Estimation of the severity of damage produced by a transverse crack

Abstract

This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.

Evaluating the severity of transverse cracks in beam-like structures by using an energy loss method

“…The crack detection methodology has also validated the results show that the location reports and the depth of the transverse cracks are successfully anticipated by using the methods presented in the paper [11,12]. This paper presents a numerical study designed to establish the dynamic response of cantilever beams with different transverse cracks, and different lengths to demonstrate that the use of the severity estimation method is reliable for detecting cracks by using the beam's natural frequencies.…”

“…In the study presented in paper [11] the authors develop an algorithm for evaluating transverse cracks in composite structures based on natural frequency changes due to cracks. Damage assessment is performed in two stages; first, the location of the crack is found and then an assessment of its severity is performed.…”

“… the curvature of the normalized modal form, having values between -1 and 1. The transverse crack severity is determined with the model presented in paper [11,12], using the following Equation ( 2):…”

“…Because at the fixed end the deformation manifests just on one side of the crack, the severity achieved here is smaller as expected. To this aim, we simulate cracks at different positions near the fixed end and find the theoretical severity from the linear regression curve, as presented in the paper [11].…”