## 4 Simulation and Experimental Verification
### Multi-Objective Optimal Design Option Strength Verification
#### 4.1.1 Modal and Vibration Verification  
The center holes of the four inner and outer baffles in the fifth wheel are fixed to limit all six degrees of freedom, and the intrinsic frequency and vibration pattern values are obtained, as shown in Table 14. The mode distributions shown in Figure 19a-c are the first-to third-order mode distributions in turn. One of the first-order intrinsic frequencies is 253 Hz, which is much higher than the external excitation frequency. Therefore, the fifth wheel does not resonate with the outside world in the constrained state.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Var1** & **Var2** & **Var3** & **Var4** & **Var5** & **Var6** & **Var7** & **Var8** & **Var9** & **Var10** \\ \hline
7.2 & 4.0, 4.8 & 20.4, 21.9 & 4.0, 5.8 & 8.0, 9.4 & 4.7, 7.0 & 5.6, 8.8 & 4.0, 7.7 & 5.0, 7.3 & 4.0, 5.6 \\
7.3 & 4.0, 4.8 & 20.1, 21.3 & 4.0, 4.9 & 8.0, 9.6 & 5.1, 6.8 & 6.2, 8.6 & 4.1, 7.3 & 5.0, 7.1 & 4.0, 5.6 \\
7.4 & 4.0, 5.0 & 19.8, 21.6 & 4.0, 5.4 & 8.0, 9.0 & 4.9, 7.0 & 6.0, 7.5 & 4.1, 5.8 & 5.0, 7.0 & 4.0, 5.1 \\
7.5 & 4.0, 4.5 & 19.4, 20.7 & 4.0, 4.6 & 8.0, 9.0 & 5.6, 6.9 & 6.0, 7.1 & 4.3, 5.1 & 5.0, 6.5 & 4.0, 5.1 \\
7.6 & 4.0, 5.1 & 18.9, 20.7 & 4.0, 5.6 & 8.0, 8.8 & 4.3, 6.6 & 6.0, 7.1 & 4.2, 5.1 & 5.0, 6.1 & 4.0, 5.2 \\
7.7 & 4.0, 4.7 & 18.8, 20.6 & 4.0, 4.8 & 8.0, 8.7 & 5.3, 6.4 & 5.9, 6.9 & 4.0, 4.6 & 5.0, 6.2 & 4.0, 5.1 \\
7.8 & 4.0, 4.3 & 18.4, 20.4 & 4.0, 4.6 & 8.0, 8.2 & 4.5, 6.7 & 6.7, 7.0 & 4.1, 4.6 & 5.0, 5.8 & 4.0, 4.5 \\
7.9 & 4.0, 4.3 & 18.1, 20.6 & 4.0, 4.4 & 8.0, 8.3 & 4.6, 6.7 & 6.9, 7.0 & 4.0, 4.7 & 5.0, 5.3 & 4.0, 4.4 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Range of values for each component for 25% lightweighting.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Order** & **First** & **Second** & **Third** & **Fourth** & **Fifth** & **Sixth** & **Seventh** & **Eighth** & **Ninth** & **Tenth** \\ \hline Frequency (Hz) & 253 & 359 & 788 & 796 & 844 & 870 & 965 & 1042 & 1180 & 1210 \\ Maximum vibration mode & 4.74 & 9.29 & 62.27 & 63.17 & 71.16 & 72.00 & 43.22 & 25.32 & 25.56 & 42.23 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Modal analysis results.  
Figure 19: The first to third vibration mode distribution diagrams of optimal design option.  
Among the first ten orders of vibration, the first, second, ninth, and tenth orders are integral modes, and the third to eighth orders are local modes.  
Among the overall modes, deformation of the first-order vibration mode occurred relatively uniformly on the saddle body. The deformation of the second-order vibration mode transitions from top to bottom, and the maximum deformation occurs on the bothetail at the lower end of the saddle. The deformation of the ninth- and tenth-order vibration modes transitions from the outside to the inside, and the maximum deformation occurs at the edge of the side of the saddle body.  
In the local modes, the maximum deformations of the third- and fourth-order vibration shapes are located in the upper transverse plate, where all the third-order deformations are downward concave, and the fourth-order deformations occur in the upper transverse plate with left-side convex and right-side concave shapes. The maximum deformation of the fifth-order vibration pattern occurred on the left side of the carriages and bulges to the right, and the maximum deformation of the sixth-order vibration pattern occurred on the right side of the carriages and bulges to the right. Severe deformation in the seventh-order vibration mode occurs on the right side of the saddle body, where the largest deformation is located at the lower end tail of the right side, while larger deformation in the eighth-order vibration mode occurs on the left side of the saddle body, where the largest deformation is located at the lower end tail of the left side.