Analytical Approach to Free Vibrations of Cracked Timoshenko Beams Made of Functionally Graded Materials

Ferezqi, Hamid Zabihi; Tahani, Masoud; Toussi, Hamid Ekhteraei

doi:10.1080/15376494.2010.488608

Cited by 24 publications

(9 citation statements)

References 19 publications

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“…Furthermore, Ke et al [5] investigated the free vibration of beams made of functionally graded materials (FGMs) with an open edge crack based on Timoshenko beam theory. Similar work for free vibrations of cracked FGM beams was performed by Ferezqi et al [6] using the wave method based on Timoshenko beam theory.…”

Section: Introductionmentioning

confidence: 85%

“…Understanding of the vibration characteristics of cracked structures is of prime importance in structural health monitoring and non-destructive damage evaluation because the predicted vibration data can be used to detect, locate, and quantify the extent of the cracks or damages in a structure. Many free vibration and dynamic response of matrix cracked beams based on the Euler-Bernoulli beam model and Timoshenko beam model are available in the literature, for example [1][2][3][4][5][6]. Among those, Krawczuk and Ostachowicz [1] calculated the eigenfrequencies of a FRC cantilever beam with a transverse on-edge…”

Section: Introductionmentioning

confidence: 98%

See 1 more Smart Citation

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

Fan

Wang

2015

Composite Structures

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Section: Introductionmentioning

confidence: 85%

Section: Introductionmentioning

confidence: 98%

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

Fan

Wang

2015

Composite Structures

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“…Yu and Chu used the p-version of the finite element method to study the transverse vibration characteristics of cracked FGB [5]. Ferezqi et al presented an analytical investigation of the free vibrations of a FG cracked Timoshenko beam employing a wave approach [6]. Lien et al used [7] an alternative approach called dynamic stiffness method to establish a new form of frequency DIAGNOSTYKA, Vol.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Chajdi¹,

Adri²,

Bikri³

et al. 2021

Diagnostyka

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Geometrically non-linear vibrations of functionally graded Euler-Bernoulli beams with multi-cracks, subjected to a harmonic distributed force, are examined in this paper using a theoretical model based on Hamilton's principle and spectral analysis. The homogenisation procedure is performed, based on the neutral surface approach, and reduces the FG beams analysis to that of an equivalent homogeneous multi-cracked beam. The so-called multidimensional Duffing equation obtained and solved using a simplified method (second formulation) previously applied to various non-linear structural vibration problems. The curvature distributions associated to the multi-cracked beam forced deflection shapes are obtained for each value of the excitation level and frequency. The parametric study performed in the case of a beam and the detailed numerical results are given in hand to demonstrate the effectiveness of the proposed procedure, and in the other hand conducted to analyse many effects such as the beam material property, the presence of crack, the vibration amplitudes and the applied harmonic force on the non-linear dynamic behaviour of FG beams.

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“…There are plenty of studies on free vibration behaviour and characteristics of uniform cross-section homogeneous and composite intact structures (Erdurcan and Cunedioğlu, 2020; Jiang et al, 2018; Kim and Shin, 2008; Mohanty et al, 2013; Zahedinejad, 2016; Zhang et al, 2020) and cracked structures (Cunedioglu, 2015; Ferezqi et al, 2010; Gayen and Chakraborty, 2016; Gayen et al, 2017a, 2017b, 2018; Han et al, 2020; Kisa and Brandon, 2000; Kisa et al, 1998; Liu et al, 2017; Papadopoulos, 2004; Papadopoulos and Dimarogonas, 1987; Shabani and Cunedioglu, 2019).…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

Cunedioĝlu

Shabani

2020

Advances in Structural Engineering

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Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

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Analytical Approach to Free Vibrations of Cracked Timoshenko Beams Made of Functionally Graded Materials

Cited by 24 publications

References 19 publications

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

Nonlinear vibration of matrix cracked laminated beams containing carbon nanotube reinforced composite layers in thermal environments

Analysis of the associated stress distributions to the nonlinear forced vibrations of functionally graded multi-cracked beams

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

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