## 5 Conclusions  
Based on fluid-structure coupling simulation method, the nonlinear dynamic mechanical characteristics of air springs were studied in this paper. An experimental platform was established to verify a numerical analysis model of air springs using the MTS testing machine, and a comprehensive investigation of the radial and axial dynamic mechanical behaviors of air springs was carried out. The results were obtained through a combination of quasistatic tension and compression tests and a dynamic radial vibration analysis. The key findings of the study are as follows:  
1. The construction of the air spring experimental platform, based on the proposed experimental principle, was successful and the validity of the established numerical analysis model was demonstrated through experimentation. This serves as a solid foundation for future studies of dynamic load simulation analyses.
2. The results from the low-frequency and low-amplitude excitation experiments of the air spring in the axial direction, conducted on the established experimental platform, demonstrate the influence of low frequency and low amplitude on the axial load. The impact of low frequency and low amplitude was found to be more pronounced in axial compression.
3. The results of the radial dynamic simulation analysis of the air spring demonstrate that there is a significant increase in radial load with increasing frequency, highlighting the substantial impact of low-frequency excitation on the axial load of the air spring.  
The results obtained from this study can provide valuable insights for future studies aimed at exploring the dynamic load characteristics of air springs under different excitation conditions. With advancements in experimental techniques and simulation analysis methods, it will be possible to expand the scope of this study and analyze the dynamic mechanical behavior of air springs under various combinations of low and high frequencies, as well as low- and high-amplitude interactions. The findings of this study will serve as a valuable reference for the optimization of damping parameters in air suspension systems, contributing to advancements in this subfield.  
Conceptualization, S.X. and T.Z.; methodology, Y.L.; validation, J.Z.; investigation, J.X.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L.; funding acquisition, S.X., T.Z. and Y.L. All authors have read and agreed to the published version of the manuscript.  
Figure 14: **(a)** Load variation at 0.25 Hz excitation frequency; **(b)** load variation at 0.50 Hz excitation frequency; **(c)** load variation at 1.0 Hz excitation frequency; **(d)** load variation at 2.0 Hz excitation frequency.  
**Funding:** This research was funded by the National Natural Science Foundation Project of China, grant numbers 52175123 and 52172409, Key Technologies R&D Program of Henan Province, China, grant number 232102240092, and Sichuan Outstanding Youth Fund, China, grant number 2022 JDJ[Q0025.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
**Conflicts of Interest:** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.