An algorithm to assess transversal cracks in composite structures based on natural frequency changes due to damage is proposed. The damage assessment is performed in two steps; first the crack location is found, and afterwards an evaluation of its severity is performed. The technique is based on a mathematical relation that provides the exact solution for the frequency changes of bending vibration modes, considering two terms. The first term is related to the strain energy stored in the beam, while the second term considers the increase of flexibility due to damage. Thus, it is possible to separate the problems of localization and severity assessment, which makes the localization process independent of the beams cross-section shape and boundary conditions. In fact, the process consists of comparing vectors representing the measured frequency shifts with patterns constructed using the mode shape curvatures of the undamaged beam. Once the damage is localized, the evaluation of its severity is made taking into account the global rigidity reduction. The damage identification algorithm was validated by experiments performed on numerous sandwich panel specimens.
Degradation of engineering structures due to corrosion affects their safety by reducing the cross-section of structural components and altering the material's mechanical characteristics. These parameter changes are observable in the shift of the natural frequencies. In the study presented in this paper, it was demonstrated that the kinetic energy distribution reflects the mass participation, thus being able to predict frequency changes due to mass loss, while the modal strain energy distribution can be properly used to indicate the location of the damage. As a result, two mathematical relations were developed by the authors, predicting the frequency changes due to the main effects of corrosion: loss of mass and loss of stiffness.
This paper is concerned with vibration based non-destructive evaluation of structures, with a focus on quantitative assessment of damage. In previous works, a reliable method to locate open cracks in beams has been proposed and tested using both data from numerical simulations and laboratory experiments. It bases on the fact the natural frequency of a bending vibrations mode attend different changes, depending on the loss of stored energy for the slice on which the damage is located. As bigger the mode shape curvature value on that location, so bigger the loss of stored energy and consequently the natural frequency decrease in that mode. Analyzing the natural frequency changes for a larger series of vibration modes, it’s possible to precisely locate damages. The authors succeed to find a single mathematical relation describing the frequency changes for all bending vibration modes, involving one term defining damage’s location and one defining its depth. While the first term changes for different modes, being defined by the mode shape curvature, the second maintain its value for all modes, being affected just by damage depth. This finding permits decoupling the location issue with that of quantitative assessment of damage. Latest researches, presented in this paper, succeed by finding the relation between the second term of the relation and some mechanical characteristics of the beam, i.e. extending the proposed method by including evaluation of damage severity. The approach is illustrated on a cantilever beam, modeled with 3D elements.
The paper presents a method to assess the crack depth in beams for which the damage location is known. Previous researches lead us to a method to identify damage locations in beams, based on a relation providing frequency changes in respect to damage location and depth. Separating the two variables it is possible to find first the damage location, and afterwards to derive the term controlling the severity. Comparing it with values indicating the frequency shift in respect to damage depth, the severity can be assessed. The paper presents a relation reflecting this dependency for any cross-section type, involving the static deflection for the healthy and damaged beam alone; it has a general character, being not influenced by the cross-section shape.
This paper deals with methods of interpreting the results of vibration measurement to identify structural changes in beam-like structures. We briefly presented an own developed damage assess method, that consider a large number of frequencies for the weak-axis banding vibration modes; it allows first a precise localization and afterwards evaluation of the damages. For the first step, recognition of the damage position, we introduce an algorithm implemented in C++ with the interface done using EXCEL features, indicating by one number the damage probable position, based on the Minkowski metrics. To avoid uncertainties, a graphic representation of all results is also presented. The method is tested for values determined by calculus for a randomly selected location, with and without measurement results debased by noise, proving its reliability.
Corrosion as material destruction affects the safety of structures, leading to more serious consequences than the simple loss of a mass. The effect of corrosion on the dynamic behaviour of structures act in two ways: the loss of mass increases the natural frequencies, opposite to the effect of stiffness loss. This paper present the results of researches made to extend the mathematical relation presenting the influence of damage location and severity on the natural frequency changes, by adding the effect mass loss. Therefore we modeled the beam once with the discontinuity and loss of mass, afterwards the damaged segment is replaced by an intact one but having the mass similar to that of the damaged segment. This permitted to plot frequency shift curves for both cases and to contrive the relations defining that curves. Finally a relation summarizing the both effects was contrived; it was confirmed both by numerical simulations and experiments.
This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.
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