## 4 Dynamic Characteristic Analysis of the Special Cable-Stayed Bridge  
The frequency spectrum of the stayed cables are intense, and the dynamic loads can stimulate more vibration modes in a wide frequency range. Therefore, the dynamic characteristics of long-span cable-stayed bridges are usually adopted using more than 10 vibration modes. In the calculation process of dynamic characteristics, the undamped free vibration equation is adopted and the initial stress effect of the deadweight is taken into consideration; the deadweight stress in the vertical direction of any point in the bridge structure is equal to the mass of the structure per unit area above this point, that is, the deadweight is converted into equivalent load. The subspace iteration method is used to extract the natural vibration frequencies and vibration modes [31; 32; 33; 34]. The first ten natural vibration frequencies and vibration mode characteristics of the bridge at the maximum cantilever state and completion stage are shown in Table 2, some vibration modes are shown in Figure 6. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Orders** & \multicolumn{2}{c}{**Natural Vibration Frequencies (Hz)**} & \multicolumn{2}{c}{**Cycle (s)**} & \multicolumn{2}{c}{**Vibration Modes**} \\ \hline \multirow{2}{*}{\(1\)} & \(\begin{array}{c}\text{Cantilever stage}\\ \text{Completion stage}\end{array}\) & 0.174 & 5.760 & \multicolumn{2}{c}{The 1 st order lateral runout} \\  & \(\begin{array}{c}\text{Completion stage}\end{array}\) & 20.255 & 0.049 & \multicolumn{2}{c}{The 1 st order torsion of longitudinal beam} \\ \hline \multirow{2}{*}{\(2\)} & \(\begin{array}{c}\text{Cantilever stage}\\ \text{Completion stage}\end{array}\) & 0.316 & 3.164 & \multicolumn{2}{c}{The 1 st order vertical runout} \\  & \(\begin{array}{c}\text{Completion stage}\end{array}\) & 22.777 & 0.044 & \multicolumn{2}{c}{The 1 st order transverse bending} \\ \hline \multirow{2}{*}{\(3\)} & \(\begin{array}{c}\text{Cantilever stage}\\ \text{Completion stage}\end{array}\) & 0.598 & 1.672 & \multicolumn{2}{c}{The 1 st order Lateral torsion} \\  & \(\begin{array}{c}\text{Completion stage}\end{array}\) & 25.600 & 0.039 & \multicolumn{2}{c}{The 1 st order vertical bending} \\ \hline \multirow{2}{*}{\(4\)} & \(\begin{array}{c}\text{Cantilever stage}\\ \text{Completion stage}\end{array}\) & 0.611 & 1.638 & \multicolumn{2}{c}{The 1 st order vertical bending} \\  & \(\begin{array}{c}\text{Completion stage}\end{array}\) & 30.269 & 0.033 & \multicolumn{2}{c}{The 2 nd order vertical bending} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The first ten frequencies and vibration modescharacteristics at the maximum cantilever state and completion stages. Figure 4: Ansys bridge model. Figure 5: The cable details. It can be seen from Table 2 that the vibration modes of the cable-stayed bridge with single cable plane steel truss girder have the following basic characteristics in the maximum cantilever state and the completion stage. 1. The vibration modes mainly include six kinds of vibration modes, namely lateral vibration, vertical vibration, torsional vibration, vertical bending vibration, lateral bending vibration, and coupled vibration. Among them, the torsion of the main girder appeared in the third order and sixth order. The reason for the torsion of the main beam is that the single cable plane does not provide enough ability to resist torsion, and therefore the torsional rigidity and the torsional frequencies are decreased. Therefore, special attention should be paid to the anti-wind capacity of bridge structures when they are being constructed. Because bridge members have different stiffnesses, the first eight orders are all the vibration modes of the main girder, and the latter two modes are the vibration modes of the auxiliary piers. 2. A long-span cable-stayed bridge is very flexible, and therefore, its natural vibration periods are usually longer.Besides, the natural vibration frequency of the bridge is large because the second phase deadload of this bridge is large.