# Influence Analysis of Traveling Wave Effect on Rail Interaction of Long-Span Suspension Bridge
## 4 Natural Vibration Characteristics Analysis and Seismic Wave Simulation  
### Analysis of Natural Vibration Characteristics  
Suspension bridges are highly geometrically nonlinear structures. When performing modal analysis in ANSYS, the effects of large deformation and stress stiffening effects (prestress effects) need to be considered. ANSYS provides many modal analysis methods: power dynamics, reduced, Block Lanczos, subspace, etc. Considering the calculation accuracy and calculation speed comprehensively, this paper adopts the Block Lanczos method for the modal analysis of the suspension bridge. The natural vibration frequency and natural vibration period of the bridge structure of the first 20 orders and the corresponding mode shape description are given, as shown in Table 3.  
According to the above modal analysis results, it can be known that:  
1. The first-order natural frequency of this bridge is 0.073 Hz, and the first-order natural vibration period is 13.629 s, which are basically consistent with the design documents and analysis reports of this bridge, and the natural vibration period is much larger than that of general bridge structures, which meets the design expectations. 2. The first 20 vibration modes include the individual vibration and coupled vibration of the main truss, the main cable and the bridge tower. The main truss vibration includes vertical bending, side bending, transverse bending, torsion and longitudinal drift, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Modeling Software**} & \multicolumn{2}{c}{**Internal Force of the Main Cable (kN)**} & \multicolumn{2}{c}{**Internal Force of the Sling (kN)**} \\ \cline{2-5}  & **MAX** & **MIN** & **MAX** & **MIN** \\ \hline Midas Civil & 712,100 & 657,100 & 5643 & 2004 \\ ANSYS & 714,618 & 659,450 & 5875 & 1785 \\
**Percentage of difference** & 0.35\% & 0.36\% & 4.11\% & \(-\)10.93\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of main cable Internal force and sling Internal force results. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode Order** & **Natural Frequency (Hz)** & **Natural Period (s)** & **Mode Shape Description** \\ \hline
1 & 0.073 & 13.629 & \multicolumn{1}{c}{Symmetrical transverse bending of main truss} \\
2 & 0.152 & 6.591 & \multicolumn{1}{c}{Antisymmetric side bending of main girders} \\
3 & 0.159 & 6.291 & \multicolumn{1}{c}{Symmetrical vertical bending of main truss} \\
4 & 0.161 & 6.195 & \multicolumn{1}{c}{Antisymmetric vertical bending of main girders} \\
5 & 0.207 & 4.836 & \multicolumn{1}{c}{Main girder torsion and main girder positive symmetrical} \\
6 & 0.256 & 3.907 & \multicolumn{1}{c}{Symmetric side bending of main cable and main girder} \\
7 & 0.266 & 3.761 & \multicolumn{1}{c}{Main girder torsion} \\
8 & 0.276 & 3.617 & \multicolumn{1}{c}{Symmetrical vertical bending of main truss} \\
9 & 0.294 & 3.405 & \multicolumn{1}{c}{Main girder torsion and main girder antisymmetric side bending} \\
10 & 0.297 & 3.367 & \multicolumn{1}{c}{Main cable side bending} \\
11 & 0.314 & 3.183 & \multicolumn{1}{c}{Main cable side bending} \\
12 & 0.323 & 3.101 & \multicolumn{1}{c}{Main cable side bending} \\
13 & 0.325 & 3.072 & \multicolumn{1}{c}{Antisymmetric side bending between main cable and} \\
14 & 0.369 & 2.712 & \multicolumn{1}{c}{Symmetric side bending of main cable and main girder} \\
15 & 0.385 & 2.597 & \multicolumn{1}{c}{Longitudinal floating and antisymmetric vertical bending of} \\
16 & 0.413 & 2.421 & \multicolumn{1}{c}{Main cable side bending and main girder torsion (side} \\
17 & 0.413 & 2.420 & \multicolumn{1}{c}{Antisymmetric side bending between main cable and} \\
18 & 0.422 & 2.369 & \multicolumn{1}{c}{Main girder torsion} \\
19 & 0.447 & 2.239 & \multicolumn{1}{c}{Longitudinal floating of main truss and antisymmetric vertical bending (side movement of bridge tower)} \\
20 & 0.470 & 2.127 & \multicolumn{1}{c}{Main cable yaw} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Natural frequency of the structure.