Detection of longitudinal cracks in long and short beams using changes in natural frequencies

Abstract

Abstract Vibration based structural health monitoring (SHM) has received considerable attention mainly due to its advantages over the conventional non-destructive methods. Crack parallel to length direction may come up in beams of layered isotropic materials or composites during fabrication and/or in service. This paper is an attempt to analyze the natural vibration of monolithic beams with longitudinal cracks for developing a method for its detection. An analytical method has been developed to address both forward problem of determination of natural frequencies knowing the beam and crack geometry details as well as inverse problem of detection of crack with the knowledge of changes in the beam natural frequencies. Both long (Euler–Bernoulli) and short (Timoshenko) beams have been examined numerically. For modeling a crack located at the free end of a cantilever, the beam is divided into three segments. For an internal crack located away from the free end of the beam, it is split into four segments. In both cases, two of the segments take care of beam portions above and below the crack. The cracked segments are constrained to have the same transverse displacements but different axial deformations. The modeling shows good accuracy for both the forward and inverse problems. The results thus show encouraging possibility of exploitation of the proposed method for crack detection in practice.