scholarly journals Crack Identification in a Cantilever Beam Using Coupled Response Measurements

1997 ◽  
Author(s):  
A. S. Sekhar ◽  
P. Balaji Prasad
Keyword(s):  
Cantilever Beam ◽  
Crack Detection ◽  
Rate Of Change ◽  
Crack Identification ◽  
Direct Response ◽  
Crack Location ◽  
Small Cracks ◽  
Axial Response ◽  
Coupled Response ◽  
System Characteristics

Identification of crack location and magnitude through measurement in changes in system characteristics, such as modal measurements has been studied by various researchers. In the present work based on the new method proposed by Gounaris et al (1996) for crack detection through coupled response measurements, experiments were carried out on a cracked cantilever beam for eigenfrequencies, bending and axial response measurements. It has been observed that the rate of change of direct response (bending) is much less at small cracks while that of the coupled response (axial) changes, substantially allowing diagnoses of smaller cracks.

Crack Identification in a Cantilever Beam Using Coupled Response Measurements

1998 ◽  
Vol 120 (4) ◽  
pp. 775-777 ◽  
Author(s):  
A. S. Sekhar ◽  
P. Balaji Prasad
Keyword(s):  
Cantilever Beam ◽  
Crack Detection ◽  
Rate Of Change ◽  
Crack Identification ◽  
Direct Response ◽  
Crack Location ◽  
Small Cracks ◽  
Axial Response ◽  
Coupled Response ◽  
System Characteristics

Identification of crack location and magnitude through measurement in changes in system characteristics, such as modal measurements, has been studied by various researchers. In the present work based on the new method proposed by Gounaris et al. (1996) for crack detection through coupled response measurements, experiments were carried out on a cracked cantilever beam for eigenfrequencies, bending, and axial response measurements. It has been observed that the rate of change of direct response (bending) is much less at small cracks, while that of the coupled response (axial) changes substantially, which allows for diagnoses of smaller cracks.

In-Plane Vibration and Crack Detection of a Rotating Shaft-Disk Containing a Transverse Crack

1998 ◽  
Vol 120 (2) ◽  
pp. 551-556 ◽  
Author(s):  
Ming-Chuan Wu ◽  
Shyh-Chin Huang
Keyword(s):  
Crack Detection ◽  
Transverse Crack ◽  
Rotation Speed ◽  
Crack Depth ◽  
Multiple Scale ◽  
Crack Identification ◽  
Response Curves ◽  
Rotating Shaft ◽  
Crack Location ◽  
Depth Rotation

Dynamic response and stability of a rotating shaft-disk containing a transverse crack is investigated. FFT analysis of response amplitudes showed that the 2Ω component (Ω: rotation speed) was excited by crack breathing and could serve as a good index for crack identification. Intensive numerical studies of crack location, crack depth, rotation speed, and sensing position on response amplitudes displayed a feasible technique for the identification of crack depth and crack location. It is achieved by intersecting the two equi-amplitude response curves of two separated sensing probes. Finally, the instability of the system caused by a crack is examined via Floquet theory and the multiple scale method. The stability diagrams, illustrated as functions of crack depth, rotation speed, and damping, are shown and discussed.

A study on the crack detection in beams using linear and nonlinear normal modes

2019 ◽  
Vol 23 (7) ◽  
pp. 1305-1321
Author(s):  
Yildirim Serhat Erdogan
Keyword(s):  
Normal Mode ◽  
Crack Detection ◽  
Normal Modes ◽  
Element Model ◽  
Nonlinear Normal Modes ◽  
Crack Identification ◽  
Crack Location ◽  
Linear And Nonlinear ◽  
Nonlinear Normal ◽  
Cracked Beams

Linear and nonlinear normal mode motions may provide promising information about the condition of mechanical structures under small and large amplitude vibrations, respectively. In this view, this study investigates the nonlinear dynamics of cracked beams through use of the nonlinear mode motion and extends the crack identification methods that utilize the linear characteristics to nonlinear vibrating structures. At first, the nonlinear normal modes of the intact and cracked beams are calculated by a continuation algorithm. A finite element model of a geometrically nonlinear prismatic beam was created based on crack stress intensity. Subsequently, a method based on normal mode motion and minimization of strain energy, which is valid for linear and nonlinear vibrating beams, was developed as an optimization problem. To this end, hybrid optimization was also used due to its capability in finding global minimum along with its computational efficiency. It was shown that the proposed crack detection technique is applicable to beams vibrating in linear and/or nonlinear regimes and well capable of detecting both crack location and severity.

The effect of crack geometry on non-destructive fault detection of EN 8 and EN 47 cracked cantilever beam

2019 ◽  
Vol 50 (3) ◽  
pp. 92-100 ◽  
Author(s):  
V Khalkar ◽  
S Ramachandran
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Crack Location ◽  
Crack Geometry ◽  
Shaped Crack ◽  
Non Destructive

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.

scholarly journals ANALYSIS AND PREDICTION OF MULTIPLE-CRACKED PLASTIC BEAM

2009 ◽  
Vol 12 (18) ◽  
pp. 37-45
Author(s):  
Hang Xuan Le ◽  
Luong Thi Hien Nguyen
Keyword(s):  
Genetic Algorithm ◽  
Cantilever Beam ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Fitness Function ◽  
High Accuracy ◽  
Crack Identification ◽  
Element Stiffness Matrix ◽  
Crack Location ◽  
Local Flexibility

This paper presents a method for identification of location and depth of a crack in a cantilever beam by means of a genetic algorithm based on the signs of crack identification are beams natural frequencies. The cracked element stiffness matrix is based on the theory that local flexibility goes up because of the appearance of cracks. Crack location and depth is identified by minimizing fitness function, which performs difference between natural frequencies calculated and measured. Results show that this method helps to make prediction with high accuracy and converging speed.

scholarly journals The effect of crack geometry on stiffness of spring steel cantilever beam

2018 ◽  
Vol 37 (4) ◽  
pp. 762-773 ◽  
Author(s):  
V Khalkar ◽  
S Ramachandran
Keyword(s):  
Free Vibration ◽  
Cantilever Beam ◽  
Crack Detection ◽  
Crack Depth ◽  
Steel Structures ◽  
Spring Steel ◽  
Cantilever Beams ◽  
Crack Location ◽  
Crack Geometry ◽  
Shaped Crack

The survival of the crack in structures always keeps the structure away from performing well in applications due to significant changes in its dynamic response. It has been observed that in service the size of the crack in structures increases with time and finally it leads to its catastrophic failure. Hence it is crucial to do the vibration study of cracked beams in regard of free vibration-based crack detection and its crack classification. Until now the vibration-based nondestructive testing methods are applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, i.e. V-shaped, U-shaped and rectangular-shaped open cracks, on the applicability of these methods has been overlooked. In order 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 the beam stiffness is investigated. In this study, the stiffness of each cracked case is computed by the deflection methods and vibration methods to ensure the strong validation. The stiffness results obtained from V-shaped, U-shaped and rectangular-shaped crack models for the same configuration are compared with each other and it is found that the results of the stiffness are comparatively more sensitive to U-shaped crack models. Through vibration study, it is found that spring steel structures are slightly sensitive to the change in crack geometries as long as the vibration characteristics are concerned. Hence, it is obvious that free vibration-based crack detection method can satisfactorily predict the location and depth of the crack in any spring steel structures irrespective of the crack geometries. Apart from this, it is also found that for the same configurations, EN 8 and EN 47 cracked cantilever beams give the identical structural integrity or structural stability property for all the cracked cases. Lastly, it is also found that as the crack depth increases by keeping the crack location constant, the stiffness of the beam decreases.

Identification of Crack Parameters in a Cantilever Beam under Uncertain End Conditions

2009 ◽  
Vol 413-414 ◽  
pp. 117-124
Author(s):  
Zhi Hua Wang ◽  
Lin Jing ◽  
Wei Wei Zhang ◽  
Hong Wei Ma
Keyword(s):  
Cantilever Beam ◽  
Characteristic Equation ◽  
Present Model ◽  
Crack Depth ◽  
Local Effect ◽  
Crack Identification ◽  
Experimental Frequency ◽  
Crack Location ◽  
End Conditions ◽  
The Difference

The local effect of “softening” at the crack location can be simulated by an equivalent spring connecting the two segments of the beam. As modelling the crack, the non-perfectly rigid clamp is also simulated as a torsional spring of unknown stiffness. Combined with the Bernoulli-Euler theories of beam, the present model is applied to derive the characteristic equation of the cantilever beam under uncertain end conditions related to the crack parameters, namely, the location and the depth of the crack. Based on this characteristic equation, an accurate crack identification method is developed to identify the location and the depth of the crack by minimizing the difference between the analytical and experimental frequency values. The proposed approach is verified by two cantilever beam experiments under ideal boundary conditions and uncertain end conditions. It is found that the location and the depth of the crack can be worked out when at least three natural frequencies are known. For crack identification of the cantilever beam under uncertain end conditions, the identified crack location of the proposed approach is more accurate than the Narkis’ method. Furthermore, the crack depth can also be obtained by the present method.

Nondestructive Detection of a Crack in a Triangular Cantilever Beam Based on Frequency Measurement

2007 ◽  
Vol 353-358 ◽  
pp. 2285-2288
Author(s):  
Fei Wang ◽  
Xue Zeng Zhao
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Frequency Measurement ◽  
Crack Size ◽  
Force Sensors ◽  
Rotational Spring ◽  
Cantilever Deflection ◽  
Crack Location ◽  
Small Force ◽  
Point Of Intersection

Triangular cantilevers are usually used as small force sensors in the transverse direction. Analyzing the effect of a crack on transverse vibration of a triangular cantilever will be of value to users and designers of cantilever deflection force sensors. We present a method for prediction of location and size of a crack in a triangular cantilever beam based on measurement of the natural frequencies in this paper. The crack is modeled as a rotational spring. The beam is treated as two triangular beams connected by a rotational spring at the crack location. Formulae for representing the relation between natural frequencies and the crack details are presented. To detect crack details from experiment results, the plots of the crack stiffness versus its location for any three natural modes can be obtained through the relation equation, and the point of intersection of the three curves gives the crack location. The crack size is then calculated using the relation between its stiffness and size. An example to demonstrate the validity and accuracy of the method is presented.

scholarly journals Dynamic Response of a Cracked Rotor With Some Comments on Crack Detection

1994 ◽  
Author(s):  
G. Meng ◽  
Eric J. Hahn
Keyword(s):  
Dynamic Response ◽  
Crack Detection ◽  
Harmonic Component ◽  
Major Axis ◽  
Vertical Axis ◽  
Crack Size ◽  
Cracked Rotor ◽  
Response Component ◽  
Crack Location ◽  
Backward Whirl

By considering time dependent terms as external excitation forces, the approximate dynamic response of a cracked horizontal rotor is analysed theoretically and numerically. The solution is good for small cracks and small vibrations in the stable operating range. For each steady state harmonic component the forward and backward whirl amplitudes, the shape and orientation of the elliptic orbit and the amplitude and phase of the response signals arc analysed, taking into account the effect of crack size, crack location, rotor speed and unbalance. It is found that the crack causes backward whirl, the amplitude of which increases with the crack. For a cracked rotor, the response orbit for each harmonic component is an ellipse, the shape and orientation of which depends on the crack size. The influence of the crack on the synchronous response of the system can be regarded as an additional unbalance whereupon, depending on the speed and the crack location, the response amplitude differs from that of the uncracked rotor. The nonsynchronous response provides evidence of crack in the sub-critical range, but is too small to be detected in the supercritical range. Possibilities for crack detection over the full speed range include the additional average (the constant) response component, the backward whirl of the response, the ellipticity of the orbit, the angle between the major axis and the vertical axis and the phase angle difference between vertical and horizontal vibration signals.

scholarly journals Crack Identification and Localization In Structural Beams Using Numerical and Experimental Modal Analysis- A Review

2020 ◽  
pp. 62-68
Keyword(s):  
Modal Analysis ◽  
Natural Frequency ◽  
Structural Damage ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Crack Identification ◽  
Engineering Structures ◽  
Aircraft Wings ◽  
Crack Location ◽  
Damaged Beams

This article presents a critical review of recent research done on crack identification and localization in structural beams using numerical and experimental modal analysis. Crack identification and localization in beams are very crucial in various engineering applications such as ship propeller shafts, aircraft wings, gantry cranes, and Turbo machinery blades. It is necessary to identify the damage in time; otherwise, there may be serious consequences like a catastrophic failure of the engineering structures. Experimental modal analysis is used to study the vibration characteristics of structures like natural frequency, damping and mode shapes. The modal parameters like natural frequency and mode shapes of undamaged and damaged beams are different. Based on this reason, structural damage can be detected, especially in beams. From the review of various research papers, it is identified that a lot of the research done on beams with open transverse crack. Crack location is identified by tracking variation in natural frequencies of a healthy and cracked beam

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