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.
Damage detection methods based on vibration analysis make use of the modal parameter changes. Natural frequencies are the features that can be acquired most simply and inexpensively. But this parameter is influenced by environmental conditions, e.g. temperature and operational loads as additional masses or axial loads induced by restraint displacements. The effect of these factors is not completely known, but in the numerous actual research it is considered that they affect negatively the damage assessment process. This is justified by the small frequency changes occurring due to damage, which can be masked by the frequency shifts due to external loads. The paper intends to clarify the effect of external loads on the natural frequencies of beams and truss elements, and to show in which manner the damage detection process is affected by these loads. The finite element analysis, performed on diverse structures for a large range of temperature values, has shown that the temperature itself has a very limited effect on the frequency changes. Thus, axial forces resulted due to obstructed displacements can influence more substantially the frequency changes. These facts are demonstrated by experimental and theoretical studies. Finally, we succeed to adapt a prior contrived relation providing the frequency changes due to damage in order to fit the case of known external loads. Whereas a new baseline for damage detection was found, considering the effect of temperature and external loads, this process can be performed without other complication.
The paper present a novel non-destructive evaluation method designed to assess damage in structural elements subjected to important axial loads, as columns are. In the prior research a reliable damage detection method was developed for beams subjected to own mass, that consider the relation existing between the energy stored in the beam in certain vibration modes and the related natural frequencies. First we found the mathematical relations expressing the healthy pillar mode shapes and frequencies with respect to the top mass. Afterward, by means of FEM, we derived the natural frequencies for the numerous damage cases, in order to define the frequency shift curves. Analogous to the case of beams, the damage location is characterized by patterns that are derived from the mode shape curvatures square of the healthy beam. The damage location becomes an inverse problem while the damage position is found by interpreting frequency measurements made on the healthy and damaged beam.
Damage detection using vibration-based methods make use of empirically derived relations to characterize the crack severity. The applicability of these relations is limited to structures with similar cross-section shape and having the same crack type. The use of these relations for composite materials is even more difficult, due to the directional dependency of the materials mechanical properties. We propose in this paper a new method to evaluate the damage severity, which is based on the global stiffness reduction. It is known that the amount of energy stored in a structure depends on its global stiffness, i.e. the value of the structure deflection under a given load. Consequently, the stiffness decrease due to a damage is signalized by an increased deflection. We defined a damage severity indicator based on the evaluation of deflection changes, which is simple to be found by a simple finite element analysis. This indicator is valid for all structures having similar cross-section shape; we used it successfully in vibration-based damage assessment.
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