Multiple crack identification in Euler beams by means of B-spline wavelet

In this paper, an effective method for identification of multiple cracks is presented based on discrete wavelet transform in a cracked beam. First, a compactly supported semi-orthogonal B-spline wavelet on interval (BSWI) is employed to construct Euler beam-bending element for free vibration analysis of cracked beams. Next, the construction of general order one-dimensional B-spline wavelets is presented and applied for damage identification in a cantilever beam modeled by wavelet-based elements. Also, principles of an appropriate wavelet selection are presented. Natural vibration modes of a cantilever beam with three cracks are analyzed using one-dimensional fourth-order B-spline wavelet. The results illustrate that BSWI elements can be used in determining the un-cracked and cracked beam natural frequencies with a high accuracy and efficiency. Moreover, the applicability of the presented method in crack identification is studied by numerical examples under several situations, such as in the presence of random noises, and the efficiency of B-spline wavelets in damage prognosis is compared with other types of wavelet functions. The obtained results show the effectiveness of B-spline wavelets in modeling of the damaged beam and identifying multiple crack locations in a free baseline scheme.

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