# Influence of the Flexible Tower on Aeroelastic Loads of the Wind Turbine
## 4 Flexible Tower Vibration Feedback Analysis
### Tower Load Error Analysis
To investigate the law of mutual influence between tower vibration and pneumatic load, we compared the relative errors of tower top angle and displacement under three tower heights, and the simulation results are shown in Figures 9 and 10. From Figures 9 and 10, it can be seen that, when the flexibility of the support structure is large, the maximum errors of displacement and the turning angle of the tower top downwind are both around 8%, while the maximum deviations of the crosswind direction are both over 12%. It can be seen that, when the flexibility of the support structure is large, ignoring the effect of the time-varying nacelle attitude feedback will make the analysis of the dynamic less accurate. It can also be seen that the relative errors of displacement and the turning angle at the top of the tower remain the same in terms of trend and magnitude. It can be seen that when the other structural parameters (blade, nacelle mass, etc.) are constant, the degree of influence of the tower bending-bending coupling bidirectional feedback on the dynamical behavior of the tower is positively correlated with the flexibility of the support structure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \begin{tabular}{c} **Height** \\ **(m)** \\ \end{tabular} & \begin{tabular}{c} **Modulus of** \\ **Elasticity (N/m\({}^{2}\))** \\ \end{tabular} & \begin{tabular}{c} **Diameter and Wall** \\ **Thickness of Tower** \\ **Top (m)** \\ \end{tabular} & \
\begin{tabular}{c} **Diameter and Wall** \\ **Thickness of Tower** \\ **Bottom (m)** \\ \end{tabular} &
\begin{tabular}{c} **Structural** \\ **Damping Ratio** \\ \end{tabular} \\ \hline
86.7 & 2.1 \(\times\) 1011 & 3.87, 0.247 & 6, 0.351 & 1\% \\
200 & 2.1 \(\times\) 1011 & 3.87, 0.247 & 6, 0.351 & 1\% \\
300 & 2.1 \(\times\) 1011 & 3.87, 0.247 & 6, 0.351 & 1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Ultra-high flexible tower parameters. Figure 8: Relative error analysis of tower top load. (**a**) Longitudinal thrust. (**b**) Lateral thrust. Figure 9: _Cont._  
Figure 10: Relative error of tower top displacement. (**a**) Longitudinal direction. (**b**) Crosswind direction. Figure 9: Relative error of tower top angle. (**a**) Pitch angle. (**b**) Lateral camber angle. As shown in Figure 11, the maximum displacements of the tower top in the downwind direction are 1.2 m, 0.82 m, 0.61 m, and 0.46 m. The maximum lateral displacements of the tower top are 0.14 m, 0.1 m, 0.08 m, and 0.07 m. It can be seen that the deflection of the tower top increases greatly when considering flexibility. Compared with the rigid foundation, the maximum tower top displacement of Case 1, Case 2, and Case 3 increases nearly 161%, 78%, and 32% in the downwind direction and nearly 100%, 42%, and 14% in the sidewind direction, respectively. As shown in Figure 12, the tower top velocity response is greatly increased when considering flexibility. Compared with the rigid foundation, the tower top velocities of Case 1, Case 2, and Case 3 increase by nearly 88%, 41%, and 14% in the downwind direction, and by nearly 55%, 23%, and 4% in the sidewind direction, respectively. From Figures 11 and 12, it can be seen that the tower top displacement and velocity response amplitude increase with decreasing base stiffness when considering base stiffness. Moreover, when the rotational stiffness gradually increases, the closer to the rigid foundation, the smaller the decrease of the top displacement and velocity response amplitude. Figure 12: Time course of tower top speed (**a**) Downwind (**b**) Sidewind direction.