Vibrations of cracked functionally graded beams: General solution and application – A review

Khiem, Nguyen Tien

doi:10.15625/0866-7136/17986

Cited by 3 publications

(3 citation statements)

References 46 publications

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“…Moreover, it is assumed that the beam is cracked at positions 0 ≤ 𝑒 1 < 𝑒 2 < ⋯ < 𝑒 𝑛−1 < 𝑒 𝑛 ≤ ℓ and all the cracks are transverse and open with depths respectively (𝑎 1 , … , 𝑎 𝑛 ) as shown in Fig. 3 [19].…”

Section: Frequency Response Function Multiple Cracked Beamsmentioning

confidence: 99%

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A novel criterion for crack detection in beam structures by frequency response functions

Khiem,

Hai,

Toan

et al. 2023

Vietnam J. Mech.

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The frequency response function (FRF) is a fruitful attribute that includes almost all dynamical characteristics of a structure such as natural frequencies and modes, damping coefficients, or resonance and antiresonance conceptions. However, the complex feature of FRF has not been thoroughly employed for structural damage detection. In the present study, a novel indicator extracted from FRFs of beam structures is developed for crack identification. The damage indicator originated from the well-known mode assurance criterion (MAC) and therefore it is termed spectral assurance criterion (SAC). First, a coherence coefficient calculated from FRFs of intact and damaged beams and called herein spectral damage index (SDI) is analyzed for examining sensitivity of FRFs to crack. Then, SAC calculated for different FRFs of the same damaged structure is employed for crack detection by the so-called contour method. Results obtained in numerical examples of the crack detection problem show that SAC is really a novel and efficient criterion for crack identification in beams from measured FRFs.

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Section: Frequency Response Function Multiple Cracked Beamsmentioning

confidence: 99%

“…Since both the functions φ 0 (x) and h (x) satisfy the first two conditions in ( 9), the solution ( 19) also satisfies the boundary conditions. Therefore, putting (19) into remaining conditions (9) at the beam's right end yields…”

Section: Frequency Response Functionmentioning

confidence: 99%

A novel criterion for crack detection in beam structures by frequency response functions

Khiem,

Hai,

Toan

et al. 2023

Vietnam J. Mech.

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“…and, therefore, frequency equation ( 21) for simply supported beam with single crack is reduced to [11] f ss (λ) + γ 1 g ss (λ, e 1 ) = 0,…”

Section: Vibration Mode and Frequency Equationmentioning

confidence: 99%

A single degree of freedom model for cracked beam

Hai¹,

Nam

2023

Vietnam J. Mech.

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This paper presents a simplified model of cracked beam by single-degree-of-freedom system. Equivalence between the beam and SDOF models means that they have the same fundamental natural frequency and similar frequency response functions (FRFs). Similarity of FRFs is checked by using the frequency-domain assurance criterion acknowledged herein as spectral similarity index (SSI). Finally, FRFs of both the cracked beam and its simplified SDOF model have been examined versus crack location and depth using the so-called spectral damage index (SDI). Numerical results show that SDI is significantly sensitive to crack and could be used as a novel indicator for crack detection in beam by measurements of frequency response functions.

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Exact closed-form dynamic stiffness matrix of damaged frames comprising Timoshenko–Ehrenfest beams

Cannizzaro,

Fiore,

Caddemi

et al. 2024

Journal of Vibration and Control

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The present work proposes the extension of an exact distributional model for cracked beams to include the local influence on axial deformation on shear deformable beams. Axial, shear and flexural concentrated flexibilities are taken into account to model the damaged sections. Shear deformability is accounted for by adopting the Timoshenko–Ehrenfest model and exact closed-form solution of the mode shapes for multiple cracked beams are derived. On this ground, the final achievement of the work consists in the original formulation of the Dynamic Stiffness Matrix (DSM) with multiple cracked sections in exact closed form. The closed-form expression of the DSM allows the assemblage of the global DSM of a structure to conduct the free vibration analysis of damaged framed structures as well as for the study of frames with semi-rigid joints. This approach has the advantage to avoid any numerical procedure for the construction of the DSM as well as the introduction of further degrees of freedom (dofs) in correspondence of the damaged sections, keeping the size of the problem the same as in the intact configuration. Natural frequencies of the frames are determined by means of the Wittrick–Williams algorithm (W–W), then the mode shapes and modal forces are subsequently obtained in closed form. The proposed approach is validated with results available in literature for two portal frames characterized by the presence of cracks and semi-rigid joints, respectively. Finally, the potentiality of the approach, also in view of practical applications, is demonstrated analysing a multi-storey frame with semi-rigid connections.

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Vibrations of cracked functionally graded beams: General solution and application – A review

Cited by 3 publications

References 46 publications

A novel criterion for crack detection in beam structures by frequency response functions

A novel criterion for crack detection in beam structures by frequency response functions

A single degree of freedom model for cracked beam

Exact closed-form dynamic stiffness matrix of damaged frames comprising Timoshenko–Ehrenfest beams

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