scholarly journals Free vibration of a cracked double-beam carrying a concentrated mass

2016 ◽  
Vol 38 (4) ◽  
pp. 279-293
Author(s):  
Nguyen Viet Khoa ◽  
Nguyen Van Quang
Keyword(s):  
Wavelet Transform ◽  
Free Vibration ◽  
Crack Detection ◽  
Mode Shapes ◽  
Sharp Change ◽  
Concentrated Mass ◽  
Crack Location ◽  
Double Beam ◽  
Arbitrary Position ◽  
The Relationship

This paper presents the free vibration of a cracked double-beam carrying a concentrated mass located at an arbitrary position. The double-beam consisting of two different simply supported beams connected by an elastic medium is modelled by using finite element method. The influence of the concentrated mass on the frequencies and mode shapes is investigated. The relationship between the natural frequency and the location of concentrated mass is established and related to the mode shapes. The numerical simulations show that when there is a crack, the frequency of the double-beam changes sharply when the concentrated mass is located close to the crack position. This sharp change can be amplified by wavelet transform and this is useful for crack detection. The crack location can be determined by the location of peaks in the wavelet transform of the relationship between frequency and mass location.

Damage Detection of Cantilever Beams Based on Derivatives of Mode Shapes

2014 ◽  
Vol 488-489 ◽  
pp. 817-820
Author(s):  
Jin Quan Guo ◽  
Fen Lan Ou ◽  
Jian Feng Zhong ◽  
Shun Cong Zhong ◽  
Xiao Xiang Yang ◽  
...  
Keyword(s):  
Mode Shape ◽  
Crack Detection ◽  
Shape Change ◽  
Approximation Error ◽  
Mode Shapes ◽  
Difference Approximation ◽  
Cantilever Beams ◽  
Crack Location ◽  
Displacement Mode ◽  
Derivatives Of

For the small crack detection (crack ration less than 5%), the derivatives of mode shapes of cantilever beams were used for crack detection in the beams. These derivatives consist of the slope, curvature and rate of curvature, which are the first, second and third derivatives of the displacement mode shape respectively. The presence of a crack results in a slight change in the mode shape of a structure which is manifested as a small discontinuity in the response at the crack location. It is hard to detect small cracks in beams using the direct data of mode shape change. But when the first, second and third derivatives of the displacement mode shape, that is the slope, curvature and rate of curvature, respectively, of the cracked cantilever beam provide a progressively better indication of the presence of a crack. However, `noise' effects due to the difference approximation error also begin to be magnified at higher derivatives so that it is not advantageous to go beyond the third derivatives of mode shapes. For the intact beam, these derivatives are smooth curves. So the local peaks or discontinuity on the slope, curvature and rate of curvature modal curves can be used to indicate abnormal mode shape changes at those positions. In this way, these local peak positions can be used to detect and locate cracks in the structure. The modal responses of the damaged and intact cantilever beams used were computed using the finite element method.

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.

Determination of mode shapes using wavelet transform of free vibration data

2013 ◽  
Vol 83 (6) ◽  
pp. 907-921 ◽  
Author(s):  
M. R. Ashory ◽  
M. M. Khatibi ◽  
M. Jafari ◽  
A. Malekjafarian
Keyword(s):  
Wavelet Transform ◽  
Free Vibration ◽  
Mode Shapes ◽  
Vibration Data

Crack Location in Beams Using Wavelet Analysis

2013 ◽  
Vol 569-570 ◽  
pp. 1021-1028 ◽  
Author(s):  
Mario Solís ◽  
Mario Algaba ◽  
Pedro Galvín
Keyword(s):  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Curve Fitting ◽  
Spline Interpolation ◽  
Mode Shapes ◽  
Steel Beams ◽  
Crack Location ◽  
Interpolation Technique ◽  
The Difference ◽  
Spline Interpolation Technique

This paper applies a methodology for damage detection in beams proposed by the authors. The methodology is based on a continuous wavelet analysis of the difference of mode shapes between a damaged state and a reference state. The wavelet transform is used to detect changes in the mode shapes induced by damage. The wavelet coefficients for each mode are added up and normalized to unity in order to obtain a clear and precise damage assessment. A curve fitting approach reduces the effect of experimental noise in the mode shapes. When only a small number of measuring points are available, a cubic spline interpolation technique provides additional “virtual” measuring points. The interpolation technique may also be used when measuring points are not equally spaced. It also serves as a softening technique of the mode shapes when applied, and no curve fitting approach is used in that case. An antisymmetric extension at both ends of the mode shapes is used to avoid the edge effect in the wavelet transform. The paper presents the results obtained for steel beams with an induced crack. Several sizes and locations of the crack have been considered. The paper addresses several issues affecting the accuracy of the proposed methodology, such as the number of measuring points and the effect of the extension, curve fitting and interpolation techniques.

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.

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 Cracks in Beams With Auxiliary Mass Spatial Probing by Stationary Wavelet Transform

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Shuncong Zhong ◽  
S. Olutunde Oyadiji
Keyword(s):  
Wavelet Transform ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Experimental Testing ◽  
Crack Depth ◽  
Accurate Estimation ◽  
Stationary Wavelet Transform ◽  
Crack Location ◽  
Order Curve ◽  
Auxiliary Mass

This paper proposes a new approach based on auxiliary mass spatial probing by stationary wavelet transform (SWT) to provide a method for crack detection in beamlike structure. SWT can provide accurate estimation of the variances at each scale and facilitate the identification of salient features in a signal. The natural frequencies of a damaged beam with a traversing auxiliary mass change due to the change in flexibility and inertia of the beam as the auxiliary mass is traversed along the beam. Therefore, the auxiliary mass can enhance the effects of the crack on the dynamics of the beam and, therefore, facilitate the identification and location of damage in the beam. That is, the auxiliary mass can be used to probe the dynamic characteristic of the beam by traversing the mass from one end of the beam to the other. However, it is difficult to locate the crack directly from the graphical plot of the natural frequency versus axial location of auxiliary mass. This curve of the natural frequencies can be decomposed by SWT into a smooth, low order curve, called approximation coefficient, and a wavy, high order curve called the detail coefficient, which includes crack information that is useful for damage detection. The modal responses of the damaged simply supported beams with auxiliary mass used are computed using the finite element method (FEM). Sixty-four cases are studied using FEM and SWT. The efficiency and practicability of the proposed method is illustrated via experimental testing. The effects of crack depth, crack location, auxiliary mass, and spatial probing interval are investigated. From the simulated and experimental results, the efficiency of the proposed method is demonstrated.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

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