## 4 Results and Discussion
### Extreme Pressure, Duration of Extreme Pressure and Impact Effects  
As enclosed housings for sound emission alleviations are always made of steel structures, the extreme aerodynamic pressure, duration of the extreme pressure, and impact effects are key factors for the structural design. The extreme pressures are defined as the maximum positive or negative pressure acting on each section when the train passes through at a speed of 350 km/h. Table 1 shows the distributions of the positive extreme value, negative extreme value, and peak-to-peak aerodynamic pressure in the longitudinal direction. \(P_{pmax}\) is the positive-extreme pressure, \(P_{mmax}\) is the negative-extreme pressure, and the peak-to-peak pressure is the absolute difference of \(P_{pmax}\) and \(P_{mmax}\) (\(P_{pmax}-P_{mmax}\)). The results show that the extreme pressures are almost symmetrical against section S6, the middle section. The extreme aerodynamic pressure at the central region is always higher than those close to the entrance/exit. In particular, the negative extreme pressure drastically increases in the range of 150 m to 350 m from the entrance/exit and reaches \(-\)2153 Pa at the middle section, more than two times higher than that at the entrance/exit sections. Different from the negative peak, the positive extreme pressure gradually increases from the entrance/exit to the middle section and reaches the maximum value of 1298 Pa at the middle section. The maximum peak-to-peak pressure is calculated as 3451 Pa. The time history of the train-induced aerodynamic pressure in Figure 10 shows the variation of the aerodynamic pressure is very complicated. It is hard to calculate the wind-induced response using this wind load. In the present study, an ideal model of the aerodynamic pressure is proposed using the duration, \(T_{d}\), and the change rate of aerodynamic pressure, \(\overline{P}\) and \(P_{pmax}\) and \(P_{mmax}\), as Figure 13 shows. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sections** & \(P_{pmax}\) **(Pa)** & \(P_{pmax}\) **(Pa)** & **Peak-to-Peak (Pa)** \\ \hline
1 & 1090 & \(-\)1020 & 2110 \\
2 & 1047 & \(-\)1088 & 2135 \\
3 & 1145 & \(-\)1607 & 2752 \\
4 & 1237 & \(-\)2076 & 3312 \\
5 & 1285 & \(-\)2111 & 3396 \\
6 & 1298 & \(-\)2153 & 3451 \\
7 & 1277 & \(-\)2023 & 3300 \\
8 & 1227 & \(-\)1963 & 3190 \\
9 & 1170 & \(-\)1212 & 2382 \\
10 & 944 & \(-\)909 & 1853 \\
11 & 799 & \(-\)936 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Distribution of the extreme pressure in the longitudinal direction of the housing for sound emission alleviation. Figure 12: The pressure distribution on the wall of the housing for sound emission alleviation when \(t=6\) s.  
The duration \(T_{d}\) is defined as the time when the aerodynamic pressure is higher than 85% of extreme pressure and the extreme pressure appears:  
\[T_{d}=T2|_{0.85P_{\max}}-T1|_{0.85P_{\max}} \tag{9}\]  
where \(T1|_{0.85P_{\max}}\) is the first instant when the pressure reaches \(0.85P_{\max}\) before the extreme pressure, \(T2|_{0.85P_{\max}}\) is the first instant when the pressure reaches \(0.85P_{\max}\) after the extreme pressure, and \(P_{\max}\) represents both positive and negative extreme pressures. The change rate of aerodynamic pressure \(\overline{P}\):  
\[\overline{P}=\frac{P_{lb}-P_{th}}{t_{lb}-t_{th}} \tag{10}\]  
where \(P_{th}\) and \(P_{ib}\) are the aerodynamic pressures at two adjacent inflection points, \(t_{ih}\) and \(t_{ib}\) are the corresponding instants. In addition, the absolute difference, \(\mid P_{th}-P_{ib}\mid\), should be higher than \(0.5P_{\max}\). Table 2 summarizes the \(T_{d}\) and maximum \(\overline{P}\) of monitoring point P3 on sections S1, S3, S6, S9, and S11. The sections close to both ends have shorter durations. The middle section S6 has the longest duration of the positive and negative extreme aerodynamic pressures. They are 1.41 s and 1.04 s, respectively. Section S1, at the entrance of the enclosed housing for sound emission alleviation, has the highest positive and negative pressure change rate.