Crack Detection through the Change in the Normalized Frequency Shape

Abstract

The objective of this work is to use natural frequencies for the localization and quantification of cracks in beams. First, to study the effect of the crack on natural frequencies, a finite element model of Euler–Bernoulli is presented. Concerning the damaged element, the stiffness matrix is calculated by the theory of fracture mechanics, by inverting the flexibility matrix. Then, in order to detect damage, we are going to show that the shape given by the change in the natural frequencies is as function of the damage position only. Thus, the crack is located by the correlation between the shape of the measured frequencies and those obtained by the finite elements, where the position that gives the calculated shape which is the most similar to the measured one, indicates the crack position. After the localization, an inverse method will be applied to quantify the damage. Finally, an experimental application is presented to show the real applicability of the method, in which the crack is introduced by using an Electrical Discharge Machining. The results confirm the applicability of the method for the localization and the quantification of cracks.