Lateral Vibration of a Consistent Continuous Beam With a Crack

A continuous cracked beam vibration theory is developed for the lateral vibration of cracked Euler-Bernoulli beams with single-edge or double-edge cracks. The Hu-Washizu-Barr variational formulation was used to develop the differential equation and the boundary conditions of the cracked beam as an one-dimensional continuum. The displacement field about the crack was used to modify the stress and displacement field throughout the bar. The crack was modelled as a continuous flexibility using the displacement field in the vicinity of the crack, found with fracture mechanics methods. The results of three independent evaluations of the lowest natural frequency of lateral vibrations for beams with a single-edge crack are presented: the continuous cracked beam vibration theory developed here, the lumped crack beam vibration analysis, and an asymptotic solution. Experimental results from aluminum beams with fatigue cracks are very close to the values predicted. A steel beam with a double-edge crack was also investigated with the above mentioned methods, and results compared well with experimental data.