Crack Identification In Beams Using Wavelet Analysis

Cracks present a serious threat to the Performance of structures since most of the structural failures are due to material fatigue. For this reason,methods allowing early detection of cracks have been the subject of intensive investigation,which help management the structure and reducing the cost for refinement. As we know defects in the structure will cause some changes in The dynamic character,such as frequency,mode shape and damp,which can be used to indicate the state of the structure. So a lot of researchers devote their attention to detect the damage in the structure and develop many methods based on the dynamic character of structure. In recent,the applying of wavelet time-frequency get the interesting of the researchers which was considered as the method can detect both local damage and the whole character of the structure. The correlative theory and technology are developing continuously.For studying the low in structural damages identification by using wavelet method, both the first mode and the deflection function has been applied to wavelet analysis, the location of the crack can detected by the sudden change in the spatial variation of the transformed response, and the intensity factor can be described by the Lipschitz exponent. At the same time, the selecting of both the wavelet and the mode shape, the influence of the crack location, the numbers of crack, the section size, the length of the beam and the material of the structures to Lipschitz exponent were also discussed.As result, some conclusion could be drawn. In the aspect of wavelet selecting, the Gaus2 wavelet is better than Gaus3 and Gaus4 both in the detection of the location of the cracks and the extent of the cracks; in the aspect of selecting mode shape, the key is to avoid that the wavelet coefficients of the vibration mode function in the location of the crack is too small or just 0. It would make the maximum peak caused by the cracks too small or even disappear. Considering the first modes is easier to get and less affected by noise compare with high modes, author think that we can choose the first mode at first, and then choose the higher modes if necessary. In regard to Lipschitz exponent, it only decide by the depth of the crack, and the influence of the crack location, the numbers of crack, the section size, the length of the beam and the material of the structures are little which can be ignored; In the aspect of damage detecting under static load, the magnitude of Lipschitz between dynamic analysis and static analysis are very close, and the magnitude and the position of the static load have little effect on the Lipschitz exponent which can be ignored too.The validity of the wavelet method to identify beam structural damage has been proved. Although this thesis mainly focus on the beam structure, the method presented here may also available for other structure, such as frame structure, arch structure, pipe structure etc.