Abstract:

In this paper, the dynamic behaviour of a beam with cracks is studied. At firsts the element stiffness matrix of the beam with cracks is derived from an integration of stress in tensity factors and then a finite element model of cracked beam is established. Applying FEM to a cantilever beam with an edge-crack,the eigenfrequencies are determined for different crack lengths and crack positions. Results show an excellent agreement in comparison with the experimental ones, A simple and direct method to determine the crack position is proposed based on the discussion of the relationship between the crack and the eigencoupie. In principle, the suggested method may be extended to complex structures, if the stress intensity factors of crack are known.

Key words: dynamic behaviour, cantilever beam, crack, finite element method （FEM）, eigencoupie