ONE-DIMENSIONAL THEORY OF CRACKED BERNOULLI-EULER BEAMS

The differential equation and associated boundary conditions for a nominally uniform Bernoulli-Euler beam containing one or more pairs of symmetric cracks are derived. The reduction to one spatial dimension is achieved using integrations over the cross-section after plausible stress, strain, displacement and momentum fields are chosen. In particular the perturbation in the stresses induced by the crack is incorporated through a local function which assumes an exponential decay with distance from the crack and which includes a parameter which can be evaluated by experimental tests. Some experiments on beams containing cuts to simulate cracks are briefly described and the change in the first natural frequency with crack depth is matched closely by the theoretical predictions.