## 2 Fundamental Principles of Quasi-Zero Stiffness
### Basic Types of QZS Vibration Isolators  
Scholars both domestically and internationally have conducted thorough and comprehensive investigations into the theoretical and dynamic characteristics of QZS vibration isolation systems, thereby offering technical underpinnings for more effectively translating theoretical inquiries into engineering applications. In researching and applying QZS vibration isolators, designing a negative stiffness structure with exceptional negative stiffness characteristics stands as the most crucial aspect. In the late 1980s, [PERSON] et al. [32] authored a seminal work on QZS vibration isolators, introducing the pertinent theory of such isolators. Additionally, the authors put forth four structures exhibiting quasi-zero dynamic stiffness characteristics, utilizing inclined springs, buckled beams, level spring-links, and cam-roller types, as depicted in Figure 2. Subsequently, research into high static and low dynamic stiffness vibration isolators has been predominantly influenced by these four models.  
Diverse structural configurations of vibration isolators have been conceived by scholars both domestically and internationally, grounded on the principle of high static and low dynamic stiffness. Their dynamic characteristics and engineering applications have been exhaustively investigated. For instance, [PERSON] et al. [33; 34] proposed a QZS vibration isolator featuring a slanting spring as the negative stiffness mechanism, as illustrated in  
Figure 1: Sketch of the characteristic curves of the QZS vibration isolator: (**a**) positive stiffness, (**b**) negative stiffness, and (**c**) quasi-zero stiffness.  
Figure 2: Four typical quasi-zero dynamic stiffness mechanisms: (**a**) the inclined spring, (**b**) buckled beam, (**c**) level spring-link, and (**d**) cam-roller types of QZS.  
Figure 3. The authors derived the conditions for the QZS characteristics of this vibration isolator through static analyses. They subsequently optimized the negative stiffness interval of the QZS isolator and analyzed the force transfer rate of the isolator under conditions of nonlinear stiffness in the inclined spring. Furthermore, the authors pioneered the concept of high static and low dynamic stiffness. They scrutinized the transfer rates of the force and displacement in the high static and low dynamic stiffness isolator, offering conditions to mitigate the amplitude jumps in the vibration isolation system. [PERSON] and colleagues also showcased a high static and low dynamic stiffness isolator utilizing permanent magnets as the negative stiffness mechanism, as depicted in Figure 4. The vibration isolator's restoring force and stiffness characteristics were ascertained through static analysis. The test results indicated that the introduction of the negative stiffness mechanism decreased the intrinsic frequency of the vibration isolator by approximately 7 Hz, thereby yielding a discernible vibration isolation effect.  
This section categorizes the existing QZS vibration isolators into the following classifications based on the design principles of the prevailing negative stiffness structures: