Crack intensity closed form solutions by frequency measurements on damaged beams

Based on Sherman and Morrison formula, the present work proposes an explicit formulation of the natural frequencies of multi-cracked beams in terms of crack intensity to avoid solution of the non linear frequency equation. Among the problems that can be tackled with an explicit formulation of the multi-cracked beam natural frequencies, in this work the crack intensity identification problem by frequency measurements is addressed. Precisely, closed form solutions of the crack intensity in terms of frequency measurements are proposed and employed for the identification in single and multi-cracked beams.