In this paper, a vibration-based damage detection method designed for thin plates is proposed. The method bases on the relation existing between the strain energy stored in the plate in several vibration modes and the respective natural frequencies. For any mode, the strain energy results as sum of the energies stored in all plate elements in that mode. It depends on the square of the mode shape curvature achieved in each element location for the given vibration mode. As a result, the energy distribution along the plate is different for each mode. By reducing the rigidity of one plate element due to a damage, the frequencies will drop in a different manner, depending on the damaged element location. This permits to define patterns that characterize the dynamic behavior of the plated for any damage location. Actually, the patterns are derived from the normalized frequency shifts attained by numerical simulations. Herein the patterns that characterize a centrally located damage of different extent are consequently derived by means of the finite element analysis and used as a benchmark in the damage detection process. These patterns are successfully used to recognize, localize and quantify damages from measurements on in real plates.
This paper proposes a vibration-based damage detection method designed for structural elements subjected to important vertical loads, as columns or pillars. The method is based on the relation existing between the energy stored in the pillar in several vibration modes and the corresponding natural frequencies. For a certain mode, this energy results as the sum of the energies stored in all pillar slices, being dependent on the rigidity and the squared of the corresponding mode shape curvature. This means that the energy distribution along the pillar is different for each mode. Thus, reducing the rigidity of one slice due to damage, the frequencies will decrease in different ways, depending on the slice location. This fact permits to contrive patterns able to characterize the effect of damage at any location along the pillar. Since the mode shapes (and the natural frequencies) are influenced by inertial forces, but in the meantime by the compression and shear forces induced by the top mass, the patterns have to be derived for each load case. The paper presents a simple mathematical expression able to predict frequency changes if damage occurs at any location along the pillar and for any top mass value. Patterns that characterize the damage location are consequently derived by using the squared mode shape curvatures of the healthy beam. The damage location becomes an inverse problem, it being found by interpreting the results of frequency measurements for the healthy and damaged state. The process of damage location is exemplified by numerical simulations.
The paper presents a method to locate discontinuities in form of transversal cracks in beams, based on vibration
measurements. Patterns characterizing frequency changes of the first ten weak-axis bending vibration modes are
determined for all possible locations on the structure, using a relation contrived by the authors. It base on the correlation
between the strain energy stored in a segment of the beam, which is proportional with the square of the mode shape
curvature of the considered vibration mode at that location, and the frequency change for this mode by the occurrence of
a discontinuity on that segment. The patters consist from a series of ten values representing the normalized relative
frequency shifts for the first ten vibration modes. For a structure similarly supported, by continuous or periodical
measurements, potential frequency changes can be detected. By processing these data the so-called damage location
index for that crack is found out, also as a series of ten values representing the relative frequency shifts of the ten
vibration modes. To precise locate the crack a pattern matching method involving the database with all possible patterns
and the damage location index is used. Knowing the location, it is easy to determine by analytic calculus the crack depth.
The method is easy to be used, provide accurate results, demands modest computational effort and has the advantage that
the measurements may be carried out in situ with rather simple equipment. The method was validated by experiments.
The paper presents a method to assess damages in beams, based on how natural frequencies of bending vibration modes
change due to damages. The authors have contrived a correlation between the strain energy stored in a segment of the
beam, which is proportional with the mode shape curvature of a considered vibration mode at that location, and the
frequency change for this mode if damage appears on that segment. For a certain mode, damages placed on inflection
points of the mode shape curvature, where the strain energy is null, will not produce changes in frequency, while
damages placed on maxima will produce the highest changes in frequency. For other locations of damage, the frequency
shift will be proportional with the mode shape curvature of the vibration mode at that location. We worked out a general
relation, which gives the frequency shift of all bending modes, with one coefficient depending on the support type. To
evaluate damages, we determine analytically the relative frequency shift as ratio between the frequency change and the
natural frequency of the undamaged beam, for the first ten vibration modes, considering various damage depths and
locations. Comparison of results with that obtained by measurements on the real beam permits detection, location and
assessment of damages in beams with high accuracy. The method was validated by experiments.