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

Abstract

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