude. In this study, aiming at settling the pressing issue for isolating the disturbance of several Hz in precision instruments in vehicles and ships, a novel geometric anti-spring isolator for the low-frequency vibration isolation is developed and its vibration isolation performance and nonlinearity characteristic are investigated mathematically and experimentally. In Section 2, the genetic algorithm was used to achieve the numerical solution to the differential boundary value problem that describes the mechanical properties of the blade spring. The stiffness nonlinearity is investigated and the dimensionless optimal design parameters of the geometric anti-spring vibration isolation structure for different nonlinear geometric parameters are obtained. Mathematical simulation based on four order Runge-Kutta algorithm is carried out to investigate the transmissibility characteristic of the geometric anti-spring isolator in Section 3. The influence of geometric parameter, excitation amplitude, load weight and viscous damping on the transmissibility of the geometric anti-spring isolator are investigated theoretically. Then, a geometric anti-spring isolator with a nonlinear geometric parameter of 0.92 is fabricated and experimentally studied. The experiment setup and results are presented in Section 4. Conclusions are drawn in Section 5. This work will enhance the understanding of vibration attenuation mechanism of geometric anti-spring structure and provide further design guidelines for the broader application of the geometric anti-spring isolator.