# A Time-History Contact Force Model of the Dynamic Load of AERORail Structures
## 5 Calculation of High-Speed Working Conditions
### Short Span High-Speed Working Condition Simulation  
The calculation parameters of 5 m, 10 m, and 15 m span AERORail structures were as described by [PERSON] et al. [5] and Section 2. The working conditions involved in the simulation are shown in Table 9:  
Figure 11: Maximum deflection over a 10 m span. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Speed in Working** & **Experimental Data** & **Single-Valley** & **Relative Error (\%)** & **Double-Valley** & **Relative Error (\%)** \\
**Condition (km/h)** & **(mm)** & **Simulation (mm)** & **Relative Error (\%)** & **Simulation (mm)** & **Relative Error (\%)** \\ \hline
5 & 30.45 & 30.67 & 0.73 & 24.32 & 20.12 \\
10 & 31.92 & 30.82 & 3.42 & 24.45 & 23.39 \\
15 & 33.61 & 30.84 & 8.24 & 24.79 & 26.25 \\
20 & 33.86 & 31.35 & 7.42 & 25.17 & 25.65 \\
25 & 34.49 & 31.42 & 8.88 & 25.32 & 26.57 \\ \hline \end{tabular}
\end{table} 
Table 8: Maximum mid-span deflection of 10 m span. Considering that the standard double-valley curve model had satisfactory accuracy in the simulation of a 5 m span, the standard double-valley curve model was used to calculate the 5 m span AERORail structure. The calculated mid-span deflection-time curve is shown in Figure 12.  
The simulation results in Figure 12 showed the following. (1) With the increase of speed, the residual vibration amplitude retained by the AERORail structure after excitation increased continuously. (2) When the speed was greater than 100 km/h, the rebound in the AERORail span became more and more obvious. (3) With the increase of speed, the two extremes of deflection generated by the two-valley curve gradually approached each other and finally merged into a single extreme value (300 km/h, 3.73 mm). (4) The condition with the maximum deflection was not the condition with the highest speed, and the extreme deflection increased first and then became smaller with the increase of speed, reaching a maximum value of 6.19 mm around 120 km/h. (5) When the speed was greater than 250 km/h, the vibration response of the AERORail was close to damped free vibration. According to the above results, the following conclusions can be drawn: (1) the dynamic response of a 5 m span under high-speed conditions gradually approached the  
Figure 12: Simulation of high-speed working condition of 5 m span. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Span m**Speed km/h & **40** & **60** & **80** & **100** & **120** & **150** & **200** & **250** & **300** \\ \hline
5 & Double & Double & Double & Double & Double & Double & Double & Double & Double \\ valley & valley & valley & valley & valley & valley & valley & valley & valley & valley & valley \\ \multirow{2}{*}{10} & Single & Single & Single & Single & Single & Single & Single & Single & Single & Single \\ valley & valley & valley & valley & valley & valley & valley & valley & valley & valley & valley \\ \multirow{2}{*}{15} & Single & Single & Single & Single & Single & Single & Single & Single & Single & Single \\ valley & valley & valley & valley & valley & valley & valley & valley & valley & valley & valley \\ \hline \hline \end{tabular}
\end{table} 
Table 9: High-speed simulation working conditions table. response of a damped free vibration system with the increase of speed; (2) the resonance speed of a 5 m span was near 120 km/h; (3) the maximum dynamic deflection of a 5 m span under the action of a standard double-valley curve model was about 6.19 mm. For the simulation of 10 m and 15 m spans, considering that the standard single-valley curve model had high calculation accuracy under these two span structures, and the contact force history curve itself was close to the single-valley curve shape under high-speed working conditions, the time force model used in the calculation of 10 m and 15 m spans was the standard single-valley curve model. The calculation results of the 10 m span under high-speed working conditions can be seen in Figure 13.  
The simulation results of the 10 m span high-speed working conditions had the following characteristics.