THE DYNAMIC BEHAVIOR AND CRACK DETECTION OF A BEAM WITH A CRACK

In this paper, an element stiffness matrix of a beam with a crack is first derived from an integration of stress intensity factors, and then a finite element model of a cracked beam is established. This model is applied to a cantilever beam with an edge-crack, and the eigenfrequencies are determined for different crack lengths and locations. Results show good agreement with experimental data. In order to consider the effect of crack closure, the modal parameters are identified by means of an identification technique in the time domain. Computation results show that the difference of the displacement response between the beam and the cracked beam, due to the effect of crack closure, is reduced; the eigenfrequency is significantly affected by the mean value of the excitation force. Finally, a simple and direct method for determining the crack position, based on a discussion of the relationship between the crack and the eigencouple (eigenvalue and eigenvector) of the beam, is proposed. In principle, the method suggested may be extended to complex structures with various cracks, if their stress intensity factors are known. © 1990.