Crack detection and location in a damaged beam vibrating under white noise

The aim of this paper is to inspect the vibrational response of a beam with an edge non-propagating crack by means of stochastic analysis, in order to detect the presence and the location of structural damage. Monte Carlo method is applied to evaluate in time domain the higher order statistics of the non-linear beam modelled by finite elements. The numerical application performed on a cantilever beam shows high sensitivity of the skewness coefficient of the rotational degrees of freedom to the non-linear behaviour of the system. By measurement of such coefficient both crack presence and position can be estimated. The proposed procedure allows treating beam with small crack even when other techniques fail to identify the crack presence.