# Mechanical Modeling and Dynamic Characteristics of a Three-Directional Vibration Absorber
## 1 Introduction
Several researchers have explored alternative three-directional vibration isolation techniques. [PERSON] et al. [14] proposed an isolation support system combining a friction pendulum system (FPS) for horizontal isolation with an air spring for vertical isolation. [PERSON] et al. [1] conducted vibration isolation analysis for satellite inertial equipment, developing a three-directional equal-stiffness rubber isolator that effectively meets the performance requirements of inertial systems. [PERSON] et al. [15] developed a triaxial vibration isolation system for sensitive instruments, analyzing its structural design and control strategy to achieve efficient vibration suppression. [PERSON] et al. [16] proposed a novel three-directional vibration isolator designed to suppress both vertical subway-induced vibrations and horizontal seismic vibrations. Their results demonstrated significant reductions in vertical vibrations and noise caused by subway operations. [PERSON] and [PERSON] [17] employed an orthogonal test method to optimize the parameters of a wedge rubber absorber, ensuring that it met the three-directional stiffness requirements. [PERSON] [18] investigated the effects of Coulomb friction on a quasi-zero stiffness (QZS) vibration isolator, which integrates a negative stiffness mechanism utilizing Euler buckling beams with a conventional linear vibration isolator. Assuming friction damping is provided by linear roller guides, the dynamic responses of the vibration isolation system and its equivalent linear counterpart are obtained using the harmonic balance method (HBM). The static and dynamic characteristics of the QZS isolator are thoroughly examined. For the linear isolator, the resonant frequency increases, and the peak transmissibility decreases with increasing Coulomb friction or decreasing excitation amplitude. However, in the case of the QZS isolator, the natural frequency is reduced due to the negative stiffness mechanism, and the amplification factor at resonance becomes negligible in the presence of friction damping. Theoretical predictions and experimental results demonstrate excellent agreement. [PERSON] (2018) proposed a three-directional vibration absorber combining metal rubber and inclined rectangular springs, establishing a dynamic theoretical model and experimental testing system. The natural frequency, dynamic stiffness, and damping ratio of the system were analyzed under various conditions. Results show that as excitation levels increase, these parameters decrease, indicating stiffness softening. The theoretical model predictions align well with experimental data. Additionally, the metal rubber damping absorber exhibits high stability and consistency across different environmental conditions. [PERSON] et al. (2019) employed a high-order nonlinear friction model to characterize the nonlinear properties of metal rubber materials. Subsequently, they established a dynamic model of the vibration isolator and conducted a numerical analysis using the harmonic balance method to investigate the response of metal rubber under random vibrations. Furthermore, a metal rubber vibration damping system was constructed to perform random vibration tests. The experimental results were analyzed to validate the vibration isolation performance of the system. This study provides novel insights into the design of metal rubber vibration damping systems. As shown in Table 1, despite these advancements, existing solutions still exhibit notable limitations. In contrast, the metal spring-based three-directional vibration isolator proposed in this study adopts an innovative simplified and modular design. While maintaining the inherent advantages of traditional metal springs (high load-bearing capacity, strong environmental resistance, and no aging issues), this design achieves superior vibration isolation performance through structural optimization.