A new continuous model for flexural vibration analysis of a cracked beam

Behzad, Mahdi; Ebrahimi, Alireza; Meghdari, Ali

doi:10.2478/v10012-007-0062-5

Cited by 11 publications

(10 citation statements)

References 16 publications

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“…To verify the analytical expressions of the J-integrals in equations (28) numerical results show that the differences between the two methods are less than 3.8%, which demonstrates that equations (28) and (32) are valid for Euler-Bernoulli beam segments. Since the top and bottom segments are assumed to have the same transverse displacements and they can slide over each other in the axial direction 21 except at their ends, the stress intensity factors KⅡ from the FE and proposed methods are compared to verify the proposed J-integral approach, as shown in Table 2. The results show that the differences between the two methods are less than 2%, which further demonstrates that the proposed J-integral approach is valid for Euler-Bernoulli beam segments.…”

Section: Verification Of the J-integralsmentioning

confidence: 99%

“…As one of accurate and comprehensive methods, a modeling and simulation method can predict the dynamic characteristics of a cracked structure and provide some guidance to early detection of crack failure. Many previous works focused on an edge crack [9,[12][13][14][15][16][17][18][19][20][21][22][23][24] and multiple edge cracks [3,10,[25][26][27][28][29][30] in cantilever or simply supported beams. Some researchers have studied delaminations in beam structures [16, 31 -46 ].…”

Section: Introductionmentioning

confidence: 99%

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A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

Liu

Zhu

Charalambides

et al. 2016

Journal of Sound and Vibration

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As one of major failure modes of mechanical structures subjected to periodic loads, embedded cracks due to fatigue can cause catastrophic failure of machineries.Understanding the dynamic characteristics of a structure with an embedded crack is helpful for early crack detection and diagnosis. In this work, a new three-segment beam model with local flexibilities at crack tips is developed to investigate the vibration of a cantilever beam with a closed, fully embedded horizontal crack, which is assumed to be not located at its clamped or free end or distributed near its top or bottom side. The three-segment beam model is assumed to be a linear elastic system, and it does not account for the nonlinear crack closure effect; the top and bottom © 2016. This manuscript version is made available under the Elsevier user license http://www.elsevier.com/open-access/userlicense/1.0/ 2 segments always stay in contact at their interface during the beam vibration. It can model effects of local deformations in the vicinity of the crack tips, which cannot be captured by previous methods in the literature. The middle segment of the beam containing the crack is modeled by a mechanically consistent, reduced bending moment. Each beam segment is assumed to be an Euler-Bernoulli beam, and the compliances at the crack tips are analytically determined using a J-integral approach and verified using commercial finite element software. Using compatibility conditions at the crack tips and the transfer matrix method, the nature frequencies and mode shapes of the cracked cantilever beam are obtained. The three-segment beam model is used to investigate the effects of local flexibilities at crack tips on the first three natural frequencies and mode shapes of the cracked cantilever beam. A stationary wavelet transform (SWT) method is used to process the mode shapes of the cracked cantilever beam; jumps in single-level SWT decomposition detail coefficients can be used to identify the length and location of an embedded horizontal crack. Closed crack; J-integral; Three-segment beam model J J J J J J      (2) where the superscript r denotes the right part. For segments BC and DE, dY=0 and T i =0; hence 0 r BC J  , 0 r DE J  (3) For segment AB, one has c c c c J J J

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Section: Verification Of the J-integralsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

Liu

Zhu

Charalambides

et al. 2016

Journal of Sound and Vibration

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“…In equation (11) terms which are underlined in the potential energy expression are clearly the nonlinear terms. Separating linear and nonlinear terms and using equations (12) and (13) the maximum potential energy expression can be expressed as…”

Section: Energy Equationsmentioning

confidence: 99%

“…Behzad et al. 11 developed a continuous model for flexural vibration analysis of a cracked beam. Loya et al.…”

Section: Introductionmentioning

confidence: 99%

“…Extended Hamilton's principle is used to develop equation of motion and then solved it by multiple scale method. Behzad et al 11 developed a continuous model for flexural vibration analysis of a cracked beam. Loya et al 12 developed a model for cracked beam with a rotational and an extensional spring and solved for natural frequencies by a perturbation technique.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach

Panigrahi

Pohit

2015

Proceedings of the Institution of Mechanical Engineers, Part C:

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The present work accounts Timoshenko beam theory followed by Ritz approximation and an iterative technique to deal nonlinear free vibration problems of cracked Functionally Graded Material (FGM) beams based on neutral surface location. Using neutral surface as a reference rather than the midsurface reduces the complexity of nonlinear problems. It is assumed that crack always remains open. Analysis is carried out for clamped-clamped and clamped-free boundary conditions. Nonlinear frequencies and mode shapes corresponding to first three mode of vibration are obtained for the first time for different crack parameters, amplitudes of vibration and material indexes. The accuracy of the present solution is verified by comparing some of the obtained results with existing solutions. It can be concluded that present results are not only accurate but the methodology is very simple and easy to perform.

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Free Vibration of the Cracked Non-uniform Beam with Cross Section Varying as Polynomial Functions

et al. 2018

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A new continuous model for flexural vibration analysis of a cracked beam

Abstract: In this paper a new continuous model for vibration analysis of a beam with an

Cited by 11 publications

References 16 publications

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips

Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach

Free Vibration of the Cracked Non-uniform Beam with Cross Section Varying as Polynomial Functions

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