Modelling of Transverse Vibration of Short Beams for Crack Detection and Measurement of Crack Extension

Lele, Suvrat P.; Maiti, Sukumar

doi:10.1006/jsvi.2002.5059

Cited by 157 publications

(67 citation statements)

References 15 publications

(20 reference statements)

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“…The contribution of the extensional spring to the strain energy of the system is small in comparison with that of the rotational spring and many authors neglect this effect to analyze the cracked beam dynamic behavior [10,14,29]. However, we have included here the presence of an extensional spring at the crack location (and the corresponding discontinuity in the vertical displacement) for coherency with the general derivation of compliance for the cracked beams presented by Okamura et al [30], (see also the work by Tharp [31]).…”

Section: Problem Formulationmentioning

confidence: 99%

“…The solution for each segment V 1 ðxÞ and C 1 ðxÞ for the left part and V 2 ðxÞ and C 2 ðxÞ for the right part can be written as [10,13,14] …”

Section: ''Direct Solution''mentioning

confidence: 99%

“…Lele and Maiti [10] have modelled the presence of a crack by means a rotational spring as in the Euler Bernoulli cracked beam problem. Krawczuk et al [29] used the same crack model to develop a spectral finite element for the Timoshenko cracked beam.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

177

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The natural frequencies for bending vibrations of Timoshenko cracked beams with simple boundary conditions have been obtained. The beam is modelled as two segments connected by two massless springs (one extensional and another one rotational). This model promotes discontinuities in both vertical displacement and rotation due to bending, which are proportional to shear force and bending moment transmitted by the cracked section, respectively. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section. The problem is also solved by the perturbation method and both procedures are applied to the case of a simply supported cracked beam. The results show that the perturbation method provides simple expressions for the natural frequencies of cracked beams and it gives good results for shallow cracks. E mail address: ppfer@ing.uc3m.es (J. Ferna´ndez Sa´ez).

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Section: Problem Formulationmentioning

confidence: 99%

“…The solution for each segment V 1 ðxÞ and C 1 ðxÞ for the left part and V 2 ðxÞ and C 2 ðxÞ for the right part can be written as [10,13,14] …”

Section: ''Direct Solution''mentioning

confidence: 99%

See 1 more Smart Citation

Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

177

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“…Except the approach in [22], all of the frequencies-based methods are model-based. Most methods for damage identification in beam-type structures rely on Euler-Bernoulli beam theory (except the shear deformable model in [15]) and modeling crack as a rotational spring. It is well known that Euler-Bernoulli beam theory over-predicts natural frequencies in short beams and high frequency bending modes.…”

Section: Limitations Of Frequency-based Methodsmentioning

confidence: 99%

Vibration-based Damage Identification Methods: A Review and Comparative Study

Fan

Qiao

2010

Structural Health Monitoring

1,609

215

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A comprehensive review on modal parameter-based damage identification methods for beam-or plate-type structures is presented, and the damage identification algorithms in terms of signal processing are particularly emphasized. Based on the vibration features, the damage identification methods are classified into four major categories: natural frequency-based methods, mode shape-based methods, curvature mode shape-based methods, and methods using both mode shapes and frequencies, and their merits and drawbacks are discussed. It is observed that most mode shape-based and curvature mode shape-based methods only focus on damage localization. In order to precisely locate the damage, the mode shape-based methods have to rely on optimization algorithms or signal processing techniques; while the curvature mode shape-based methods are in general a very effective type of damage localization algorithms. As an implementation, a comparative study of five extensively-used damage detection algorithms for beam-type structures is conducted to evaluate and demonstrate the validity and effectiveness of the signal processing algorithms. This brief review aims to help the readers in identifying starting points for research in vibration-based damage identification and structural health monitoring and guides researchers and practitioners in better implementing available damage identification algorithms and signal processing methods for beam-or plate-type structures.

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“…Zheng and Fan [7] used modified Fourier series to investigate vibration of the cracked Timoshenko beams with different boundary conditions. Lele and Maiti [8] proposed a new method based on the Timoshenko beam theory considering shear effects. In this method, the characteristic equation to obtain the natural frequencies for the cantilever cracked beam is expressed as an eighth-order determinant equated to zero.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

Torabi¹,

Afshari²,

Heidari-Rarani³

2014

ujme

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In this paper, differential quadrature element method (DQEM) is used to analyze the free transverse vibration of a multiple cracked non-uniform Timoshenko blade rotating with a constant angular velocity. The blade's deflection is assumed to be small so that the nonlinear terms can be neglected. Governing equations, compatibility conditions at the damaged cross-sections and boundary conditions are derived and formulated by the differential quadrature rules. First, the precision of the proposed method is confirmed by the exact solutions available in the literature. Then, the effect of angular velocity value as well as the location, depth and numbers of the cracks are investigated on the natural frequencies of the blade. The advantages of the proposed method are applicable for blades with any arbitrary variable section and less time-consuming for cases with several cracks.

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Modelling of Transverse Vibration of Short Beams for Crack Detection and Measurement of Crack Extension

Cited by 157 publications

References 15 publications

Natural frequencies for bending vibrations of Timoshenko cracked beams

Natural frequencies for bending vibrations of Timoshenko cracked beams

Vibration-based Damage Identification Methods: A Review and Comparative Study

Free Vibration Analysis of a Rotating Non-Uniform Blade with Multiple Open Cracks Using DQEM

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