Damage Detection in Beam Structures Based on Frequency Measurements

Vestroni, Fabrizio; Capecchi, Danilo

doi:10.1061/(asce)0733-9399(2000)126:7(761)

Cited by 172 publications

(89 citation statements)

References 18 publications

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“…The weak formulation of (8)- (12) consists in finding v A H⧹f0g such that (17) and the eigenvalues can be determined by solving the chain of minimum problems…”

Section: An Equivalent Eigenvalue Problemmentioning

confidence: 99%

“…Finally, for the sake of completeness, we recall that several contributions on the crack identification problem considered in this paper are available. Apart from variational techniques, see, for example, [14][15][16][17][18][19][20][21], the approach generally adopted consists in solving numerically the nonlinear system of the frequency equations written for the first two natural frequencies. We refer, among others, to the studies carried out in [22][23][24][25][26].…”

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confidence: 99%

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Unique determination of a single crack in a uniform simply supported beam in bending vibration

Fernández-Sáez

Morassi

Pressacco

et al. 2016

Journal of Sound and Vibration

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“…The weak formulation of (8)- (12) consists in finding v A H⧹f0g such that (17) and the eigenvalues can be determined by solving the chain of minimum problems…”

Section: An Equivalent Eigenvalue Problemmentioning

confidence: 99%

mentioning

confidence: 99%

Unique determination of a single crack in a uniform simply supported beam in bending vibration

Fernández-Sáez

Morassi

Pressacco

et al. 2016

Journal of Sound and Vibration

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“…In general terms, the damage parameters are determined such that the natural frequencies of the mechanical model are closest (in a least squares sense) to those found experimentally; see Ruotolo and Surace (1997), Cerri and Vestroni (2000), Vestroni and Capecchi (2000), Khiem and Lien (2004) and, for a linearized version suitable in the case of small cracks, Patil and Maiti (2003) and Rubio (2009). More recently, Khiem and Toan (2014) proposed a procedure for multiple-crack detection in beams by natural frequency measurements.…”

Section: Introductionmentioning

confidence: 99%

“…two unknowns for each crack, the position and the severity), and then numerically solving the system formed by the characteristic equation written for all the natural frequencies in terms of the damage parameters (Cerri and Vestroni, 2000;Vestroni and Capecchi, 2000;Attar, 2012;Mazanoglu and Sabuncu, 2012). Inverse transcendental eigenvalue problems for the identification of multiple open cracks in a longitudinally vibrating rod were considered by Singh (2009).…”

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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“…This property was subsequently extended by Hearn and Testa [10] and used for the implementation of a damage detection strategy in beam-like structures. Vestroni and Capecchi developed in a series of papers [23], [4], [24] a method for the identification of localized damage, such as cracks or notches, in beam structures based on the minimization of an objective function constructed with the differences between the experimental values of the natural frequencies and their counterparts obtained from a numerical model of the system. The procedure involves a first stage in which the damage is to be located, and a subsequent stage in which its intensity is estimated.…”

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 Detection in Beam Structures Based on Frequency Measurements

Cited by 172 publications

References 18 publications

Unique determination of a single crack in a uniform simply supported beam in bending vibration

Unique determination of a single crack in a uniform simply supported beam in bending vibration

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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