Free Vibration Analysis of a Beam with Multiple Cracks

The crack is modeled as an equivalent massless rotational spring in this paper and the recursive method is employed to investigate the free vibrations of the Euler-Bernoulli beams with an arbitrary number of cracks under different boundary conditions. First, by using the continuity condition equations at crack locations, we can get the relationship of undermined coefficients of the characteristic equation between the adjacent two beams. Then the dimensionless natural frequencies can be obtained by boundary conditions, and the mode shapes also can be obtained easily. The accurate and effective of the proposed method are verified by comparing with the methods presented in reference. Then the effect of the location and depth of the cracks on the natural frequencies of the beam is studied.