In this article, the process of identifying an open edge crack in functionally graded material (FGM) beams is investigated using frequency response of the structure. For this purpose, a finite element model of the cracked beam is constructed to predict the vibration characteristics of the beam. Considering mixed-mode I and II fracture conditions, the crack is simulated as a local flexibility and the cracked element stiffness is determined from the fracture mechanics. The equation of motion for free vibration of a cracked FGM cantilever is solved and the effects of crack location and crack size on its natural frequencies are investigated. The results obtained by the present frequency analysis are indicated to be in a good agreement with ones from the literature. In the end, by plotting the frequency contours corresponding to the first three modes and choosing the intersection of the contour lines, the crack parameters (crack size and location) are determined. The numerical results indicate that the present approach is of high crack quantification efficiency and is able to be utilized in structural health monitoring (SHM).
