introducing a new crack disturbance function for transverse vibration analysis of a cracked beam

in this paper, in order to analyze the transverse vibration of a uniform bernoulli-euler beam containing one single edge crack, a new continuous model is proposed for the cracked section. to this end, by using the fracture mechanics, the crack is modeled as a continuous disturbance in the stress and strain fields. by applying the hamilton’s principle, the equation of motion and the corresponding boundary conditions of the system are derived. the resulting equation is solved by the galerkin method, and the natural frequencies and mode shapes are obtained. in order to consider the opening and closing effects of the crack, the stiffness at the crack location is modeled by a bilinear function. the results show that the changes in vibration frequencies for a breathing crack are smaller than ones caused by an open crack. the results have been validated by the experimental and theoretical data reported in the previous studies. there is a good agreement between the results obtained through the proposed method and those obtained from the reported experimental data. this agreement shows that present model is more accurate than the previous ones, and it can predict the vibration behavior of beams more precisely.