A Continuous Model for Forced Vibration Analysis of a Cracked Beam

In this paper the equation of motion and corresponding boundary conditions has been developed for forced bending vibration analysis of a beam with an open edge crack. A uniform Euler-Bernoulli beam and the Hamilton principle have been used in this research. The natural frequencies and the forced response of this beam have been obtained using the new developed model in conjunction with the Galerkin projection method. The crack has been modeled as a continuous disturbance function in displacement filed which could be obtained from fracture mechanics. The results show that the first natural frequency will reduce when the crack depth ratio increases. Also the rate of this reduction depends on the position of the crack. In addition it can be seen that the FRF amplitude for a cracked beam is more than a similar uncracked beam before the first natural frequency. But just after the first natural frequency the amplitude of vibration of a healthy beam is more than a cracked beam. There is an excellent agreement between the theoretical results and those obtained by the finite element method.