## 5 Results and Discussion
### Analysis of the Dynamic Response of the Vehicle Carbody  
In this section, we analyze the dynamic response of the vehicle carbody expressed as the power spectral density of the vertical acceleration before and after weighting with the weighting function corresponding to the mean comfort method and the weighting function corresponding to [PERSON]'s method, respectively. The results of this analysis will be the basis for explanations regarding the significant results obtained via the two methods of assessing ride comfort (ride comfort index \(N_{MVZ}\) and ride comfort index Wz), under \begin{table}
\begin{tabular}{l l} \hline \(m_{c}=34\),000 kg & \(2k_{cc}=1.2\) MN/m \\ \(m_{b}=3200\) kg & \(2k_{cc}=4\) MN/m \\ \(l_{c}=1,963,840\) kg\(\cdot\)m\({}^{2}\) & \(2k_{cc}=256\) kN/m \\ \(l_{b}=2048\) kg\(\cdot\)m\({}^{2}\) & \(2c_{cc}=34.28\) kNs/m \\ \(EI=3.158\times 10^{9}\) Nm\({}^{2}\) & \(2c_{cc}=50\) kNs/m \\ \(m_{mc}=35224\) kg & \(2c_{0c}=2\) kNs/m \\ \(L_{c}=26.4\) m & \(4k_{ab}=4.4\) MN/m \\ \(22c_{c}=19\) m & \(4k_{ab}=52.21\) kNs/m \\ \(2d_{b}=2.56\) m & \(k_{m2}=88.998\) MN/m \\ \(h_{c}=1.3\) m; \(h_{b}=0.2\) m & \(c_{mc}=53.117\) kNs/m \\ \hline \end{tabular}
\end{table} 
Table 4: Reference parameters of the vehicle model. Figure 5: Correlation between ride comfort index \(N_{MV}\) and ride comfort index \(W_{z}\). the same conditions of vehicle running. The purpose of this analysis is to highlight the dominant vibration modes of the carbody and their effect upon the dynamic response of the carbody before and after frequency weighting. The diagrams (a) in Figures 6-8 display the dynamic response in the carbody reference points, expressed as the power spectral density of the vertical acceleration.At the carbody center (Figure 6), thepower spectral density of the acceleration is dominated by the bounce vibration (at 1.17 Hz). In the reference points located above the two bogies (Figures 7 and 8), the dominant vibration modes of the carbody are the pitch (at 1.53 Hz) and the bounce. At high velocities, the peaks corresponding to the carbody bending can be seen in all the carbody reference points (at 8 Hz). This vibration mode has a more important weight at the carbody center [46]. The resonance frequency of the carbody bending is noticed to be in the maximum area of the sensitivity interval of the human body to the vertical vibrations considered by the mean comfort method. Consequently, the ride comfort assessed on the basis of the ride comfort index \(N_{MVZ}\) is expected to be greatly affected when the weight of such vibration mode is important. Figure 6: Correlation between ride comfort index \(N_{MV}\) and ride comfort index \(W_{2}\).Power spectral density of acceleration (PSD acceleration) in reference point C in (m/s)\({}^{2}\)/Hz: (**a**) unweighted; (**b**) weighted with weighting function \(H_{ab}\); (**c**) weighted with weighting function \(B\). Figure 8: Correlation between ride comfort index \(N_{MV}\) and ride comfort index \(W_{2}\).Power spectral density of acceleration (PSD acceleration) in reference point \(B_{2}\) in \((\text{m}/\text{s}^{2})^{2}/\text{Hz}\): (**a**) unweighted; (**b**) weighted with weighting function \(H_{ab}\); (**c**) weighted with weighting function \(B\). Figure 7: Correlation between ride comfort index \(N_{MV}\) and ride comfort index \(W_{2}\).Power spectral density of acceleration (PSD acceleration) in reference point \(B_{1}\) in \((\text{m}/\text{s}^{2})^{2}/\text{Hz}\): (**a**) unweighted; (**b**) weighted with weighting function \(H_{ab}\); (**c**) weighted with weighting function \(B\). The diagrams (b) of the Figures 6-8 feature the power spectral density of the carbody vertical acceleration weighted with the weighting function \(H_{ab}\), corresponding to the mean comfort method.Due to this weighting filter, bending becomes the dominant vibration mode at the carbody center, at high velocities (see Figure 6), which creates the premise that the ride comfort may be greatly affected.