Structural Crack Parameters Identification Based On Wavelet Element

The appearance of crack and its extension under stress effect usually cause structural damage and lead to catastrophic security accidents, so the early identification of cracks to guarantee the safety of structure is significant in engineering practice. Vibration diagnosis is widely used in engineering fault diagnosis for its convenience and wavelet finite element has high computation precision in singularity problems for its multiresolution analysis, so the parameter identification based on wavelet finite element of a crack in the cantilever beam is mainly discussed in this thesis.The derivatives of sacling functions and connection coefficients of Daubechies and Coiflet wavelets are calculated. The multiresolution of wavelet is brought in finite element by using scaling function as an interpolation function, then Daubechies wavelet based beam element and Coiflet wavelet based beam element are constructed, and the numerical examples show their high accuracy in beam bending problems and vibration problems.The wavelet finite element analysis of the transverse vibration of a cracked beam is developed based on the massless rotational spring model, and the natural frequencies are solved, whose accordance with the analytical results shows the accuracy of wavelet finite element. By providing the first three natural frequencies as an input, graphs of contour lines are plotted, and the intersection of the three curves predicts the possible crack location and size. The simulation example verifies the feasibility of wavelet finite element method in crack detection.The experiment of the beam vibration is designed. The frequencies of the cantilever beam are measured by modal testing, and then the crack parameters are identified by the wavelet element model. The result shows the method is very effective.