A NEW APPROACH FOR VIBRATION ANALYSIS OF A CRACKED BEAM

In this paper the equations of motion and corresponding boundary conditions for bending vibration of a beam with an open edge crack has been developed by implementing the Hamilton principle. A uniform Euler-Bernoulli beam has been used in this research. The natural frequencies of this beam have been calculated using the new developed model in conjunction with the Galerkin projection method. The crack has been modeled as a continuous disturbance function in displacement field which could be obtained from fracture mechanics. The results show that the natural frequencies of a cracked beam reduce by increasing crack depth. There is an excellent agreenlent between the theoretically calculated natural frequencies and those obtained using the finite element method.