Crack detection of a beam-like bridge using 3D mode shapes

Abstract

In this paper, mode shapes of a 3D cracked beam with a rectangular cross section are analyzed for crack detection. The influence of coupling mechanism between horizontal and vertical bending vibrations due to the 3D crack model on the mode shapes is investigated. Due to the coupling mechanism the mode shapes of a beam are twisted in space. They change from plane curves to space curves. This phenomenon can be used for crack detection. The existence of the crack can be detected when the mode shapes are space curves. Also, the mode shapes of a cracked beam bridge have distortions or sharp changes at the crack position. Therefore, the position of the crack can be determined as a position at which the mode shapes exhibit such distortions or sharp changes. Moreover, using the mode shapes in 3D crack model, a crack with depth as small as 1% of the beam height can be detected, while in previous studies using 2D crack model, distortions in the mode shapes caused by a small crack cannot be detected. These results are new and can be used for crack detection of a beam bridge. The stiffness matrix of a 3D cracked element obtained from fracture mechanics is presented and numerical simulations are provided in this paper.