# Microcrack Detection Using Spectral Response Data Alone
## 3 Crack Inspection with Simple Specim
Those responses were well matched with the experimental modal test results in Table 1.  
The coherence functions were calculated using the FRFs in both specimens, as shown in Figures 9a, 10a and 11a, respectively. All six coherence functions were sensitive to two frequencies: resonance frequency at ~1090 Hz and sideband frequency at 1150 Hz. These results verified the previous study of microcrack detection. The crack indicator at the sideband frequency decreased rapidly regardless of the measurement location, and the coherence values near the resonance frequency varied according to the measurement location. The indicating frequency at the minimum coherence values was lower at #1,  
Figure 8: Acceleration response of two specimens: (**a**) X-Y plane (front), (**b**) X-Y plane (rear), and (**c**) X-Z plane. #2 (front face in X-Y plane) than #3, #4 (rear face in X-Y plane) near 1090 Hz. In case of X-Z plane, the sensitivity near the resonance frequency at 1090 Hz was not remarkable and additional sensitive frequency could be found at 1145 Hz because the X-Z plane was out-of-plane of the bending mode shape at 1090 Hz. Therefore, the suitable frequency for microcrack detection is the sideband frequency rather that the resonance frequency as in the FRF case. The same coherence function was used with response data alone for crack detection, and the results for the cracked and the uncracked face (see Figure 3) are shown in Figure 10. Crack indicator in X-Y plane (rear): (**a**) frequency response function and (**b**) acceleration only. Figure 11: Crack indicator in X-Z plane: (**a**) frequency response function and (**b**) acceleration only. Figure 9: Crack indicator in X-Y plane (front): (**a**) frequency response function and (**b**) acceleration only. Figures 9b, 10b and 11b, respectively. For the X-Y plane (front), locations #1 and #2 were both very sensitive to the sideband frequency, whereas the sensitivity to the resonance frequency differed with the measurement position. For the X-Y plane (rear), locations #3 and #4 both showed similar sensitivity to the resonance frequency; by contrast, location #3 (near the crack) showed high sensitivity to the sideband frequency whereas location #4 did not. The coherence function in X-Z plane was not similar to X-Y plane; the most sensitive frequency was at ~1121 Hz and the least sensitive frequencies were 1090 Hz and 1145 Hz. The difference results in X-Z plane were caused by the orthogonality between two resonance frequencies in cracked specimen. So, the sensitivity in microcrack detection was dependent on the measurement position, and the mode shape of target structure will be critical factor to select the suitable position of sensor location. The crack indicator obtained using the FRF was relatively consistent for all measurement locations and seemed less dependent on the distance from the crack position if the measurement location was in-plane with the critical mode shape of cracked specimen. The only limitation was the sideband frequency at #4. An inspection methodology that is independent of the crack position will be beneficial because it is difficult to determine the exact location of a crack in a target structure in advance. In case of out-of-plane measurement, the sensitivity of crack detection was partially applicable at sideband frequency and not valid for the resonance frequency. As shown in Figures 9a, 10a and 11a, this advantage holds even for crack inspection using the response data alone, although the crack indicator at each measurement location showed a different coherence value in the resonance frequency zone when the measurement position belonged to in-plane mode with the critical mode shape. The sideband frequency decreased rapidly except at measurement location #4, and these results were similar to the FRF cases.