Crack identification of functionally graded beams using continuous wavelet transform

This paper proposes a new damage index for the crack identification of beams made of functionally graded materials (FGMs) by using the wavelet analysis. The damage index is defined based on the position of the wavelet coefficient modulus maxima in the scale space. The crack is assumed to be an open edge crack and is modeled by a massless rotational spring. It is assumed that the material properties follow exponential distributions along the beam thickness direction. The Timoshenko beam theory is employed to derive the governing equations which are solved analytically to obtain the frequency and mode shape of cracked FGM beams. Then, we apply the continuous wavelet transform (CWT) to the mode shapes of the cracked FGM beams. The locations of the cracks are determined from the sudden changes in the spatial variation of the damage index. An intensity factor, which relates to the size of the crack and the coefficient of the wavelet transform, is employed to estimate the crack depth. The effects of the crack size, the crack location and the Young's modulus ratio on the crack depth detection are investigated.