Crack intensity closed form solutions by frequency measurements on damaged beams

The present work proposes an explicit formulation of the natural frequencies of multi-cracked beams in terms of crack intensity. Use of the Sherman and Morrison formula, calibrated on reference frequency values of multi-cracked beams over a specified range of crack intensity is made. Evaluation of the reference frequencies of multi-cracked beams is obtained by means of a generalised function approach which does not require enforcement of continuity conditions at the cracked cross sections. The proposed explicit expressions of natural frequencies are then straightforwardly applied to infer closed form expressions of the crack intensity in terms of frequency measurements. The latter closed form expressions are employed for the identification of the crack intensity in single and multi-cracked beams.