## 4 Results and Discussion
### Radial Dynamic Mechanical Characteristics of the Air Spring
#### 4.2.2 Influence of Excitation Frequency on Radial Load Characteristics  
To examine the influence of the excitation frequency on the radial load characteristics of the air spring, the air spring was inflated with an initial air pressure of 0.3 MPa, and the reference point was subjected to radial excitations of 2 mm in amplitude, with excitation frequencies of 0.25, 0.5, 1.0, and 2.0 Hz. Figure 13 presents the relationship between the excitation frequency and the radial load of the air spring over time. As depicted in Figure 13, the radial load behavior of the air spring was subject to variation as a result of different radial excitation frequencies. As time elapsed, the radial load peak values of the air spring prior to 1.2 s exhibited minimal variation and did not change insignificantly. However, after 1.2 s, the radial load peak values of the air spring exhibited significant variations with the increase in excitation frequency. The radial load peak value increased linearly with the increase in frequency. The maximum load peak  
Figure 11: Variation in air spring load over time under radial amplitude excitation. values of the air spring at excitation frequencies of 0.25, 0.5, 1.0, and 2.0 Hz were recorded as 1.1, 2.1, 4.0, and 8.1 kN, respectively. Figure 12: (**a**) Change in load with displacement when amplitude is 2.0 mm; (**b**) change in load with displacement when amplitude is 2.0 mm; (**c**) change in load with displacement when amplitude is 1.5 mm; (**d**) change in load with displacement when amplitude is 0.5 mm. Figure 13: Variation in radial load of air spring over time under different excitation frequencies. Figure 14 illustrates the change trend of the radial load of the air spring under an excitation amplitude of 2.0 mm and an initial air pressure of 0.3 MPa. The radial load was observed to vary as the air spring undergoes displacement vibration under different excitation frequencies. The study provides insight into the relationship between the radial load and displacement vibration under various excitation frequencies and serves as a valuable reference for further analyses of the radial dynamic mechanical characteristics of air springs. As depicted in Figure 14, the radial load of the air spring exhibited significant variations in response to the changes in displacement. The radial load increased substantially when the displacement exceeded 2.8 mm. Upon closer examination of Figure 14c, it is apparent that there was a distinct difference between the first and second half cycles at a frequency of 1.0 Hz. The first half cycle exhibited a relatively moderate change in radial load, while the radial load peak in the second half cycle exhibited a noticeable increase and demonstrated a periodic variation trend. As depicted in Figure 14, the radial load of the air spring exhibited distinct changes in response to varying excitation frequencies. The peak load of the air spring changed substantially with increasing displacement vibration. At frequencies of 1.0 Hz and 2.0 Hz, a significant difference was observed between the first and second half cycles of the vibration cycle, with the load change in the first half cycle being relatively moderate and the radial load peak of the air spring in the second half cycle displaying a significant increase with a periodic change trend. Additionally, at the 1/4 cycle and 2/4 cycle, the load of the air spring fluctuated within a similar amplitude range, while local fluctuations were observed in the 2/4 cycle. The regular radial load vibration began to emerge in the latter half of the 3/4 cycle and 4/4 cycle. The results of the analysis indicate that the excitation frequency has a significant impact on the radial load of the air spring and cannot be neglected. This study presents a comprehensive examination of the dynamic load characteristics of air springs under low-frequency and low-amplitude excitations. The research was limited by the constraints of the experimental conditions and the inherent properties of superelastic materials.