The use of antiresonances for crack detection in beams

Dilena, Michele; Morassi, Antonino

doi:10.1016/j.jsv.2003.07.021

Cited by 103 publications

(85 citation statements)

References 17 publications

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“…The general case of identification of a single crack having any level of severity in a rod with smooth variable profile has been recently considered by the authors of the present paper in [29]. Among other things, it was shown in [29] that Dilena and Morassi's result [27] can be extended to this more general setting.…”

Section: Introductionmentioning

confidence: 99%

“…30 Narkis's theory was extended in [26] by showing that the choice of the first two natural frequencies is optimal in order to avoid non-uniqueness. Later on, Dilena and Morassi [27] showed that the fundamental frequency of a uniform rod under free-free and supported-free (e.g., cantilever) end conditions allows for the unique determination of the crack, so removing the spurious solution 35 due to the symmetry of the problem.…”

Section: Introductionmentioning

confidence: 99%

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Crack identification in elastically restrained vibrating rods

Fernández-Sáez

Morassi

Rubio

2017

International Journal of Non-Linear Mechanics

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In this paper we consider the problem of identifying an open crack in a longitudinally vibrating rod with smooth variable profile by minimal eigenfrequency data. The crack is assumed to be open during vibration and it is modelled by an elastic spring acting along the beam axis. Most, if not all, the results available in the literature for this inverse problem refer to ideal end conditions, that is the rod is either under free or supported end conditions. As an example of almost optimal result, it is known that the knowledge of the fundamental (positive) natural frequency of the rod under free-free and cantilever end conditions allows for the unique determination of the crack, without any restriction on the damage severity. In this paper we show that the analysis of the analogous crack identification problem for rods under elastically restrained end conditions leads to different results and that, in general, the knowledge of the fundamental frequency belonging to two spectra associated to different end conditions is not sufficient for the uniqueness of the solution. The method we used to solve the inverse problem is of constructive type and it is based on general properties of Preprint submitted to International Journal of Non-Linear Mechanics December 17, 2016 the eigenfrequencies as functions of the position and severity of the crack. The identification procedure has been tested numerically on rods under various damage scenarios. Numerical results agree well with the theory, even in presence of noisy input data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Crack identification in elastically restrained vibrating rods

Fernández-Sáez

Morassi

Rubio

2017

International Journal of Non-Linear Mechanics

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“…The perturbative approach used by Morassi was different from that of Narkis and, following Hearn and Testa [10], it was essentially based on the determination of an explicit expression of the first order derivative of the natural frequencies with respect to the damage severity in terms of quantities of the undamaged configuration of system. The uniqueness of the crack location in symmetric beams was resolved by Dilena and Morassi [6], who suggested to include appropriate anti-resonant frequency measurements in the input data.…”

Section: Introductionmentioning

confidence: 99%

“…The above-mentioned methods by Narkis [15], Morassi [14] and Dilena-Morassi [6] have been applied up to now to beams in axial or bending vibration under ideal boundary conditions, namely for beams with free, pinned or clamped ends. As far as we are aware, and despite the elastic constraints often represent a more realistic description of the boundary conditions of the real structural systems, studies on the identification of damage in beams with elastic constraints are rather rare.…”

Section: Introductionmentioning

confidence: 99%

Crack identification in rods and beams under uncertain boundary conditions

Dilena

Dell’Oste

Morassi

2017

International Journal of Mechanical Sciences

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This paper deals with the inverse problem of identifying a crack in a rod in axial vibration with partially unknown end conditions from a minimum number of resonant frequency variations. It is assumed that the crack is small and is modelled by an elastic spring acting along the rod axis. A first set of results concerns a uniform bar with both ends restrained by means of elastic springs having unknown flexibility. Under the hypothesis that the flexibility caused by the crack is small and of the same order of the flexibility of the elastic end constraints, it is shown that the inverse problem can be formulated in terms of the variations of the first three natural frequencies measured from the undamaged bar under ideal condition of fixed ends. It is proved that knowledge of this set of eigenfrequency variations can uniquely determine the overall flexibility induced by the end conditions, and the position (up to symmetry) and severity of the crack, by means of closed form expressions. The identification method can be also applied to axial vibrations of uniform cantilevers with elastically restrained end condition, and to transversely vibrating uniform beams either under elastic transverse support at both ends or under cantilever end conditions. The method was verified by numerical simulation and, in the case of the cantilever in bending vibration, by experimental data. Numerical analysis allowed to study in detail some singular situations occurring in the mathematical formulation of the inverse problem and to test the robustness of the method to errors on the data.

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“…The main contribution of the present research is the rigorous unique determination of the crack position and severity, by means of a constructive algorithm, without any a priori assumption on the smallness of the damage. It should be recalled, in fact, that a well-established theory is available for our problem in case of small crack [9][10][11]. The smallness of the damage allows us to linearize the inverse problem in a neighborhood of the undamaged configuration, see also [12] for a theory which includes second-order terms in the eigenvalues expansion with respect to the crack severity.…”

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confidence: 99%