## 3 Case Study  
### Modal Test Verification of Low Frequency Flexible Solar Wing  
In order to preliminarily verify the proposed ultralow-frequency flexible structure modal test method based on the Digital Image Correlation method, the ultralow-frequency flexible solar wing array in the unfolded state is taken as the test object. The flexible solar wing is composed of two solar wings with exactly the same size. The material properties are shown in Table 1. The flexible solar wing array is suspended by a suspension rope, and its size and installation are shown in Figure 4:  
\begin{table}
\begin{tabular}{c c c c} \hline
**Density/(kg/m3)** & **Elastic Modulus/(GPa)** & **Poisson’s Ratio** & **Thickness/(mm)** \\ \hline
2700 & 70 & 0.33 & 5 \\ \hline \end{tabular}
\end{table}
Table 1: Solar wing material properties.  
Figure 4: Dimensional drawing of ultralow-frequency flexible solar wing array with the speckle pasting position and the camera placement position.  
Figure 3: Flow chart of modal identification of ultralow-frequency flexible structure.  
The equipment used in the test is as follows:  
1. DHDAS dynamic signal acquisition and analysis system, the sampling frequency is 25.6 Hz, the sampling point is 512, and the frequency domain resolution is 0.05 Hz;
2. A piezoelectric acceleration sensor, model CA-YD-107 sensitivity 2.73 pC/ms\({}^{-2}\);
3. Force hammer, model CL-YD-303, sensitivity 3.99 pC/N;
4. Two SONY FDR-AX40 cameras, the camera frame number is 20 fps, that is, the sampling frequency is 20 Hz;  
Paste the speckle patches on the side of the solar wing mechanism, a total of 7, numbered from D1 to D7, and the acceleration sensor A1 is arranged at the spot of D2 which are shown in Figure 4.  
The test adopts multi-point excitation and single-point measurement, and is carried out by the hammering method. Seven points such as D1-D7 are selected as excitation points, and each measurement point is hammered in turn on the back of the solar wing mechanism, and the structure response is recorded by the DHDAS dynamic signal acquisition and analysis system. At the same time, the image of the solar wing mechanism is collected through the camera, and the displacement response data of the measuring point in 0-20 s is calculated by the DIC method, and the modal parameters of the solar wing mechanism are obtained through modal identification. The traditional contact measurement results are compared with the DIC test results to verify the feasibility and accuracy of the proposed ultralow-frequency flexible structure modal test based on the Digital Image Correlation method.  
Figure 5 is the amplitude-frequency diagram of DHDAS and DIC method. Table 2 shows the comparison between DHDAS system identification frequency and DIC identification frequency. From the comparison results, it can be seen that the DHDAS system identification frequency and the DIC method identification frequency error are small, the first order frequency error is 2.80%, and the second order frequency error is \(-\)1.30%, indicating that the effective optical test data can be used to obtain a higher-precision structure. The modal frequency results verify the feasibility and accuracy of the proposed ultralow-frequency flexible structure modal test method based on the DIC method.  
Figure 5: Frequency response function diagram.  
The results of the DHDAS system's identification and the DIC method of identification of the vibration shape are shown in Figure 6 below:  
According to the theory of modal confidence, the MAC value of mode shape of DHDAS identification is compared with that of the mode shape of DIC method identification. It can be seen from Figure 7 that the modal shape obtained based on the DIC method is compared with the modal shape obtained by the DHDAS system. The matching degree is high, and the MAC value contrast is greater than 0.9, which verifies the feasibility of the low-frequency flexible structure experimental modal test method based on the DIC method.