Identification of Cracks in Functionally Graded Material Beams Using the H-Version of Finite Element Method

In this article, we analyze the effect of transverse cracks on natural frequencies a Euler-Bernoulli functional gradient beam. The studied beam was discretized into finite elements and global matrices motion equation are determined by applying Lagrange to kinetic deformation energies. material properties considered vary in directions thickness, gradation is described power-law distribution, stiffness cracked element based reduction cross-section. numerical results obtained compared with those available previous study. Finally, case studies were carried out analyses influence power law index, depth opposition crack for different boundary conditions; these demonstrate advantage FGM over purely metal