# Vibration Response Law of Aircraft Taxing under Random Roughness Excitation
## 5 Results and Discussion  
### Vibration Response Analysis of Aircraft Taxing under Different Pavement Types  
The PSD distributions of CGA, PSA, NGDLC, and MGDLC under typical roughness excitations of both asphalt pavement and concrete pavement during a 100 km/h taxiing of a B737-800 aircraft are shown in Figure 6a to Figure 6d, respectively. Overall, the PSD distribution of each vibration response is similar for both pavement types, as shown in Figure 6. The red and black lines show a similar trend of rising and falling, and the sensitivity frequencies corresponding to each peak are almost the same. However, the vibration response corresponding to concrete pavement roughness at around 2.6 Hz decreases dramatically. This is attributed to the segmental characterization of the concrete pavement roughness model, which has few broken slabs or cracks within the concrete slab and high flatness.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Runways** & \(\mathbf{C_{1}}\) & \(\mathbf{\alpha}\) & \(\mathbf{w_{1}}\) \\ \hline
18 runways in China & 0.0089–0.235 (0.025) & 0.00009–0.1503 (0.04) & 1.369–3.527 (2.4) \\
19 runways abroad & 0.007–0.147 (0.025) & 0.000015–0.0103 (0.005) & 1.21–3.22 (2.5) \\
**Runways** & \(\mathbf{C_{2}}\) & \(\mathbf{w_{2}}\) & \\
18 runways in China & 0.049–0.597 (0.08) & 1.813–3.13 (2.5) & \\
19 runways abroad & 0.029–0.308 (0.08) & 1.59–2.86 (2.2) & \\ \hline \end{tabular}
\end{table}
Table 4: Cement pavement fitting parameters’ distribution.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Unit** & **Value** & **Description** \\ \hline \(k_{\text{f}}\) & N/m & 58,027 & stiffness coefficient of front landing gear buffer \\ \(K_{\text{l}}\) & N/m & 996,531 & stiffness coefficient of left rear landing gear buffer \\ \(K_{\text{r}}\) & N/m & 996,531 & stiffness coefficient of right rear landing gear buffer \\ \(k_{\text{f}}\) & N/m & 1,966,300 & stiffness coefficient of front landing gear tire \\ \(k_{\text{l}}\) & N/m & 2,812,900 & stiffness coefficient of left rear landing gear tire \\ \(k_{\text{r}}\) & N/m & 2,812,900 & stiffness coefficient of right rear landing gear tire \\ \(C_{\text{f}}\) & N\(\cdot\)s/m & 131,500 & damping coefficient of front landing gear buffer \\ \(C_{\text{l}}\) & N\(\cdot\)s/m & 572,500 & damping coefficient of left rear landing gear buffer \\ \(C_{\text{r}}\) & N\(\cdot\)s/m & 572,500 & damping coefficient of right rear landing gear buffer \\ \(c_{\text{f}}\) & N\(\cdot\)s/m & 131,500 & damping coefficient of front landing gear tire \\ \(\alpha\) & N\(\cdot\)s/m & 4066 & damping coefficient of left rear landing gear tire \\ \(c_{\text{r}}\) & N\(\cdot\)s/m & 4066 & damping coefficient of right rear landing gear tire \\ \(l_{x}\) & kg\(\cdot\)m\({}^{2}\) & 3,394,953 & rotational inertia of aircraft around \(x\)-axis \\ \(l_{y}\) & kg\(\cdot\)m\({}^{2}\) & 1,866,711 & rotational inertia of aircraft around \(y\)-axis \\ \(a\) & m & 2.86 & horizontal distance from left landing gear to \(y\)-axis \\ \(b\) & m & 2.86 & horizontal distance from right landing gear to \(y\)-axis \\ \(d\) & m & 14.6 & horizontal distance from front landing gear to \(x\)-axis \\ \(e\) & m & 1 & horizontal distances from rear landing gear to \(x\)-axis \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{c c c c} \hline
**Runways** & \(\mathbf{C}\) & \(\mathbf{\alpha}\) & \(\mathbf{w}\) \\ \hline
2 runways in China & 0.0907–0.119 (0.1) & 0.00054–0.0014 (0.0009) & 2.199–2.285 (2.24) \\
18 runways abroad & 0.0227–1.206 (0.1) & 0.00019–0.00178 (0.0005) & 2.042–3.162 (2.3) \\ \hline \end{tabular}
\end{table}
Table 3: Asphalt pavement fitting parameters’ distribution.