Detection of Arbitrary Number of New Cracks Appearing in a Beam with Pre-existing Cracks

Abstract

This paper is concerned with development of a scheme to detect fresh crack(s) in a beam with pre-existing crack(s). The cracks have been modeled by rotational springs. Relationship has been derived through energy method involving natural frequency, mode shape of uncracked beam, crack location(s) and size(s). Natural frequencies of the beam in the two states, before and after development of fresh crack(s), are the basis for the detection. Case studies have been done with uniform and stepped long beam(s). For the case studies, frequencies data have been generated through finite element method. Cantilever beams are examined with crack sizes in the range 15–50 % of section depth. Crack locations are varied within 92 % of the span from the fixed end. In the case of two pre-existing cracks and one fresh crack, the maximum errors in predicting location and size are 1.98 and 4 % respectively. In the case of one pre-existing crack and two fresh cracks the same errors are 6.99 and 8.33 % respectively. In the case of two-stepped cantilever beam with one initial crack and one fresh crack, the errors are 15 and 5.26 % respectively. The accuracy of prediction is thus very encouraging. One advantage of the proposed method is that it gives directly the location and size of the new crack(s).