VIBRATION OF A CRACKED CANTILEVER BEAM

A continuous cracked bar vibration model is developed for the lateral vibration of a cracked Euler-Bernoulli cantilevered beam with an edge crack. The Hu-Washizu-Barr variational formulation was Ic sed to devel op the differential equation and the boundary conditions for the crack ed beam as an one-dimensional continuum. The crack was modelled as a c ontinuous flexibility using the displacement field in the vicinity of the crack found with fracture mechanics methods.The results of three i ndependent evaluations of the lowest natural frequency of lateral vibr ations of an aluminum cantilever beam with a single-edge crack are pre sented: the continuous cracked beam vibration model, the lumped crack model vibration analysis, and experimental results. Experimental resul ts fall very close to the values predicted by the continuous crack for mulation. Moreover, the continuous cracked beam theory agrees better w ith the experimental results than the lumped crack flexibility theory.