TESTING THE MATHEMATICAL RELATION FOR DERIVING THE PATTERNS OF A TRANSVERSAL CRACK IN CANTILEVER BEAMS

Abstract

The paper presents a method for detecting transversal cracks in steel beams of rectangular cross-section, which is centered on the vibration response of the tested component. We have plotted the relative frequency shift curves for two cantilever beams with different thicknesses, both subjected to a transversal crack of 20% depth. The curves were plotted for several crack positions resulted by removing the crack with a step of 5mm along the beam. As a result, we obtained the crack patterns, which consist of a set of frequency shifts for several out-of-plain vibration modes. We also demonstrate a mathematical relation, which allows the prediction of the frequency drop of beams with transversal cracks. The equation is based on the energies stored in the beam’s section in the undamaged, respectively, in the damaged state. The severity of the damage was calculated from the stiffness of the slice subjected to the biggest bending moment occurred for the beam loaded with dead mass.