A CONSISTENT CRACKED BAR VIBRATION THEORY

A consistent continuous cracked bar vibration theory is developed. The stress and displacement held about the crack was used to modify the s tress and displacement held throughout the bar, and reduction to one s patial dimension was achieved by integrating the stress and displaceme nt fields throughout the bar cross-sections so that the total displace ment would be exact. The resulting linear differential equation with v ariable coefficients has the modified displacement field due to the cr ack imbedded in it. Any number of cracks can be introduced into the di fferential equation as modifications of the displacement field. A nume rical solution and a first order perturbation solution are presented f or the prediction of changes in longitudinal vibration natural frequen cies of a fixed-free bar with a single open-edge transverse crack. To assess the validity of the assumptions made experiments on aluminum ba rs with fatigue cracks were performed. The analytical results correlat e very closely with experimental results with better correlation than the local flexibility solution. (C) 1997 Academic Press Limited.