2015
DOI: 10.1590/1679-78251723
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A Novel Methodology Using Simplified Approaches for Identification of Cracks in Beams

Abstract: In this paper, natural frequency based forward and inverse methods are proposed for identifying multiple cracks in beams. Forward methods include simplified definition of the natural frequency drops caused by the cracks. The ratios between natural frequencies obtained from multi-cracked and un-cracked beams are determined by an approach that uses the local flexibility model of cracks. This approach does not consider nonlinear crack effects that can be easily neglected when the number of cracks is not excessive… Show more

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Cited by 12 publications
(9 citation statements)
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“…The cubic polynomial function was used for the regression due to the best fitting performance and the connection with the character of influence of a thickness reduction on the resulting structural stiffness. The estimation of the crack depth relationship with the local stiffness reduction based on polynomials is widely used in the literature (see e.g., [ 82 , 83 , 84 , 85 ]). The exemplary plot and the results of regression are presented in Figure 10 .…”
Section: Results Of Damage Quantificationmentioning
confidence: 99%
“…The cubic polynomial function was used for the regression due to the best fitting performance and the connection with the character of influence of a thickness reduction on the resulting structural stiffness. The estimation of the crack depth relationship with the local stiffness reduction based on polynomials is widely used in the literature (see e.g., [ 82 , 83 , 84 , 85 ]). The exemplary plot and the results of regression are presented in Figure 10 .…”
Section: Results Of Damage Quantificationmentioning
confidence: 99%
“…The level of amplitude was raised until a final failure occurred. Failure has been defined as 2% drop in the natural frequency (Mazanoglu, 2015).…”
Section: Methodsmentioning
confidence: 99%
“…e displacement u o takes different expressions depending on the support conditions of the shaft beam [52]. From (16), the relation between ω c and ω nc (frequency ratio) can be calculated in terms of D, L, and λ m and two parameters called g and f that depend on the support restrains:…”
Section: Model Of the Cracked Shaft Beam A Cracked Euler-mentioning
confidence: 99%
“…Over the last four decades, from the 70s to the present day, many researches have focused on developing nondestructive maintenance methods founded on the vibration measurement characteristics, clearly the mode shapes and natural frequencies, for instance, some of them are presented in [3,[5][6][7][8][9][10], besides, some extensive reviews can be found in [11][12][13][14]. Some of these works are based on the fact that it is possible to estimate the crack parameters by measuring the changes in the natural frequency (inverse problem), since the natural frequencies can be measured accurately and most easily in comparison with other dynamic characteristics of a structure and the experimental errors do not significantly change their values [15,16]. Before considering the crack identification inverse problem, the direct problem should be studied, that is, the determination of natural frequencies of the cracked element, assuming the crack parameters are known.…”
Section: Introductionmentioning
confidence: 99%