Fault detection in a cantilever beam based on measurements of natural frequencies

Based on Bernoulli-Euler theories of beam vibration, the dynamics of a cracked cantilever beam is treated for bending vibrations. The local effect of "softening" at the crack location can be simulated by an equivalent spring connecting the two segments of the beam. Analysis of this model results in characteristic equations, which relate the natural frequencies to crack characteristics. Furthermore, from this expression, one accurate crack identification method is developed, which only require the variation of the first several natural frequencies due to the crack, with no other information needed concerning the beam geometry or material and the crack depth or shape. The proposed approach is verified by simulated damage in the form of one-side cracks in a cantilever beam.