Assessing multiple cracks in beams by a method based on the damage location coefficients

Abstract

In this paper, we analyze the case of structural integrity assessment when the beams have several cracks. The relationship between the location and the severity of one crack and the resulting frequency shift is known. That is why we can design databases containing many defects for which we can calculate precisely the frequency changes and the subsequent damage location coefficients. When the natural frequency evolution of several vibration modes is monitored, we can find alteration due to the crack. Comparing the results of the measurements with the values contained in the database, for instance by involving a bin-by-bin dissimilarity estimator, we can find the location and severity of the crack. For multiple cracks, this approach was not investigated. In this study, we design a database for two cracks affecting at the same time the beam. For these cracks, which have various severities and locations, we calculated the frequency changes by applying the superposition principle. Afterward, we find the frequency shifts for a test structure by means of the finite element method. The comparison between the damage location coefficients in the database and the signature of the damages achieved by simulation is made by the software we have developed in Visual Basic for Application in Excel. We succeed to find the severity and the location of the two cracks for all considered crack configurations.