Damage Detection on a Beam with Multiple Cracks: A Simplified Method Based on Relative Frequency Shifts

Gilbert-Rainer Gillich,Nicoleta Gillich,Zoltan-Iosif Korka,Cristian Tufisi,Magd Abdel Wahab,Nuno M M Maia,Marius Vasile Pop

doi:10.3390/s21155215

Gilbert-Rainer Gillich, Nicoleta Gillich + Show 5 more

Open Access

https://doi.org/10.3390/s21155215

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Abstract

Identifying cracks in the incipient state is essential to prevent the failure of engineering structures. Detection methods relying on the analysis of the changes in modal parameters are widely used because of the advantages they present. In our previous research, we found that eigenfrequencies were capable of indicating the position and depth of damage when sufficient vibration modes were considered. The damage indicator we developed was based on the relative frequency shifts (RFS). To calculate the RFSs for various positions and depths of a crack, we established a mathematical relation that involved the squared modal curvatures in the healthy state and the deflection of the healthy and damaged beam under dead mass, respectively. In this study, we propose to calculate the RFS for beams with several cracks by applying the superposition principle. We demonstrate that this is possible if the cracks are far enough from each other. In fact, if the cracks are close to each other, the superposition method does not work and we distinguish two cases: (i) when the cracks affect the same beam face, the frequency drop is less than the sum of the individual frequency drops, and (ii) on the contrary, cracks on opposite sides cause a decrease in frequency, which is greater than the sum of the frequency drop due to individual damage. When the RFS curves are known, crack assessment becomes an optimization problem, the cost function being the distance between the measured RFSs and all possible RFSs for several vibration modes. Thus, the RFS constitutes a benchmark that characterizes damage using only the eigenfrequencies. We can accurately locate multiple cracks and estimate their severity through experiments and thus prove the reliability of the proposed method.

Highlights

The vibration-based damage detection methods have been widely used in recent decades because of the advantages they offer over traditional methods
Taking advantage of the fact that we can create a database that contains the eigenfrequencies for many damage scenarios, we have developed a damage detection method based on multimodal analysis
These are locations where the crack produces no energy decrease and it has no effect on the eigenfrequencies; this is explained from Figure 4, by the fact that the crack position for this mode number is at an inflection point, and, it cannot be taken into consideration

Summary

Introduction

The vibration-based damage detection methods have been widely used in recent decades because of the advantages they offer over traditional methods. They enable finding the location and size of the damage from vibration signals, collected from one or few measurement points not necessarily close to the damaged region. The idea on which these non-destructive testing methods are based is the relationship between the local stiffness reduction due to the crack and the modal parameter changes. Comprehensive reviews on this topic are accomplished in [1,2]. For small-sized damages, the capability of observing slight frequency changes is essential

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Conclusion