Modelling of vibration of beam in presence of inclined edge or internal crack for its possible detection based on frequency measurements

Nandwana, B. P.; Maiti, Sukumar

doi:10.1016/s0013-7944(97)00078-7

Cited by 80 publications

(40 citation statements)

References 18 publications

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“…In particular, for j = c the beam is cracked, while for j = n the beam is non-cracked. It is derived from Table 2, that the results of the present study are generally close to the results of references [23] and [24]. It is noteworthy that the study of reference [23] has applied for a Timoshenko beam.…”

Section: Two-dimensional Modelsupporting

confidence: 87%

“…It is derived from Table 2, that the results of the present study are generally close to the results of references [23] and [24]. It is noteworthy that the study of reference [23] has applied for a Timoshenko beam. Furthermore, the results from the work in [24] correspond to an internal crack of the same severity with the studied crack case.…”

Section: Two-dimensional Modelsupporting

confidence: 87%

See 1 more Smart Citation

Vibration Analysis of Cracked Beams Using the Finite Element Method

Bouboulas¹,

Georgantzinos²,

Anifantis³

2012

Advances in Vibration Engineering and Structural Dynamics

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Section: Two-dimensional Modelsupporting

confidence: 87%

Section: Two-dimensional Modelsupporting

confidence: 87%

Vibration Analysis of Cracked Beams Using the Finite Element Method

Bouboulas¹,

Georgantzinos²,

Anifantis³

2012

Advances in Vibration Engineering and Structural Dynamics

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“…Firstly, the computational time required for calculating the time-domain responses of a more complex model class is longer. Secondly, a model class with more uncertain parameters will result in a larger number of minimization variables in the minimization of the J function in equation (14). This in terms will lead to a larger number of iteration steps in the numerical optimization process, and therefore, a longer computational time.…”

Section: 3mentioning

confidence: 99%

“…A comprehensive review of recent developments can be found in Sohn et al (2004). Most of the crack detection methods in the literature have focused on single-crack cases (Cawley & Adams 1979; Rizos et al 1990; Liang et al 1991;Narkis 1994;Nandwana & Maiti 1997). For methods that have addressed multi-crack situations, it has been assumed that the number of cracks was known in advance.…”

Section: Introductionmentioning

confidence: 99%

Multicrack Detection on Semirigidly Connected Beams Utilizing Dynamic Data

Lam

Leung

2008

J. Eng. Mech.

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The problem of crack detection has been studied by many researchers, and many methods of approaching the problem have been developed. To quantify the crack extent, most methods follow the model updating approach. This approach treats the crack location and extent as model parameters, which are then identified by minimizing the discrepancy between the modeled and the measured dynamic responses. Most methods following this approach focus on the detection of single-crack or multi-crack in situations in which the number of cracks is known. The main objective of this paper is to address the crack detection problem in a general situation in which the number of cracks is not known in advance.The crack detection methodology proposed in this paper consists of two phases. In the first phase, different classes of models are employed to model the beam with different numbers of cracks, and the Bayesian model class selection method is then employed to identify the most plausible class of models based on the set of measured dynamic data in order to identify the number of cracks on the beam. In the second phase, the posterior (updated) probability density function (PDF) of the crack locations and the corresponding extents is calculated using the Bayesian statistical framework. As a result, the uncertainties that may have been introduced by measurement noise and modeling error can be explicitly dealt with.The methodology proposed herein has been verified by and demonstrated through a comprehensive series of numerical case studies, in which noisy data was generated by a Bernoulli-Euler beam with semi-rigid connections. The results of these studies show that the proposed methodology can correctly identify the number of cracks even when the crack extent is small. The effects of measurement noise, modeling error, and the complexity of the class of identification model on the crack detection results have also been studied and are discussed in this paper.

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“…Liang et al [9] have given a method similar to the above, but it requires measurement of three transverse natural frequencies of the beam. The method has been extended to stepped beams [10], cantilever beams with inclined edge cracks and internal cracks [11], geometrically segmented beams [12], etc. There is a need to see if this approach can be used for short beams, where the e!ects of shear deformation and rotational inertia are not negligible.…”

Section: Introductionmentioning

confidence: 99%