## 4 Current Progress of Magnetic Negative Stiffness in QZS Isolators
### QZS-Based Permanent Magnet Negative Stiffness Elements
Furthermore, the research encompasses a comparative analysis of the isolation efficacy between platforms with and without MNSSs, showcasing the MNSSs' capability in broadening the low-frequency isolation bandwidth and markedly enhancing the platform's low-frequency vibration isolation performance. In conclusion, the seminal contribution of this study lies in the design of an innovative airborne optoelectronic QZS platform, markedly enhancing the low-frequency vibration isolation efficacy via its pioneering structural configuration and damping mechanism, thereby substantially bolstering the stability and measurement precision of airborne optoelectronic systems. As shown in Figure 24, [PERSON] [70] has proposed a magnetic ring array (MRA) characterized by high-amplitude negative stiffness. This design endeavors to enhance the low-frequency performance of a heavy-duty precision micro-vibration isolator by employing axially perpendicularly magnetized magnetic rings to configure an array structure generating high-amplitude negative stiffness. The study not only advances the structural design of the magnetic ring array but also formulates an analytical model elucidating its magnetic force and stiffness, while scrutinizing the impact of geometrical parameters on stiffness for optimization purposes. The study validates the efficacy of the MRA through comparative analysis with existing vibration isolation schemes. Furthermore, the study incorporates a series of experiments to substantiate the validity of the analytical model and evaluate the performance of the MRA. The experimental findings reveal that the integration of the MRA diminishes the natural frequency of the vibration isolation experimental set-up from 4.75 Hz to 1.13 Hz and attenuates the peak of the one-third octave band velocity spectrum from 5.03 \(\upmu\)m/s @ 5 Hz to 2.60 \(\upmu\)m/s @ 1.25 Hz, thereby corroborating the efficacy of the MRA in enhancing the micro-vibration isolation performance. This offers a pioneering solution in the realm of micro-vibration isolation, especially tailored for low-frequency vibration isolation in heavy precision equipment. Through the introduction of a high-amplitude negative stiffness MRA, the study showcases a substantial impact in decreasing the natural frequency and enhancing the vibration isolation performance. The design of the MRA yields high negative stiffness, a crucial element for heavy precision micro-vibration isolation. The experimental results demonstrate that the incorporation of MRAs markedly diminishes the natural frequency and peak vibration transmission of the vibration isolation system, effectively enhancing low-frequency vibration isolation performance. MRAs notably attenuate the random vibration transmission from the ground to the loaded platform, consequently mitigating micro-vibrations. MRAs  
Figure 23: Schematic of the APQZSP: (**a**) prototype of the APQZSP; (**b**) folded beam spring; (**c**) MNSS; and (**d**) comparison between the APQZSP and its linear counterpart. exhibit positive stiffness far from equilibrium, thereby possessing a relatively limited effective working range. The precise geometric parameters necessary for implementing MRAs can be rather intricate to design and manufacture, necessitating contemplation of the mounting space, machining, magnetization, and assembly challenges. In conclusion, while MRAs confer notable benefits in terms of the micro-vibration isolation performance, their design and implementation present inherent limitations and challenges. Rectangular permanent magnets constitute a significant research domain. As shown in Figure 25, [PERSON] [71] experimentally explored nonlinear oscillators featuring negatively stiffened magnetic springs. The study concentrates on employing repulsive magnets to achieve negative springs with varying nonlinearities and stiffnesses by adjusting the gap between them.