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We propose in this paper a method to detect cracks in circular plates clamped at the circumference. It consists in analyzing and interpreting the frequency changes that occur due to a circular arc crack. We show that the effect of the crack depends on the strain energy loss, which actually is proportional to the curvature achieved by the affected region in the radial direction. Three types of cracks are considered herein to demonstrate this dependency, differing by their length. Modal analysis is performed involving a professional simulation software for the intact plate, and that with the generated cracks. We found a perfect fit when we compared the curvature of the plate in the radial direction obtained with the analytical relation with the frequency values for the crack displaced along the radius. Therefore, using the curvature of several vibration modes we can obtain damage patterns that can be used to locate circular cracks.

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.

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.

The paper presents a study regarding the vibration behavior of Euler-Bernoulli beams which have cracks with complex shapes. The aim is to show that diverse orientations of the crack branches occurring in a given region of the structure produce different changes of the eigenfrequencies for the different vibration modes, dependent on the position and propagation angle of the crack. The research is conducted employing the finite element analyses, which are used to describe the dynamic response of a structure affected by a transversal open crack followed by two branches, each oriented at a different angle. These cracks are traditionally referred to as Y-shaped crack. We calculated the relative frequency shifts for the first six transverse vibration modes and extracted the damage signature for the considered branched crack location. The damage signatures can be used as patterns in damage detection procedures, transforming the procedure of detecting the crack position and severity from the eigenfrequency changes in an inverse problem.

This paper introduces a method to detect damages in L-shaped frames. The problem of identifying cracks in such structures arises from the low frequency changes due to damage. In the early stage, cracks are hard to be assessed. We present two distinct parts: the assessment of the dynamic behavior of L-shaped and description of the damage evaluation method. In the first part, the mathematical relations contrived for the natural frequencies and mode shapes respectively curvatures are introduced. Afterward, the distribution of the modal energy is found and associated with effects produced by a crack with a given depth in different locations. Findings are used to identify the crack location and severity. Accurate frequency evaluation, a crucial aspect since low frequency changes are expected, was made by employing an algorithm developed by the authors. The damage assessment method with the integrated frequency evaluation algorithm is employed to evaluate the health of an L-framed structure.