# Preliminary Flutter Stability Assessment of the Double-Deck George Washington Bridge
## 6 Discussion  
The flutter stability of the George Washington bridge was investigated for the two different configurations, i.e., the original single-deck and the current double-deck. Due to the lack of literature data on the aerodynamic parameters for the bridge under consideration, two simplifications were introduced for the description of the motion-related wind loads:  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Bridge Configuration**} & \multicolumn{8}{c}{**Flutter Velocity [m/s]**} \\ \cline{2-9}  & **[PERSON] [41]** & **[PERSON] [42]** & **[PERSON] [42]** & **[PERSON] [43]** & **[PERSON] [44]** & **[PERSON] and [PERSON] [45]** & **Present Work** \\ \hline Single-deck & 39.56 & 36.08 & 36.21 & 36.09 & 38.70 & 46.45 & 40 \\ Double-deck & 121 & 113.86 & 114.44 & 113.87 & 89.23 & 97.76 & 107–79 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flutter velocity according to different simplified formulations.  
one for the calculation of flutter derivatives and the other for the application of aerodynamic loads on the two decks of the current configuration.  
The method adopted for the calculation of flutter derivatives allows them to be obtained by analytical formulations based on the steady-state aerodynamic coefficients. The latter parameters were calculated by CFD simulations using the finite element software ANSYS FLUENT. The application of the method provided good results on the bridges chosen for validation, namely the Great Belt and the Akashi Kaykio. The main advantage lies in the relative simplicity of the calculation of the steady-state aerodynamic coefficients, on which the formulation is based. In fact, the computational cost required is much lower than that which characterizes the CFD analyses necessary for a direct numerical calculation of flutter derivatives. Of course, this approach furnishes approximate predictions. To further validate the method, comparisons should be extended to several bridge decks for which both steady-state aerodynamic coefficients and flutter derivatives are available. Once the flutter derivatives were defined, the flutter analysis was performed by a finite element ANSYS Mechanical APDL model endowed with MATRIX27 elements [31].  
With regards to the double-deck configuration, two alternative methods were adopted for the definition and application of aeroelastic loads: a first one where lift and moment actions, based on static coefficients of the whole section, are applied to the top deck only; and a second one where lift and moment actions, based on static coefficients of the single-deck section, are applied to both upper and lower decks. Both methods introduce simplifications from the aerodynamic viewpoint. The former provides predictions similar to those of the simplified formulas calibrated for the airfoil. The latter is more aligned with the results provided by simplified formulations accounting for the difference between airfoil and deck cross-sections. With respect to the modal frequencies, the two methods provide similar trends for increasing wind speed, a 4% difference in the critical frequency estimation, and the same prediction of the flutter mode. According to the results of this study, the presence of the lower deck has raised the flutter wind velocity by more than 200%.  
Although a definitive validation of the numerical results was not possible, due to the lack of experimental data, the authors believe that the results obtained here can be used for future comparisons with others obtained by different methods. In addition, the proposed approach provides an approximate way for estimating the flutter velocity of double-deck long-span bridges in the absence of more detailed analyses.