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The paper presents a study dedicated to analyzing the sensitivity of structures with open contours to cracks. For this purpose, we analyze the particular case of the I-beam made by welding, for which we want to see how the frequencies of different modes of vibration change when a crack occurs in the weld joint between the web and the flange. The research is done using numerical simulations performed with the ANSYS program, from which the natural frequencies are obtained depending on the depth and extent of the crack. A large number of vibration modes and two types of boundary conditions are taken into account. We found that the frequency changes are small but still detectable and depend on the beam fixation mode. This makes it possible to detect cracks in the weld joint if the vibration modes where the decrease in frequency is significant are analyzed.

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.

In this paper, we present a simple predictive model to estimate the natural frequencies of steel cantilever beams with branched cracks. The model considers the cracked beam as a beam with constant cross-section, on which acts an equivalent bending moment. This bending moment takes into account the modification of the rigidity on the beam segment on which the crack extends in the longitudinal direction and the additional rotation that occurs in the slices located at the ends of the damaged segment. Along with the theoretical background and the deduced mathematical model, we present several cases of deterioration defined by the depth of the transverse crack branch respectively the position and the extension of the longitudinal branch. These examples prove the accuracy of the predictions regarding the change of the natural frequencies due to the damage obtained with the proposed model.

The current paper presents an algorithm for locating transverse cracks present in Euler–Bernoulli steel beams, by considering the relative frequency shifts (RFSs) measured for the weak-axis vibration modes and the mode shape curvatures. To apply the algorithm, we first determine, by means of the finite element method (FEM), the natural frequencies for the first four bending vibration modes for the healthy beam fixed-free and fixed-fixed end conditions. Afterward, we introduced transverse cracks with known depth and location and determined again the natural frequencies. As a next step, we use an original algorithm to plot the potential severity curves (PSCs) for the four modes and find the intersection, which indicates the crack severity and location. It was found that the method is reliable for determining the location of transverse cracks just by using the measured natural frequency and the squared normalized modal curvatures (SNMCs) for both imposed boundary conditions.

We propose in this paper a mathematical relationship to calculate the natural frequency shifts of beams due to multiple cracks. The relationship is based on the application of the superposition principle. A crack alters the frequencies for the bending vibration modes in a particular manner, with respect to the crack depth and location. We have shown that the affected beam have the same natural frequencies as a healthy beam with a smaller thickness; this thickness has to be calculated separately for each vibration mode. As a consequence, we can consider the next crack affects healthy beams, one different beam for each considered mode. Subsequent cracks affect a bigger number of beams. For the last crack, we have to calculate the frequencies for a number of beams that is the number of the considered vibration modes to the power equal with the number of cracks. To automate the process of calculating the resulted natural frequencies, we have written a program in Visual Basic for Excel Applications (VBEA), which permits finding the natural frequencies of a beam with up to nine cracks. This application can calculate the natural frequencies for four beam types: with fixed-free, fixed-fixed, simply supported and free-free restraints. The results obtained by calculating the frequencies for several damage scenarios and boundary conditions fit those obtained from simulations by involving the finite element method.