## 2 Measurement of Damping Parameters
### Damping Parameter Identification Test  
In this section, the damping ratio of Fe-12 Cr-3 Al damping alloy materials is determined using the half-power bandwidth method with the sweep frequency testing on a shaker. The specific test process can be summarised as follows. First, the modal frequencies of the specimen are tested in a broad frequency band using the hammering method, and then the test specimen with Fe-12 Cr-3 Al damping alloy materials is excited with a shaker in the form of a base excitation with a constant amplitude sweep frequency excitation. The  
Figure 2: The principle of the half-power bandwidth method: (**a**) half-power bandwidth and (**b**) 3 dB bandwidth. sweep frequency band can be selected as 75-125% of the modal frequency of the first order with a proper sweeping speed (usually less than 1 Hz/s). The response signal is acquired with a lightweight acceleration sensor mounted on the specimen. The acquired time-domain raw data is processed with the short-time Fourier transform (STFT) to obtain the frequency response map under the sweep-frequency excitation. Finally, the half-power bandwidth method is used to identify the damping parameter. Exciting the specimen with sweep-frequency signals containing different orders of nature frequency, then the damping ratio of each order can be obtained. In addition, the PCB 086C01 modal force hammer was used for modal testing, high power amplifier 9363-EM type electromagnetic shaker was used for sweep frequency excitation, a BK-4517 acceleration sensor was used for data acquisition, and LMS Test. lab vibration analysis software (The version number of the software is: Simcenter Testlab 2021.1) was used for data analysis. The shaker and the test system are shown in Figure 3.  
The specimens for this test are depicted in Figure 4a. The specimens are categorised into two groups, one group consisting of Fe-12 Cr-3 Al alloy material and the other consisting of Q235 carbon steel material, with each group comprising three specimens. The specimens are identical in appearance, and the specific geometric dimensions of the specimens are illustrated in Figure 4b, with the units being millimetres. The modal test was conducted by the hammering method to obtain the modal frequency of Fe-12 Cr-3 Al alloy specimens in a wide frequency band from 0 to 2000 Hz. The specimen is fixed in the cantilevered position on the fixture with a clamping zone of 30 mm. Figure 4: The test specimens: (**a**) Specimens drawing and (**b**) Schematic diagram of geometric dimensions. Figure 3: The shaker and test system. The arrangement of the force hammer and accelerometer measurement points is shown in Figure 5. The spectrum obtained by the hammering method is shown in Figure 6.  
The spectrum shows that the force hammer test yields two orders of nature frequency of the damping alloy specimen in the frequency range of 0-2000 Hz, namely 168.8 Hz and 1194 Hz, respectively. On the basis of the two orders of modal frequencies obtained from the hammering method, sweep frequency excitation tests were performed in the range of 75-125% of the two orders of modal frequencies. The damping ratio corresponding to each order of modal frequency of the Fe-12 Cr-3 Al specimen was determined using the half-power bandwidth method. Two measurement points were set up in the shaker sweep excitation test, including cantilever beam outer measurement point 1 and cantilever beam root measurement point 2, and the arrangement of the test points is shown in Figure 7. In addition, cantilever beam outer measurement point 1 is located on one side of the free end of the specimen, with a distance of 5 mm from both end faces, while cantilever beam root measurement point 2 is situated on the central axis of the specimen, at a distance of 10 mm from the clamping end face. Figure 5: The knocking point and measuring point of the acceleration sensor. Figure 6: The spectrum of damping test.