Crack Detection in Cantilever Shaft Beam Using Natural Frequency

Since long it has been observed that the size of the crack in structures increases with time, and finally, it may lead to its catastrophic failure. Hence, it is crucial to do the vibration study of cracked structures with regard to vibration-based crack detection and the classification of cracks. So far, vibration-based non-destructive testing method is applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, that is, V-shaped and U-shaped, on the applicability of these methods has been overlooked. To investigate this issue, artificially cracks are made on the cantilever beam. By free vibration analysis, the effect of crack geometry, crack depth, and crack location on natural frequency is investigated. The natural frequency results obtained from V-shaped and U-shaped models for the same crack configurations are compared with each other and it is revealed that the results are not much sensitive for the change of crack geometry. Hence, it is clear that free vibration-based crack detection method approximately predicts the crack parameters, that is, crack location and crack depth, in structures irrespective of the crack geometry. It is also found that for the same configuration, results of natural frequency are comparatively on the lower side for U-shaped crack models than V-shaped crack models. In this study, the natural frequency of each cracked case is computed by a theoretical method and numerical method and shows good agreement. Finally, it is also observed that structural integrity of a cracked cantilever beam is a function of crack location.

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Experimental verification of detection and prediction of multiple cracks by vibrations, FEM and ANN

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-06-2013-0040 ◽

2014 ◽

Vol 10 (3) ◽

pp. 290-303

Author(s):

Prasad Ramchandra Baviskar ◽

Vinod B. Tungikar

Keyword(s):

Modal Analysis ◽

Natural Frequency ◽

Crack Detection ◽

Vertical Plane ◽

Multiple Cracks ◽

Transverse Cracks ◽

Content Type ◽

First Case ◽

Natural Frequency Analysis ◽

Good Agreement

Purpose – The purpose of this paper is to address the determination of crack location and depth of multiple transverse cracks by monitoring natural frequency and its prediction using Artificial Neural Networks (ANN). An alternative to the existing NDTs is suggested. Design/methodology/approach – Modal analysis is performed to extract the natural frequency. Analysis is performed for two cases of cracks. In first case, both cracks are perpendicular to axis. In second case, both cracks are inclined to vertical plane and also inclined with each other. Finite element method (FEM) is performed using ANSYSTM software which is theoretical basis. Experimentation is performed using Fast Fourier Transform (FFT) analyzer on simply supported stepped rotor shaft and cantilever circular beam with two cracks each. Findings – The results of FEM and experimentation are validated and are in good agreement. The error in crack detection by FEM is in the range of 3-15 percent while 5-20 percent by experimentation. The database obtained by modal analysis is used to train the network of ANN which predicts crack characteristics. Validity of method is investigated by comparing the predictions of ANN with FEM and experimentation. The results are in good agreement with error of 7-16 percent between ANN and FEM while 9-21 percent between ANN and experimental analysis. Originality/value – It envisages that the method is capable. It is an effective as well as an alternate method of fault detection in beam/rotating element to the existing methods.

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CRACK DETECTION USING NATURAL FREQUENCY REDUCTION DUE TO CHANGE IN COMPLIANCE

10.1063/1.3114332 ◽

2009 ◽

Author(s):

M. A. Hussain ◽

M. A. Johnson ◽

Donald O. Thompson ◽

Dale E. Chimenti

Keyword(s):

Natural Frequency ◽

Crack Detection

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Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades

Shock and Vibration ◽

10.1155/2017/1785759 ◽

2017 ◽

Vol 2017 ◽

pp. 1-18 ◽

Cited By ~ 6

Author(s):

Hailong Xu ◽

Zhongsheng Chen ◽

Yongmin Yang ◽

Limin Tao ◽

Xuefeng Chen

Keyword(s):

Natural Frequency ◽

Vibration Amplitude ◽

Crack Detection ◽

Vibration Characteristics ◽

Lumped Parameter Model ◽

Crack Model ◽

Breathing Crack ◽

Vibration Localization ◽

Lumped Parameter ◽

Amplitude Increase

Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs). Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.

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Dynamic Response of Tubular T-Joints Under the Influence of Propagating Cracks

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2828804 ◽

1996 ◽

Vol 118 (1) ◽

pp. 71-78 ◽

Cited By ~ 3

Author(s):

D. I. Nwosu ◽

A. S. J. Swamidas ◽

J. Y. Guigne´

Keyword(s):

Natural Frequency ◽

Crack Detection ◽

Crack Depth ◽

Bending Moment ◽

Frequency Change ◽

T Joints ◽

Finite Element Program ◽

Crack Location ◽

Percent Change ◽

Frequency Changes

This paper presents an analytical study on the vibration response of tubular T-joints for detecting the existence of cracks along their intersections. The ABAQUS finite element program was utilized for carrying out the analysis. Frequency response functions were obtained for a joint with and without cracks. The joint was modeled with 8-node degenerate shell elements having 5 degrees of freedom per node. Line spring elements were used to model the crack. The exact crack configuration (semielliptical shape, Fig. 5(b)), as observed from numerous experimental fatigue crack investigations at the critical location, has been achieved through a mapping function, that allows a crack in a planar element to be mapped on to the tube surface. The natural frequency changes with respect to crack depth show little changes, being 4.82 percent for a 83-percent crack depth for the first mode. On the other hand, significant changes have been observed for bending moment and curvature as a function of crack depth. For an 83-percent chord thickness crack, a 97-percent change in bending moment at points around the crack vicinity, and 34.15 to 78 percent change in bending moments, for those locations far away from the crack location, have been observed. Natural frequency change should be combined with other modal parameters such as “bending moment (or bending strain)” and “curvature” changes for crack detection. The presence of the crack can be detected at locations far away from the crack location using such sensors as strain gages.

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A Lumped Inertia Force Method for Vibration Problems

Aeronautical Quarterly ◽

10.1017/s0001925900003759 ◽

1966 ◽

Vol 17 (2) ◽

pp. 127-140 ◽

Cited By ~ 7

Author(s):

A. V. Krishna Murty

Keyword(s):

Distribution Function ◽

Natural Frequency ◽

Linear Displacement ◽

Mode Shapes ◽

Fourth Power ◽

Inertia Force ◽

Lumped Mass ◽

Displacement Distribution ◽

Transverse Vibrations ◽

Cantilever Shaft

SummaryA rational method of lumping inertia forces by considering the equilibrium of the vibrating element has been developed. This method requires the selection of a suitable displacement distribution function over each element. The closer it is to the true mode shape, the better the result.Considering a linear displacement distribution function over each element, the natural frequencies and mode shapes are obtained for transverse vibrations of a stretched string, torsional vibrations of a cantilever shaft (fixed at one end and free at the other) and transverse vibrations of a uniform cantilever beam. It is found that, even with a few elements, a reasonable accuracy can be obtained in the natural frequency, while the mode shapes are exact in the first two cases and almost exact in the third at the points considered.In Appendix A, it is shown that, for the torsional vibration of a uniform cantilever shaft and with a linear displacement function over each element, this method gives exact mode shapes at the points considered, while the natural frequency is always an upper bound and the error follows an inverse square law when the number of elements considered is large.In Appendix B, it is shown that a combination of this method with the conventional lumped mass method reduces the error in the natural frequency. The error follows an inverse fourth-power law when the number of elements considered is large and the mode shapes are exact at the points considered.This method can incorporate better displacement distribution functions, to obtain better results and convergence, and can easily be adapted to the buckling of columns, the vibration of beam columns and forced vibrations, as well as more complicated problems such as the vibration or buckling of plates and shells.

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704 A Crack Detection Method Based on Natural Frequency Change (2^ Report)

The Proceedings of Ibaraki District Conference ◽

10.1299/jsmeibaraki.2008.167 ◽

2008 ◽

Vol 2008 (0) ◽

pp. 167-168

Author(s):

Tadashi HORIBE ◽

Kuniaki TAKAHASHI ◽

Kiyoshi OHMORI

Keyword(s):

Natural Frequency ◽

Crack Detection ◽

Detection Method ◽

Frequency Change

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