# Dynamic Impact Factor and Resonance Analysis of Curved Intercity Railway Viaduct
## 5 Conclusions  
In order to evaluate the dynamic response and resonance of a curved viaduct under intercity vehicle load, the VTBS model with the curved bridge was developed, in which the curved part of the bridge adopted the \"straight\" form instead of curved. The calculation reliability of the model was elucidated by the numerical results from the existing literature. The theoretical resonance conditions of the bridge were calculated, and the bridge responses under various speeds were determined. Moreover, the dynamic time-history responses of vertical and radial displacement of the bridge under resonant speed were analyzed. Finally, to systematically analyze the dynamic response of the curved bridges, the bridge IFs under different spans, curved radius, and vehicle speeds were calculated.  
The conclusions drawn from this study are as follows.  
1. It is observed that the results from the numerical calculations are consistent with the theoretically computed results. However, there are certain disparities in some instances. There may be some differences.
2. Under the different resonant speeds, the response curves of bridge mid-span moving force under vehicle load show varying trends. Under the low order resonant speed, the dynamic response trend of the bridge is regular, and the vehicle still has a large range of free vibrations after leaving the bridge. The dynamic response curve of the bridge is rough under high-order resonant velocity.
3. Both the vertical and radial IFs of the curved intercity rail bridge are not affected by the curve radius.
4. From the parameter analysis, it is concluded that the reasonable natural vibration characteristics of the bridge can be selected according to different design speeds for structural optimization, which can effectively reduce the dynamic factor of a curved bridge.  
Figure 11: Radial _IF_ of bridges under different frequencies and curved radius: (**a**) \(R\) = 400 m; (**b**) \(R\) = 500 m; (**c**) \(R\) = 600 m; (**d**) \(R\) = 700 m; (**e**) \(R\) = 800 m; (**f**) \(R\) = 900 m.  
**Author Contributions:** Conceptualization, J.W. and C.C.; methodology, X.L.; software, X.L.; validation, X.L. and C.C.; formal analysis, J.W.; investigation, J.W. and C.C.; data curation, X.L.; writing--original draft preparation, J.W. and M.W.; writing--review and editing, J.W. and M.W.; visualization, M.W.; supervision, J.W.; project administration, J.W.; funding acquisition, J.W. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by [Henan Provincial Department of science and technology] grant number [182107000007] and [Fujian University of Technology] grant number [GY-Z21181], and The APC was funded by [Henan Provincial Department of science and technology] grant number [182107000007].  
**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 within the article.  
**Conflicts of Interest:** The authors declare no conflict of interest.