Analytical and experimental crack identification of beam structures in air or in fluid

Abstract

In this paper a new method for crack identification in beams is presented. The transverse surface crack is considered to remain always open. Using this method the crack location and depth can be determined. The method is based on the basic observation that the eigenmodes of any cracked structure are different from those of the uncracked one. The differences are due to the slope discontinuity of the vibration eigenmodes at the crack location. The basic idea in this paper is to correlate the mode differences with the crack depth and location. These correlated differences are chosen to be (a) the ratio of two amplitude measurements in two positions and (b) the distance of the node of the vibrating mode from the left end, while the structure is vibrating under harmonic excitation in resonant condition. The analytical results presented here are also experimentally proven. In a free-free beam the two first eigenmodes are measured and the node distance of the uncracked and the cracked beam are used in pre-plotted diagrams to verify the crack location and depth. Here, it is also theoretically proved that the above results for the beam are the same in both the air and the water. This is valid irrespective of whether the damping effect is taken into consideration or not.