## 4 Dynamic Vibration Test of Primary Mirror Assembly  
To accurately evaluate the dynamic response of the primary mirror assembly in an external dynamic environment, the accuracy of relevant theoretical and simulation analyses can be verified through dynamic tests. The diameter of the primary mirror is \(\phi\)740 mm, its thickness is 150 mm, and its weight is 47 kg (including the primary mirror, the invar insert, the flexural mount, the primary mirror substrate, connecting screws, and the related components of the material and structural form), which is completely consistent with the project design. The primary mirror assembly is connected to the shaker through an aluminum vibrating fixture, whose size is 1000 mm \(\times\) 1000 mm \(\times\) 45 mm. The dynamic test is performed at the environmental test station. The mirror assembly and the vibration fixture are installed on an LMS-V964 9-ton electromagnetic shaker (BK Company, Copenhagen, Denmark). During the test, the mirror assembly and the vibration fixture are connected by steel screws. The connection relationship remains unchanged during the transfer operation. The shaker applies excitation to the mirror assembly and then performs sine frequency sweep, sinusoidal vibration, and random vibration tests on the reflector assembly in sequence. The vibration test process is shown in Figure 14.  
During the dynamic test, an acceleration sensor is required for measurement, and the sensor bonding position is shown in Figure 15. The 1# sensor is a three-axis acceleration sensor, and its three orthogonal measurement directions are consistent with the coordinate axis directions in Figure 15; 2#-8# are all single-axis acceleration sensors. The 2# sensor is glued to the side of the aluminum triangle plate, while the other sensors are glued to the upper surface of the main mirror. Figure 15 shows the bonding position and the measurement direction of sensors 2#-8# (where the measurement direction of 5# and 8# is parallel to the \(Z\) direction, that is, the vertical mirror direction). The acceleration sensors cannot be removed until the vibration test in the \(X\), \(Y\), and \(Z\) directions is completed. The test site of the main mirror assembly is shown in Figure 16. \begin{table}
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Table 1: Comparison of calculation efficiency between FEA and state space. Figure 14: Flowchart of the mechanical vibration test. A frequency sweep test is performed on the reflector in the range of 10-2000 Hz. As shown in Figure 17, errors occur between the theoretical model and the actual structure. However, the frequency response curve and the peak response are the same. The first resonance peak is selected, that is, the moving motion state of the excitation extension in the direction of X/Y/Z, which is the first-order natural frequency. The maximum test value of the first-order natural frequency of the mirror assembly in the X direction is 213.702. Figure 16: Vibration test of the primary mirror assembly. Figure 15: Sensor bonding position. Figure 17: Results of the sine sweep test: (**a**) X direction sine sweep test; Fx = 213.702 Hz. (**b**) Y direction sine sweep test; Fy = 220.444 Hz. (**c**) Z direction sine sweep test; Fz = 298.413 Hz. Hz, the natural frequency of the simulation analysis is 228.95 Hz, and the relative error is 6.7%. The maximum test value of the first-order natural frequency of the mirror assembly in the Y direction is 220.444 Hz, the natural frequency of the simulation analysis is 228.95 Hz, and the relative error is 3.7%. The maximum test value of the first-order natural frequency of the mirror assembly in the Z direction is 298.413 Hz, the natural frequency of the simulation analysis is 318.42 Hz, and the relative error is 6.3%. The trend in the frequency response curve of the simulation analysis is roughly the same as that of the frequency sweep test.