# Dynamic Load Test and Contact Force Analysis of the AERORail Structure
## 4 Conclusions  
Based on the modal test and the natural frequency determined, the contact force between the vehicle and rail of AERORail was studied under the vehicle load on different spans; the conclusions are listed as follows:  
1. Through the modal test and modal analysis results of the 30 m span and five-pole supported AERORail, the measured modal parameters and the finite element analysis modal parameters are compared. The results show that in some cases, the finite element analysis results can provide the modal parameters required for vertical vibration analysis, but in the lateral direction, the source of error between the two still needs to be deeply studied.
2. By means of parameter identification, signal truncation, resampling and filtering, contact force calculation and error correction, the contact forces of different spans AERORail at different speeds can be obtained.
3. In most cases, the statistical characteristics of the contact force, including the mean and maximum value, have no significant correlation with the velocity; in the case of small spans, the contact force will have two troughs, and in the larger spans and higher velocities, the contact force is a single-valley curve, indicating that the vibration of the structure, vehicle travel time, and wheel-axle contact are the main factors at small spans; when the speed is higher, the contact force curve will have more obvious fluctuations, but peak regularity is consistent.
4. From the overall perspective of the three spans and five speeds, the contact force time-history curve has the following characteristics: the mean value of the contact force fluctuates in the range of 1800 N-4500 N with different working conditions; the maximum value of the contact force fluctuates in the range of 6000 N-11,000 N; there is no correlation between statistical characteristics such as the mean and maximum force and speed; at the start and end times, the contact force calculated by the identification algorithm is small and the fluctuation introduced by the algorithm is mainly reflected in the beginning and end of the contact force time-history curve area.
5. Comprehensively considering the travel time, contact force and deformation law of vehicles passing through a span structure, it is determined that the maximum contact force is still directly generated by the upper moving load when the span is large, while the small span is significantly affected by the dynamic characteristics of the structure.  
Conceptualization, F.L. and P.W.; methodology, Z.G., Y.C. and P.W.; validation, Z.G. and Y.C.; formal analysis, Z.G. and Y.C.; writing--original draft preparation, Z.G. and Y.C.; writing--review and editing, F.L.; visualization, Z.G.; supervision, F.L.; project administration, F.L.; funding acquisition, F.L. All authors have read and agreed to the published version of the manuscript.  
Figure 17: Time of maximum contact force.  
**Funding:** This research was supported by the National Natural Science Foundation of China (Grant No. 50708072, No. 51378385) and was supported by the Fundamental Research Funds for the Central Universities of China (Grant No. 22120180318).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data used to support the findings of this study are included in the article.  
**Conflicts of Interest:** The authors declare that they have no conflict of interest.