scholarly journals Multiple crack identification in stepped beam by measurements of natural frequencies

2014 ◽  
Vol 36 (2) ◽  
pp. 119-132
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung ◽  
Vu Thi An Ninh
Keyword(s):  
Crack Detection ◽  
Natural Frequencies ◽  
Rayleigh Quotient ◽  
Crack Identification ◽  
Multiple Cracks ◽  
Simple Relationship ◽  
Multiple Crack ◽  
Scanning Method ◽  
New Approach ◽  
Efficient Procedure

A new approach is proposed for calculating natural frequencies and crack detection in a stepped cantilever beam with arbitrary number of cracks. This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. The proposed technique called crack scanning method is illustrated and validated by numerical results.

scholarly journals Change in mode shape nodes of multiple cracked bar: I. The theoretical study

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Linh Khue
Keyword(s):  
Explicit Expression ◽  
Mode Shape ◽  
Crack Detection ◽  
Theoretical Study ◽  
Multiple Cracks ◽  
Axial Vibration ◽  
Multiple Crack ◽  
Important Indicator ◽  
Natural Modes ◽  
Exact Positions

In present paper change in position of mode shape nodes induced by multiple cracks in bar is studied with purpose to use for the multiple crack detection from measured mode shape nodes. First, there is derived an explicit expression for natural modes in axial vibration of multiple cracked bar that allows obtaining exact positions of the node in the case of single and double crack. The change in mode shape nodes induced by multiple cracks provides an important indicator for crack localization in bar. Finally, a procedure for multiple crack detection by using mode shape nodes has been proposed and examined in an example of application.

Multiple crack identification in frame structures using a hybrid Bayesian model class selection and swarm-based optimization methods

2017 ◽  
Vol 17 (1) ◽  
pp. 39-58 ◽  
Author(s):  
Laleh Fatahi ◽  
Shapour Moradi
Keyword(s):  
Bayesian Model ◽  
Artificial Bee Colony Algorithm ◽  
Artificial Bee Colony ◽  
Natural Frequencies ◽  
Optimization Methods ◽  
Crack Identification ◽  
Multiple Crack ◽  
Bee Colony ◽  
Model Class ◽  
Model Class Selection

Crack identification in engineering structures has been widely investigated by researchers. Most of the literature on multiple crack identification, however, has focused on rather simple structures like beams and it is often assumed that the number of cracks is known while this is not a practical assumption. In this article, multiple crack identification in frame structures is investigated based on experimental vibration data using the Bayesian model class selection and swarm-based optimization methods to identify both the number of cracks and their characteristics. To this end, first, the numerical model of the intact frame is updated based on the natural frequencies of the intact state using the particle swarm inspired multi-elitist artificial bee colony algorithm. After updating the intact model of the structure, a set of numerical models of the cracked frame with different numbers of cracks is constructed. Since the number of cracks is not known a priori, the Bayesian model class selection is employed to find the most plausible model class in order to predict the number of cracks. Then, the parameters of the cracks are identified using the particle swarm inspired multi-elitist artificial bee colony algorithm. Instead of pinpointing to one optimal solution obtained after a large number of function evaluations, a set of best solutions whose objective values are less than 10−5 are recorded and the regions where the best solutions are concentrated are identified to see how the solution would differ if less number of function evaluations is employed. To fully assess the effectiveness of this approach, both numerical and experimental examples are utilized. The results confirm the effectiveness of the proposed method for identifying multiple cracks in the frames using a few experimental natural frequencies of the structure. The effect of using more natural frequencies on the accuracy of the location and depth of the cracks is also studied.

A hybridised CSAGA method for damage detection in structural elements

2018 ◽  
Vol 19 (4) ◽  
pp. 407 ◽  
Author(s):  
Sasmita Sahu ◽  
Priyadarshi Biplab Kumar ◽  
Dayal R. Parhi
Keyword(s):  
Damage Detection ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Clonal Selection ◽  
Multiple Cracks ◽  
Clonal Selection Algorithm ◽  
Hybrid Technique ◽  
Structural Elements ◽  
Cracked Structures ◽  
Cracked Structure

In recent years, significant developments have been noticed in nondestructive techniques for damage detection in cracked structures. Some of the proposed methods can be used to find out the existence of the crack; other methods locate and simultaneously find out the damage severity. In the current investigation, a novel hybridised method is proposed for damage detection in structural elements. The proposed method can be used to investigate both location and nature of damage in structures within a reasonable time limit. The problem in the current analysis requires a set of dynamic parameters that depend on the dynamics of the cracked structure due to the presence of the crack. In the present study, the first three natural frequencies of a structure are considered as the inputs to find out the damage location. A finite element method is used to generate the first three natural frequencies of a cracked cantilever beam with multiple cracks. A method hybridizing the nature-inspired artificial intelligence techniques has been implemented for crack detection. Here, clonal selection algorithm and genetic algorithm have been integrated to design the framework of the hybrid technique. The changes in the natural frequencies are given as inputs to the hybrid technique and the output from the technique is the locations of damage.

Crack detection of plate structures using differential quadrature method

2012 ◽  
Vol 227 (7) ◽  
pp. 1495-1504 ◽  
Author(s):  
S Moradi ◽  
P Alimouri
Keyword(s):  
Finite Length ◽  
Crack Detection ◽  
Optimization Problem ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Bees Algorithm ◽  
Crack Identification ◽  
Open Crack ◽  
Quadrature Method

In this study, the problem of crack identification in plates is investigated using the differential quadrature method. The crack, which is assumed to be open, is modeled by the extended rotational spring. The crack, with finite length, divides the plate into six segments. Then, the differential quadrature is applied to the governing differential equations of motion of each segment and the corresponding boundary and continuity conditions. An eigenvalue analysis will be performed on the resulting system of algebraic equations to obtain the natural frequencies of the cracked plate. Here, the crack detection practice is considered as an optimization problem, and the location, size, and depth of the crack are regarded as the design variables. The weighted sum of the squared errors between the measured and computed natural frequencies is used as the objective function. The Bees algorithm, a swarm-based evolutionary optimization technique, is used to solve the optimization problem. To insure the integrity and robustness of the presented method, extensive experimental case studies are carried out on the cantilever plates having a finite-length open crack parallel to the clamped edge. The results show that the crack parameters can be predicted well by the presented methodology.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

scholarly journals Detection of multiple cracks in a beam by means natural frequencies of transverse vibrations

2020 ◽  
pp. 19-26
Author(s):  
Иван Михайлович Лебедев ◽  
Ефим Ильич Шифрин
Keyword(s):  
Arbitrary Number ◽  
Natural Frequencies ◽  
Multiple Cracks ◽  
Transverse Cracks ◽  
Numerical Examples ◽  
Transverse Vibrations ◽  
End Conditions

Рассматривается задача обнаружения множественных, поперечных трещин в стержне с помощью собственных частот поперечных колебаний. В недавней статье авторов доказано, что любое количество трещин однозначно восстанавливается по трем спектрам, отвечающим трем различным типам краевых условий. В статье также предложен алгоритм идентификации повреждений, вносимых трещинами. Помимо этого, высказано предположение, что для однозначной идентификации трещиноподобных дефектов на самом деле достаточно знать два спектра. Для проверки этого предположения разработана модификация предложенного ранее численного алгоритма. Рассмотрены численные примеры. Полученные результаты дают основание полагать, что высказанное предположение справедливо. A problem of detection of multiple transverse cracks in a beam by means of natural frequencies of transverse vibrations is considered. It is proved in the recent paper of the authors that an arbitrary number of cracks can be uniquely determined by three spectra corresponding to three types of the end conditions. An algorithm of reconstruction the damages corresponding the cracks is also developed. In addition, it was assumed that the cracks can be detected using only two spectra. To verify this supposition a modification of the previously developed algorithm is proposed. Numerical examples are considered. The obtained results confirm the assumption.

scholarly journals Crack Detection through the Change in the Normalized Frequency Shape

Vibration ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 56-68
Author(s):  
Mustapha Dahak ◽  
Noureddine Touat ◽  
Tarak Benkedjouh
Keyword(s):  
Stiffness Matrix ◽  
Electrical Discharge ◽  
Inverse Method ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Electrical Discharge Machining ◽  
Element Model ◽  
Experimental Application ◽  
Flexibility Matrix ◽  
Crack Position

The objective of this work is to use natural frequencies for the localization and quantification of cracks in beams. First, to study the effect of the crack on natural frequencies, a finite element model of Euler–Bernoulli is presented. Concerning the damaged element, the stiffness matrix is calculated by the theory of fracture mechanics, by inverting the flexibility matrix. Then, in order to detect damage, we are going to show that the shape given by the change in the natural frequencies is as function of the damage position only. Thus, the crack is located by the correlation between the shape of the measured frequencies and those obtained by the finite elements, where the position that gives the calculated shape which is the most similar to the measured one, indicates the crack position. After the localization, an inverse method will be applied to quantify the damage. Finally, an experimental application is presented to show the real applicability of the method, in which the crack is introduced by using an Electrical Discharge Machining. The results confirm the applicability of the method for the localization and the quantification of cracks.

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