Simulation and detection of small crack-like surface flaws and slots in simply-supported beams using curvature analysis of analytical and numerical modal displacement data

Abstract

Purpose The purpose of this paper is to employ analytical and numerical techniques to generate modal displacement data of damaged beams containing very small crack-like surface flaws or slots and to use the data in the development of damage detection methodology. The detection method involves the use of double differentiation of the modal data for identification of the flaw location and magnitude. Design/methodology/approach The modal displacements of damaged beams are simulated analytically using the Bernoulli-Euler theory and numerically using the finite element method. The principle used in the analytical approach is based on changes in the transverse displacement due to the localized reduction of the flexural rigidity of the beam. Curvature analysis is employed to identify and locate the structural flaws from the modal data. The curvature mode shapes are calculated using a central difference approximation. The effects of random noise on the detectability of the structural flaws are also computed. Findings The analytical approach is much more robust in simulating modal displacement data for beams with crack-like surface flaws or slots than the finite element analysis (FEA) approach especially for crack-like surface flaws or slots of very small depths. The structural flaws are detectable in the presence of random noise of up to 5 per cent. Originality/value Simulating the effects of small crack-like surface flaws is important because it is essential to develop techniques to detect cracks at an early stage of their development. The FEA approach can only simulate the effects of crack-like surface flaws or slots with depth ratio greater than 10 per cent. On the other hand, the analytical approach using the Bernoulli-Euler theory can simulate the effects of crack-like surface flaws or slots with depth ratio as small as 2 per cent.