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. In addition, an expression, which removes the necessity of repeating natural frequency analyses, is given for identifying the connection between the crack depths and natural frequency drops. These simplified approaches play crucial role in solving inverse problem using constituted crack detection methodology. Solution needs a number of measured modal frequency knowledge two times more than the number of cracks to be detected. Efficiencies of the methods are verified using the natural frequency ratios obtained by the finite element package. The crack detection methodology is also validated using some experimental natural frequency ratios given in current literature. Results show that the locations and depths ratios of cracks are successfully predicted by using the methods presented.

Damage Identification and Quantification in Beams Using Wigner-Ville Distribution

“…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 .…”

The effect of manufacturing defects on the high-cycle fatigue of electron-beam-welded Ti-6Al-4V titanium alloy: experimental and numerical analysis

“…The level of amplitude was raised until a final failure occurred. Failure has been defined as 2% drop in the natural frequency (Mazanoglu, 2015).…”

Elliptical Crack Identification in a Nonrotating Shaft

“…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:…”

“…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.…”