## 4 Dynamic Characteristic Analysis of the Special Cable-Stayed Bridge
The first vibration mode is lateral vibration of the main girder, which is the basic vibration mode of the bridge. Lateral vibration can indicate that the transverse stiffness of the main girder \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Orders** & **Natural Vibration Frequencies (Hz)** & **Cycle (s)** & **Vibration Modes** \\ \hline \multirow{3}{*}{5} & Cantilever stage & 0.723 & 1.383 & The 2 nd order reverse bending \\  & Completion stage & 32.326 & 0.031 & The 2 nd torsion of longitudinal beam \\ \hline \multirow{3}{*}{6} & Cantilever stage & 0.856 & 1.168 & The torsion of the girder \\  & Completion stage & 33.933 & 0.029 & bending-torsional coupling \\ \hline \multirow{3}{*}{7} & Cantilever stage & 1.013 & 0.987 & The 1 st order vertical bending \\  & Completion stage & 45.683 & 0.022 & Symmetrical vertical bending \\ \hline \multirow{3}{*}{8} & Cantilever stage & 1.021 & 0.979 & Lateral bending torsion coupling \\  & Completion stage & 47.841 & 0.021 & Lateral swing of bridge tower \\ \hline \multirow{3}{*}{9} & Cantilever stage & 1.210 & 0.826 & Auxiliary pier swing \\  & Completion stage & 51.992 & 0.019 & Vertical bending \\ \hline \multirow{3}{*}{10} & Cantilever stage & 1.255 & 0.797 & Auxiliary pier reverse bending \\  & Completion stage & 52.083 & 0.0192 & Bending torsion coupling \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 6: Some vibration modes: **(a)** The 1 st-order mode; **(b)** the 5 th-order mode; **(c)** the 6 th-order mode; **(d)** the 7 th-order mode; **(e)** the 8 th-order mode; **(f)** the 9 th-order mode. in cantilever stage is less than the longitudinal stiffness. The frequency is greater than 1 Hz when the whole bridge is in the seventh order, which shows that the overall stiffness of the structure is smaller. 3. It can be seen from Table 2 that the modes of vibration at the cantilever stage are intense. In the narrow frequency range from 0.174 Hz to 1.254 Hz, 10 vibration modes are distributed, therefore, it is suggested that more vibration modes should be adopted when the dynamic characteristics of this type of cable-stayed bridges are analyzed. 4. Compared with the maximum cantilever state, the vibration modes of the completed bridge mainly include lateral bending, vertical bending, and torsion coupling. The steel truss girder cable-stayed bridge with single cable plane in the semi-floating system has relatively large rigidity and a short natural vibration period of 0.049 s. The first-order vibration mode is the longitudinal torsion of the left side beam of the upper deck system, which is the basic vibration mode of the completed bridge. It shows that the rigidity of the left side longitudinal beam is low and it conforms to the maximum force of the side longitudinal beam. The lateral bending vibration mode of the main girder appears earlier than the vertical bending vibration modes, which is consistent with small width span ratio. The bridge adopts the form of a single cable plane cable-stayed bridge, which has the characteristics of poor torsional resistance and low torsional rigidity, therefore, it conforms to the torsional vibration mode of structure in the 5 th, 6 th, and 10 th order modes. The main beam is a steel truss with large structural size; the tower is a concrete tower with relatively small size. Therefore, the stiffness of the main girder of the cable-stayed bridge is smaller than those of the pylon.