https://marz.kau.edu.sa/Files/320/Researches/70650_43625.pdf

A crack is a type of damage that can lead to catastrophic failure when it grows in a structure. Thus prediction of cracks is a very important problem that has to be addressed. Some studies have been done on non-destructive techniques to identify cracks. Research interest in this area has been growing up quickly. In this study, a beam made of aluminum was used for detecting cracks using vibration characteristics. A method to identify cracks in an aluminum beam was derived from the equation of the dynamic stiffness. Rotational springs were used to model the cracks in the beam and the frequency response function was calculated using a spectral element model using Finite Element Model (FEM). This procedure provides a relationship between the frequency response and crack structure. The inverse problem was solved repetitively for crack positions and sizes using the Newton-Raphson method. The finite element model was formulated to simulate the results and to provide vibration overall amplitude measurements. The results showed at certain crack size, the amplitude increases with increasing crack depth for all crack positions. At crack size of 12 mm, an increase of 4.5% in amplitude was obtained for 60 mm crack position at a depth of 1.6 mm compared to its value at a depth of 0.16 mm. Similarly, it was 8.4% at crack size of 16 mm. Also, the amplitude varies inversely with position. Furthermore, at certain crack position, the amplitude increases with increasing crack depth for all crack sizes. At crack position of 75 mm, an increase of 12.6% in amplitude was obtained for 20 mm crack size at a depth of 1.6 mm compared to its value at a depth of 0.16 mm. Similarly, it was 5.4% at crack position of 150 mm. Finally, the amplitude increases as crack size increases at a certain depth.