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

1996 ◽  
Vol 118 (1) ◽  
pp. 71-78 ◽  
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.

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.

Effect of a Circumferential Arc Crack on the Vibration Characteristics of a Flexible Spinning Disk

2007 ◽  
Author(s):  
Nikhit N. Nair ◽  
Hamid N. Hashemi ◽  
Grant M. Warner
Keyword(s):  
Crack Opening ◽  
Equations Of Motion ◽  
Crack Depth ◽  
Bending Moment ◽  
Rotating Disk ◽  
Vibration Characteristics ◽  
Coupled Systems ◽  
Mode Shapes ◽  
Critical Speeds ◽  
Crack Location

The vibration characteristics of a circumferentially cracked rotating disk are investigated. The disk is assumed to be axisymmetric, flexible and clamped at the center. The crack increases the local flexibility of the disk at the crack location and is modeled as linear and torsional springs, connecting the two segments of the disk. The spring constants are evaluated by considering crack opening displacements due to bending moment and shear force at the crack location. The equations of motion of two segments of the disk, for disk operating in vacuum as well as subjected to shear fluid flow are developed. Using the Finite Difference Technique, the coupled systems of equations are solved and the natural frequencies and mode shapes are obtained. The mode shapes are seen to be comparatively flattened in the inner region of the disk separated by the crack and heightened towards the periphery of the disk. Shear fluid loading reduces the critical speeds and results in a quicker onset of instability. The degree of instability caused by the crack is a function of crack depth and location. Critical speeds increase with increasing crack distance from the central clamp and decrease with increasing crack depth.

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.

scholarly journals Restoration of Natural Frequency of Cracked Cantilever Beam Using CNT Composite Patch: A Finite Element Study

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mahmoud Nadim Nahas ◽  
Mahmoud Ali Alzahrani
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Fe Simulation ◽  
Crack Depth ◽  
High Strength ◽  
Crack Location ◽  
Weight Concentration ◽  
Beam Depth ◽  
Initiation And Propagation ◽  
Low Stiffness

Cyclic loadings cause fatigue to the elements of machines leading to crack initiation and propagation. This phenomenon decreases the age of the elements. In particular, cracks decrease the stiffness of the parts and lower the parts natural frequency, leading to failure under normal working conditions. This paper introduces a new application to carbon nanotube (CNT) composites in the repairing process of a cracked specimen to restore the natural frequency of the specimen. Commonly, patches are made of high strength and high stiffness materials. This paper shows that even low stiffness materials, such as epoxy reinforced with CNT, can contribute to the repair of a cracked specimen. A 2D finite element (FE) simulation is used to study the effects of bonding CNT composite patches over the crack location to repair cracked metal specimens. The effects of the patch thickness, length, and CNTs weight concentration ratio are investigated. Results showed an increase in the natural frequency of 31% compared to the cracked specimen at a crack depth of 70% of the beam depth and at a distance of 20% of the total beam length from the support.

scholarly journals Influence of Crack on Modal Parameters of Cantilever Beam Using Experimental Modal Analysis

2018 ◽  
Vol 1 (1) ◽  
pp. 16-23 ◽  
Author(s):  
Siva Sankara Babu Chinka ◽  
Balakrishna Adavi ◽  
Srinivasa Rao Putti
Keyword(s):  
Numerical Analysis ◽  
Modal Analysis ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Damping Ratio ◽  
Crack Depth ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Crack Location

In this paper, the dynamic behavior of a cantilever beam without and with crack is observed. An elastic Aluminum cantilever beams having surface crack at various crack positions are considered to analyze dynamically. Crack depth, crack length and crack location are the foremost parameters for describing the health condition of beam in terms of modal parameters such as natural frequency, mode shape and damping ratio. It is crucial to study the influence of crack depth and crack location on modal parameters of the beam for the decent performance and its safety. Crack or damage of structure causes a reduction in stiffness, an intrinsic reduction in resonant frequencies, variation of damping ratios and mode shapes. The broad examination of cantilever beam without crack and with crack has been done using Numerical analysis (Ansys18.0) and experimental modal analysis. To observe the exact higher modes of beam, discretize the beam into small elements. An experimental set up was established for cantilever beam having crack and it was excited by an impact hammer and finally the response was obtained using PCB accelerometer with the help sound and vibration toolkit of NI Lab-view. After obtaining the Frequency response functions (FRFs), the natural frequencies of beam are estimated using peak search method. The effectiveness of experimental modal analysis in terms of natural frequency is validated with numerical analysis results. This paper contains the study of free vibration analysis under the influence of crack at different points along the length of the beam.

Detection of Cracks in Stationary Rotors via the Modal Frequency Changes Induced by a Roving Disc

2014 ◽  
Author(s):  
Z. N. Haji ◽  
S. O. Oyadiji
Keyword(s):  
Natural Frequencies ◽  
Crack Depth ◽  
Mode Shapes ◽  
Crack Identification ◽  
Open Crack ◽  
Suggested Approach ◽  
Rotor Systems ◽  
Crack Location ◽  
High Crack ◽  
Frequency Changes

In this study, a crack identification approach based on a finite element cracked model is presented to identify the location and depth ratios of a crack in rotor systems. A Bernoulli-Euler rotor carrying an auxiliary roving disc has been used to model the cracked rotor, in which the effect of a transverse open crack is modelled as a time-varying stiffness matrix. In order to predict the crack location in the rotor-disc-bearing system, the suggested approach utilises the variation of the normalized natural frequency curves versus the non-dimensional location of a roving disc which traverses along the rotor span. The merit of the suggested approach is to identify the location and sizes of a crack in a rotor by determining only the natural frequencies of the stationary rotor system. The first four natural frequencies are employed for the identification and localisation of a crack in the stationary rotor. Furthermore, this approach is not only efficient and practicable for high crack depth ratios but also for small crack depth ratios and for a crack close to or at the node of mode shapes, where natural frequencies are unaffected.

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

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

A statistics and optimization-based approach for crack parameter identification in curved beams

2017 ◽  
Vol 17 (4) ◽  
pp. 1008-1028 ◽  
Author(s):  
Palash Dey ◽  
Sudip Talukdar
Keyword(s):  
Genetic Algorithm ◽  
Response Surface ◽  
Crack Detection ◽  
Crack Depth ◽  
Research Work ◽  
Integrated Approach ◽  
Curved Beams ◽  
Horizontally Curved ◽  
Crack Location ◽  
Thin Walled

This article presents a study for detecting crack parameters (crack location and crack-depth ratio) in horizontally curved thin-walled channel section beams utilizing only dynamic information from a post-damage event based on combined statistical and optimization tools. A combined response surface methodology and genetic algorithm have been utilized in the present research work. Finite element computations based on design of experiment have been used in order to obtain the coefficients of a second-order polynomial model for the response surface function. Genetic algorithm is then used as a searching tool to determine the optimum parameters by minimizing an objective function which is formed as the root mean square of the errors between the computed responses from response surface functions and measured responses. Two cases of different subtended central angles are considered to illustrate the approach. Each case required 18 laboratory experiments to provide measured input to the proposed integrated approach. It was found that large variation can occur in the calculation of natural frequencies of thin-walled beams, when the effect of warping stiffness is neglected in mathematical model. This study reveals that the precision of the localization and quantification of cracks are dependent on subtended angle. The present method has great potential in crack detection as it does not require the response of an uncracked beam as baseline criteria.

Development of a Novel Algorithm for a Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. Karthikeyan ◽  
R. Tiwari ◽  
S. Talukdar
Keyword(s):  
Natural Frequency ◽  
Crack Detection ◽  
Beam Theory ◽  
Crack Size ◽  
Forced Response ◽  
Crack Model ◽  
Beam Model ◽  
Crack Location ◽  
Forced Responses ◽  
Crack Element

The present work aims at the development of a method for the crack detection, localization and sizing in a beam based on the transverse force and response signals. The Timoshenko beam theory is applied for transverse vibrations of the beam model. The finite element method is used for the cracked beam forced vibration analysis. An open transverse surface crack is considered for the crack model, which contains standard five flexibility coefficients. The effect of the proportionate damping is also included. A harmonic force of known amplitude with sine-sweep frequency is used to dynamically excite the beam, up to few flexible modes, which could be provided with the help of an exciter. In practice, linear degrees of freedom (DOFs) can be measured quite accurately; however, rotational DOFs are difficult to measure accurately. All rotational DOFs, except at crack element, are eliminated by a dynamic condensation scheme; for elimination of rotational DOFs at the crack element, a new condensation scheme is implemented. The algorithm is iterative in nature and starts with a presumption that a crack is present in the beam. For an assumed crack location, flexibility coefficients are estimated with the help of forced responses. The Tikhonov regularization technique is applied in the estimation of bounded crack flexibility coefficients. These crack flexibility coefficients are used to obtain the crack size by minimizing an objective function. With the help of the estimated crack size and measured natural frequency, the crack location is updated. The procedure iterates till the crack size and location get stabilized up to the desired level of accuracy. The algorithm has a potential to detect no crack condition also. The crack flexibility and damping coefficients are estimated as a by-product. Numerical examples, with the simply supported and cantilevered beams, are given to justify the applicability and versatility of the algorithm in practice. With the numerically simulated forced responses, which have the noise contamination and the error in the natural frequency measurements, the estimated crack parameters (i.e., the crack location and size) are in good agreement.

scholarly journals Numerical and experimental studies for crack detection of a beam-like structure using element stiffness index distribution method

2017 ◽  
Vol 39 (3) ◽  
pp. 203-214
Author(s):  
Nguyen Viet Khoa ◽  
Quang Van Nguyen ◽  
Nguyen Dinh Kien ◽  
Cao Van Mai ◽  
Dao Thi Bich Thao
Keyword(s):  
Stiffness Matrix ◽  
Crack Detection ◽  
Crack Depth ◽  
Experimental Studies ◽  
Mode Shapes ◽  
Stiffness Index ◽  
Distribution Method ◽  
Crack Location ◽  
Index Distribution ◽  
Global Stiffness Matrix

In this paper, numerical and experimental studies for crack detection of structures using "element stiffness index distribution" are presented. The element stiffness index distribution is defined as a vector of norms of sub-matrices corresponding to element stiffness matrices calculated from the reconstructed global stiffness matrix of the beam. When there is a crack at an element, the element stiffness index of that element will be changed. By inspecting the change in the element stiffness index distribution, the crack can be detected. A significant peak in the element stiffness index distribution is the indicator of the crack existence. The crack location is determined by the location of the peak and the crack depth can be determined from the height of the peak. The global stiffness matrix is calculated from the measured frequency response functions instead of mode shapes to avoid limitations of the mode shape-based methods for crack detection. Numerical simulation results for the cases of beam-like structures are provided. The experiment is carried out to justify the efficiency of the proposed method.

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