# Comparative Study on Vibration Characteristics of Biaxial Carbon/Glass Hybrid Wind Turbine Blades
## 5 Analysis of Blade Vibration Characteristics
### Vibration Characteristic Analysis  
Three types of blades were introduced into the transient structural wind field. Due to the maximum shape variation in the leading edge vertex of the airfoil at the blade tip, the displacement time variation curves in the X, Y, and \(Z\) directions were monitored, and the data were fitted to obtain the displacement time variation diagrams of the three types of blades, as shown in Figures 17-19. From the above figure, it can be seen that the curve tends to converge without divergence, and the displacement of the monitoring points gradually decreases and stabilizes in all directions. A1 takes longer to reach equilibrium compared to A2 and A3. From the X and Y directions, the equilibrium time for A2 and A3 is 3 s and the equilibrium time for A1 is 5 s. From the Z direction, the equilibrium time for A2 and A3 is 2.5 s, and the equilibrium time for A1 is 4 s.  
The total deformation of A2 and A3 intensifies during the first 3 s, and then shows periodic changes over time. A1 was affected by deformation in three directions in the first 4 s, resulting in an increase in total deformation. During the period of 4 to 5 s, the  
Figure 17: Maximum Displacement Curve of Blade in X-Direction. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mode** & **A\({}_{1}\)/(Hz)** & **A\({}_{2}\)/(Hz)** & **A\({}_{3}\)/(Hz)** \\ \hline
1 & 1.1622 & 1.5567 & 1.6993 \\
2 & 4.1850 & 5.6070 & 6.1202 \\
3 & 7.3824 & 9.8382 & 10.7360 \\
4 & 8.8847 & 11.7420 & 12.8360 \\
5 & 10.9560 & 14.3170 & 15.6960 \\
6 & 13.5870 & 17.9140 & 19.6110 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Numerical Table of Blade Modal Frequencies. direction showed periodic changes, while the X and Y directions remained unstable. After 5 s, the total deformation also showed periodic changes over time. Due to blade deformation being determined by three directions, the first cycle of vibration for A1, A2, and A3 blades is 0.3007 s, 0.2745 s, and 0.2584 s. The second cycle is 0.3492 s, 0.3020 s, and 0.3005 s. The third cycle is 0.3001 s, 0.2515 s, and 0.2330 s. The first cycle is 3.3260 Hz, 3.6430 Hz, and 3.8700 Hz. The second cycle is 2.8637 Hz, 3.3113 Hz, and 3.3278 Hz. The third cycle is 3.3320 Hz, 3.9760 Hz, and 4.2916 Hz. From the above data, it can be seen that under the action of a 10 m/s wind field, the vibration frequencies of the three types of blades are all higher than their corresponding first order frequency and lower than their corresponding second order frequency. However, the vibration frequency of A1 is similar to its second order natural frequency, so the amplitude difference between A1, A2, and A3 is relatively significant. From the figure, it can be seen that the deformation of the blades in the Z direction is large, and the deformation degree in the X and Y directions is relatively small. The performance of A2 and A3 is significantly better than that of A1, but the performance improvement between A2 and A3 is not significant. Figure 19: Maximum Displacement Curve of Blade in Z-Direction. Figure 18: Maximum Displacement Curve of Blade in Y-Direction. The vibration modes of the three types of blades are similar, and the main vibration form of the blades is waving. In order to better understand the deformation process of the blades, it is necessary to conduct stress analysis on the surface of the blades. Due to the symmetry of the wind turbine blades, take A3 blades with good performance for analysis, as shown in Figure 20.  
From the above figure, it can be seen from the spanwise axis that the stress on the blade is mainly concentrated along the 1/3 of the spanwise direction of the blade. This is due to the interaction between air and the blade, which exerts a force on the blade, resulting in stress and deformation of the blade. These deformations and stress distributions will in turn affect the flow state of air, thereby altering the characteristics of fluid motion.