Enriched Finite Element for Modal Analysis of Cracked Plates

In this Paper, the extended finite element method (X-FEM) is adopted then numerically implemented for the analysis of the vibratory behaviour of isotropic homogeneous plates having a through crack located at various positions. The mathematical model includes the effects of rotary inertia and transverse shear deformation. Various applications including plates with central crack and edge crack are considered. The results obtained in terms of Eigen frequencies with respect to the crack length show a net decrease in the frequency with an increase in the crack length. This physical effect is more pronounced for particular vibratory modes as it also depends on the nature of the crack. Overall, the present results compare well with the experimental, analytical, and numerical results consulted in the literature.