MODELING AND VIBRATION ANALYSIS OF A CANTILEVER COMPOSITE BEAM WITH A TRANSVERSE OPEN CRACK

Eigenfrequencies of a cantilever beam, made from graphite-fiber reinforced polyimide, with a transverse on-edge non-propagating open crack are investigated. Two models of the beam are presented. In the first model the crack is modelled by a massless substitute spring. The flexibility of the spring is calculated on the basis of fracture mechanics and the Castigliano theorem. The second model is based on the finite element method (FEM). The undamaged parts of the beam are modelled by beam finite elements with three nodes and three degrees of freedom at the node. The damaged part of the beam is replaced by the cracked beam finite element with degrees of freedom identical to those of the non-cracked one. The effects of various parameters (the crack location, the crack depth, the volume fraction of fibers and the fibers' orientation) upon the changes of the natural frequencies of the beam are studied. Computation results indicate that the decrease of the natural frequencies not only depends on the position of the crack and its depth, as in the case of isotropic material, but also that these changes strongly depend on the volume fraction of the fibers and the angle of the fibers of the composite material.