# Design, Experiment, and Improvement of a Quasi-Zero-Stiffness Vibration Isolation System
## 1 Introduction  
In many practical examples, an isolator usually shows the vibration isolation effect when the excitation frequency is over \(\sqrt{2}\) times the natural frequency of the linear isolation system. The isolation frequency range will usually be expanded when the natural frequency of the isolator system is reduced, the cost of which is a reduction in the stiffness of the linear vibration isolation system, which causes an undesirably large static deflection [1; 2]. To overcome this problem, nonlinear vibration isolation systems based on the quasi-zero-stiffness (QZS) have been investigated that have the properties of high-static and low-dynamic stiffness. A QZS system has a localized zero stiffness in the equilibrium state that meets the requirement of a low natural frequency and a low static deformation at the same time. Numerous ways have been developed to realize a QZS system [3; 4; 5; 6; 7; 8]. A typical form of QZS was designed by [PERSON] et al. [9], who proposed a simple QZS system consisting of a vertical spring acting in parallel with two oblique linear springs. The above-mentioned QZS system was improved by [PERSON] et al. [10]. The oblique linear springs were replaced by two nonlinear pre-stressed oblique springs. It was found that the QZS system could produce a smaller dynamic stiffness in larger displacements near the equilibrium position, which helps to improve the performance of vibration isolation. In [PERSON] et al. [11], a vibrationisolator, inspired by the origami-based foldable cylinders, was designed to serve as a nonlinear springs with a quasi-zero stiffness. [PERSON] and [PERSON] [12] proposed a three-direction isolation platform, which demonstrated the QZS property in three directions and achieved a much larger displacement range around the equilibrium position. The cam-roller-spring mechanism was designed to realize the negative stiffness spring of the QZS system [13]. In [PERSON] and [PERSON] [14], a novel low-frequency isolation model was developed, where the nonlinear stiffness spring was realized by using a pneumatic cylinder through the mechanical structure of the wedge-roller-spring and cam-roller-spring mechanisms. [PERSON] and [PERSON] [15] designed a vibration isolation system for a vehicle seat that conformed to QZS theory. In [PERSON] et al. [16], a vibration isolator with a high-static low-dynamic stiffness was constructed through a continuous rotating shaft, where such an isolator had the properties of linear damping and a cubic equivalent stiffness. The mechanical structures with a negative stiffness are key components for the QZS system. In [PERSON] et al. [17], the QZS system is made up of three springs, two of which are to reduce the dynamic stiffness of the isolator. [PERSON] et al. [18] proposed a two-stage isolation system with springs and two different definitions of the nonlinear transmissibility were compared. Some other kinds of springs have been investigated by researchers. [PERSON] et al. [19] developed a kind of QZS system using buckled beams to generate a negative stiffness. [PERSON] et al. [20] presented a prototype vibration isolator based on a foldable cylinder with a torsional buckling pattern for the negative stiffness. [PERSON] et al. [21] designed a special planar spring to manage a wide range of loads and the QZS system had a better vibration isolation performance compared with linear isolators. [PERSON] et al. [22] proposed a 3D QZS system, where the negative stiffness spring was a pre-deformed, scissor-like structure, and the efficacy of a sensor system based on QZS was investigated. [PERSON] et al. [23] developed a novel passive vibration isolator for an ultra-precision sensing system, utilizing a buckled plate spring with a ball joint. [PERSON] et al.