Study on crack detection of beam using harmonic responses

In this paper, a torsional spring is adopted to simulate a crack in a cantilever beam, approximated dispilacement and slope modes of the cracked cantilever beam are obtained. Its displacement and slope responses under single harmonic excitation and zero initial conditions are obtained by using approximated modes. It is shown that slope responses of the cracked cantilever beam has stepping type change at crack location and its partial derivative with respect to x has peak type change. From these dynamiic characteristics of cracked cantilever beam, a crack detection criterion using slope responses under harmonic excitation is proposed. Moreover, numerical examples and experimental results show that the crack location and depth can be identified by proposed criterion.