A CONSISTENT CRACKED BAR VIBRATION THEORY

A consistent continuous cracked bar vibration theory is developed. The stress and displacement field about the crack was used to modify the stress and displacement field throughout the bar, and reduction to one spatial dimension was achieved by integrating the stress and displacement fields throughout the bar cross-sections so that the total displacement would be exact. The resulting linear differential equation with variable coefficients has the modified displacement field due to the crack imbedded in it. Any number of cracks can be introduced into the differential equation as modifications of the displacement field. A numerical solution and a first order perturbation solution are presented for the prediction of changes in longitudinal vibration natural frequencies of a fixed-free bar with a single open-edge transverse crack. To assess the validity of the assumptions made experiments on aluminium bars with fatigue cracks were performed. The analytical results correlate very closely with experimental results with better correlation than the local flexibility solution.