The dynamic analysis of a cracked Timoshenko beam by the spectral element method

Krawczuk, Marek; Palacz, Magdalena; Ostachowicz, Wiesław

doi:10.1016/s0022-460x(02)01387-1

Cited by 143 publications

(68 citation statements)

References 13 publications

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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%

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Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

176

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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%

“…Krawczuk et al [29] used the same crack model to develop a spectral finite element for the Timoshenko cracked beam. However, the cited authors do not consider any discontinuity in the transverse deflection at the cracked section.…”

Section: Introductionmentioning

confidence: 99%

Natural frequencies for bending vibrations of Timoshenko cracked beams

Loya

Rubio

Fernández-Sáez

2006

Journal of Sound and Vibration

176

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“…Also, the SFE model of a cracked Timoshenko beam is presented in [Krawczuk et al 2003], where a massless spring, with bending and shear flexibilities computed using Castigliano's theorem and the laws of fracture mechanics is used to model the crack. A review of damage detection using SFEM is presented in [Ostachowicz 2008].…”

Section: Introductionmentioning

confidence: 99%

A wave-based damage index for the analysis of the filtered response of damaged beams

Apetre

Ruzzene

Hanagud

et al. 2008

JOMMS

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This paper introduces a wave propagation-based damage index which relies on the evaluation of the strain energy distribution associated with propagating waves. The presence of localized damages typically distorts the wavefield by causing reflections and diffractions. The evaluation of such distortions, in reference to the wavefield corresponding to the undamaged structure, can be used as an indicator which potentially locates, quantifies and classifies the damage.The damage index formulation is first illustrated through a numerical model of a beam with a small notch, modeled as a localized thickness reduction. The beam's wave propagation response is simulated through the combined application of perturbation techniques and the spectral finite element method. The perturbation approach and a first order model for the beam capture the coupling between bending and axial behavior caused by the damage, and allow the prediction of mode conversion phenomena. The perturbation solution allows direct comparison between undamaged and damaged strain energy contributions, which are directly associated with perturbation solutions of different orders. The resulting damage index locates the damage along the beam length and estimates its severity.Experimentally, the damage index is implemented by considering full wavefield measurements obtained through a scanning laser vibrometer. The undamaged reference response is derived directly from measurements on the damaged component, through the application of a filtering procedure operating in the wavenumber/frequency domain.

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“…크 랙을 가지는 보 형태의 구조물의 해석은 오일러-베 르누이 보 이론을 적용한 연구 (4,5) 와 티모센코 보 이 론을 적용하여 크랙이 전체 구조물의 동특성에 미치 는 영향에 대한 연구 결과가 발표되고 있다 (6) . 최근 종동력을 받는 티모센코 보의 안정성에 미치는 크랙 의 영향에 대한 연구 (7) 와 다중크랙을 갖는 보의 고유 진동수 변화에 대한 연구도 발표되어지고 있다 (8,9) .…”

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Study on Detection of Crack and Damage for Cantilever Beams Using Vibration Characteristics

Son

Ahn²,

Yoon³

2009

Transactions of the Korean Society for Noise and Vibration Engi

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In this paper, the purpose is to investigate the natural frequency of a cracked Timoshenko cantilever beams by FEM(finite element method) and experiment. In addition, a method for detection of crack in a cantilever beams is presented based on natural frequency measurements. The governing differential equations of a Timoshenko beam are derived via Hamilton's principle. The two coupled governing differential equations are reduced to one fourth order ordinary differential equation in terms of the flexural displacement. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The detection method of a crack location in a beam based on the frequency measurements is extended here to Timoshenko beams, taking the effects of both the shear deformation and the rotational inertia into account. The differences between the actual and predicted crack positions and sizes are less than 6 % and 23 % respectively.

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The dynamic analysis of a cracked Timoshenko beam by the spectral element method

Cited by 143 publications

References 13 publications

Natural frequencies for bending vibrations of Timoshenko cracked beams

Natural frequencies for bending vibrations of Timoshenko cracked beams

A wave-based damage index for the analysis of the filtered response of damaged beams

Study on Detection of Crack and Damage for Cantilever Beams Using Vibration Characteristics

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