# Research on Effective Design Methods of Core Beam of Full Bridge Aeroelastic Model
## 6 Conclusions  
In this study, numerical solutions of torsion constant of simply-connected sections are presented, two effective core beam design methods are proposed to address the difficulties in the design of reduced-scale models, and the proposed methods are verified with an aeroelastic model of an actual suspension bridge. The conclusions are summarized as follows:  
1. For simple simply connected sections, such as rectangular sections, the simple five-point difference method is recommended to determine the torsion constant. For complex simply connected sections, such as U-shaped cross sections, the generalized difference method and finite element method can be used to determine the torsion constant.
2. For the ANSYS optimization method, the initial values of the section parameters of the core beams are required. If the initial values are not well-designed, the ANSYS optimization method is prone to fall into a local optimal solution. This study derives the numerical solution method for the torsion constant of rectangular and U-shaped sections commonly used in aeroelastic models, and proposes the genetic algorithm in the form of the total error of the section parameters. Through the optimization process, it is found that the genetic algorithm is easy to find out with the global optimization solution. It not only converges at a fast speed, but also leads to results of high quality and reliability. Since the investigated concerns can deal with any reduced-scale model, the proposed solution is of general validity and can be extended to many other different cases.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode** & **Targeted (Hz)** & **Measured (Hz)** & **Error (\%)** \\ \hline
1 st-Positive symmetrical vertical bending & 1.859 & 1.818 & \(-\)2.234 \\
1 st-Antisymmetric vertical bending & 1.280 & 1.270 & \(-\)0.795 \\
1 st-Positive symmetrical torsional & 4.582 & 4.430 & \(-\)3.323 \\
1 st-Positive symmetrical lateral bending & 6.302 & / & / \\
1 st-Positive symmetrical lateral bending & 0.874 & 0.879 & 0.4801 \\
1 st-Antisymmetric lateral bending & 2.804 & 2.734 & \(-\)2.483 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Major frequency characteristics of the full-bridge aeroelastic model.  
Figure 30: Aeroelastic model dynamic characteristics testing.  
Each part in the design of an aeroelastic model is crucial to perfectly examine the aerodynamic performance of the full bridge in a wind tunnel, and these parts play different roles but are closely related. This study only provides meaningful research on the optimization design of the cross-sectional size of the core beam. However, different scaled models or simplified aerodynamic shapes may have significant differences in their aerodynamic performance, which means there is still a long way to go for future research on the rationality of scaled and simplified aerodynamic shapes.  
[PERSON] and [PERSON] conceived the idea of this research; [PERSON], wrote the paper; [PERSON] and [PERSON] reviewed and revised the paper. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Grant Number 51578233 and 51938013).  
The data, models, and codes that support the findings of this study are available from the corresponding author.  
The authors declare no conflict of interest.