Damage identification in Euler frames

Greco, Annalisa; Pau, Annamaria

doi:10.1016/j.compstruc.2011.10.007

Cited by 37 publications

(33 citation statements)

References 18 publications

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“…Table 1 shows different cases for the crack location and the ratio of the crack depth to section height d/h, along with the corresponding first four natural frequencies, calculated accurately up to the fifth decimal place using the method described in [10]. It is generally reported that the minimum number of required natural frequencies for crack detection is three, as in [33]. Referring to Fig.…”

Section: Numerical Examplesmentioning

confidence: 96%

“…The cracked beam finite element was used at the crack location and the method was verified experimentally. Greco and Pau [33] incorporated the rotational spring stiffness in the exact dynamic stiffness matrix of a cracked frame. The optimisation criterion was the least sum of squares of the differences between the theoretical and experimental values of the variation between the uncracked and cracked natural frequencies with respect to the uncracked frequencies.…”

Section: Introductionmentioning

confidence: 99%

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Crack localisation in frames using natural frequency degradations

Labib

Kennedy

Featherston

2015

Computers & Structures

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Section: Numerical Examplesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Crack localisation in frames using natural frequency degradations

Labib

Kennedy

Featherston

2015

Computers & Structures

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“…However, the approach generally requires subtle analysis in order to deal with the possible nonconvexity of the error function and, as a consequence, with the appearance of multiple local and global minima. In connection with this point, see the interesting analysis presented in Vestroni and Capecchi (2000) and the recent contribution by Greco and Pau (2012) on crack identification in a frame.…”

Section: Introductionmentioning

confidence: 99%

Identification of two cracks with different severity in beams and rods from minimal frequency data

Rubio

Fernández-Sáez

Morassi

2014

Journal of Vibration and Control

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It has been known for a long time that the problem of identifying two small cracks in a simply supported beam from the first three natural frequencies can be analytically formulated and solved if the two cracks have equal severity. In this paper we extend this result to the case of cracks with different severity. Each crack is simulated by a rotational elastic spring and the inverse problem is solved in terms of the damage-induced changes in the first four natural frequencies. Closed-form expressions of the damage parameters in terms of the measured frequencies are obtained. The results can be extended to the identification of two cracks in a longitudinally vibrating beam based on a suitable set of natural frequency and antiresonant frequency data. Numerical simulations support the theory, and show that if accurate input data are available and the cracks are not too close, then damage identification leads to satisfactory results.

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“…The procedure is based on the so-called crack scanning method, recently proposed by the same authors, and on an improved Rayleigh's quotient type technique for calculating the crack induced changes in the natural frequencies. The detection of concentrated damage in more complex structures, such as parabolic arches or frames, by measured frequency variations has been approached in the papers by Pau et al [17], [9]. Caddemi and Caliò [2], [3] have recently developed a multiple crack damage identification procedure in beams based on closed form solutions of the free vibration problem.…”

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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Damage identification in Euler frames

Cited by 37 publications

References 18 publications

Crack localisation in frames using natural frequency degradations

Crack localisation in frames using natural frequency degradations

Identification of two cracks with different severity in beams and rods from minimal frequency data

Crack identification in rods and beams under uncertain boundary conditions

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