## 3 Static Analysis
### Parameter Analysis  
Different parameters have different influences on a suspension system. In order to evaluate the mechanical properties of the system, the value ranges for parameters need to be further determined. The dimensionless force-deflection characteristic curves under different values of \(\alpha\) are shown in Figure 3. With an increase in the value of \(\alpha\), the curvature of the curve is changed. Among these curves, the flatness degree of the curve is even higher at \(0.6<\alpha<1\). As shown in Figure 4, by MATLAB numerical calculation, it can be found that with an increase in displacement, the restoring force curve of the system is on a downward trend, and the proposed structure has obvious negative stiffness characteristics. When \(\gamma_{1}<1\), the occurrence time of the first peak of the curve is faster and the change of the corresponding displacement is smaller. When \(\gamma_{1}\geq 1\), the force change trend of the system in the vertical direction is gentle, which indicates that the seat has better vibration isolation performance, and the selection of the NSS parameters is ideal. It is found that the dimensionless force \(F^{\prime}\) of the system peaks in a short time period when the value of \(\gamma_{1}\) is especially small. Therefore, this situation should be avoided to occur when designing parameters so as not to affect the dynamic characteristics of the suspension system. In addition, by contrasting and analysis, the results show that a change in \(\alpha\) affects the trend of the overall force change of the system. With an increase in \(\alpha\), the force change trend accelerates, indicating that the vibration amplitude of the seat in the vertical direction increases which reduces the driver's ride comfort. Therefore, it is recommended that \(\alpha\) not take a larger value, and rather, try to make the stiffness of the horizontal spring smaller than that of the vertical spring. Figure 5 shows the dimensionless force-deflection characteristic curves with different values of \(\gamma_{2}\). The results show that when the value of \(\gamma_{2}\) is greater than 1, curve changes vary regularly, which is similar to an elongated sinusoidal curve, with existing maximum and minimum peak values. It indicates that the dimensionless force \(F^{\prime}\) between the two peaks decreases with an increase in displacement, and inversely in the other positions, the value of \(F^{\prime}\) increases with an increase in displacement. However, when the value of \(\gamma_{2}\) is less than 1, the initial value of the dimensionless force \(F^{\prime}\) begins to change irregularly, and the value of \(F^{\prime}\) decreases with an increase in displacement. In this case, although the stiffness of the suspension system is negative stiffness, it is not suitable for the design of the above negative stiffness model structure. When \(\gamma_{2}<1\), the shape of stiffness curve is convex parabola, and the stiffness reaches the maximum peak value in the static equilibrium position. However, when it is distant enough from the static equilibrium position, the stiffness of the system is always negative, and the vibration isolation system is in an unstable state. Considering the nonlinear characteristics of the suspension system and multiple design parameters, the dimensionless dynamic stiffness of the system should be used to evaluate the vibration isolation system so that the appropriate suspension configuration parameters can be selected. As can be seen in Figure 6, as the value of \(\gamma_{1}\) becomes larger, the basic outline of the stiffness characteristic curves of system does not change obviously, while the curvature of the stiffness characteristic curve changes. For dimensionless displacement \(x^{\prime}<0\), when the value of \(\alpha\) increases, the absolute values of stiffness of the suspension system also increases.