On the static deformation and frequency analysis of functionally graded porous circular beams

Sayyad, Atteshamuddin S.; Avhad, Pravin V.; Hadji, Lazreg

doi:10.1016/j.finmec.2022.100093

Cited by 30 publications

(10 citation statements)

References 44 publications

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“…and applying the superposition principle, the solution of equation (11) for the cracked nanobeam can be obtained as…”

Section: Free Vibrations Of Multiple Cracked Fgm Nanobeamsmentioning

confidence: 99%

“…where the first term is the solution (18) of the intact FGM nanobeam, and the second term is the solution (23) of the cracked nanobeam at the distance e. Based on the recurrent relation, the solution of equation (11) for the nanobeam with multiple cracks can be obtained as…”

Section: Free Vibrations Of Multiple Cracked Fgm Nanobeamsmentioning

confidence: 99%

“…Currently, there are about ten size effect theories, and each of these theories has a determined number of constants to manifest the behaviour of the material. [3][4][5][6][7][8][9][10][11] For this reason, Eringen's Nonlocal Elasticity Theory (NET), 12 Modified Couple Stress Theory 13 and Consistent Couple Stress theory 14 have been chosen to analyse nanostructures because of only one additional parameter required. Generally, the NETbased models have been used for nanostructures whereas modified versions of couple stress theories have been utilised for microstructures.…”

Section: Introductionmentioning

confidence: 99%

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Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Lien,

Dinh,

Thang

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams with arbitrary boundary conditions based on the Nonlocal Elasticity Theory (NET) and the Timoshenko beam theory are presented. The NET considering the size effect of nanostructures is applied. FGM properties vary nonlinearly along the height of the beam. A crack model using two springs with stiffness depending on the crack depth is applied. The proposed solutions are provided explicitly as functions of integration constants determined from the standard boundary conditions. Frequency equations, that established in the form of the determinant of the matrix 3 × 3 order for arbitrary boundary conditions, are applied to analyse free vibration. Expressions for the mode shapes are given explicitly. The effects of geometry, material, nonlocal and crack parameters on the free vibration of the multiple cracked nanobeam are then analysed in detail.

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“…and applying the superposition principle, the solution of equation (11) for the cracked nanobeam can be obtained as…”

Section: Free Vibrations Of Multiple Cracked Fgm Nanobeamsmentioning

confidence: 99%

Section: Free Vibrations Of Multiple Cracked Fgm Nanobeamsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Lien,

Dinh,

Thang

2023

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…The polynomial HSDTs employ the Taylor series expansion [8][9][10][11] for the transverse shear and normal deformation. However, the non-polynomial models consider a warping function to accommodate the shear deformation through exponential [12][13][14], trigonometric [15][16][17], hyperbolic [18][19][20], inverse trigonometric [21], and inverse hyperbolic [22][23][24] approaches, and many more. The non-polynomial models involve fewer unknowns and substantially reduce the complexity of modeling in comparison to the higher-order polynomial theories.…”

Section: Introductionmentioning

confidence: 99%

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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“…The flexural vibration analysis of beams made of FGMs with various boundary conditions was considered using Chebyshev collocation method by Wattanasakulpong and Chaikittiratana [22]. Sayyad et al [23] studied the static deformation and free vibration analysis of simply supported porous FG circular beams considering the effects of even and uneven porosities using Navier solution. A modified series solution for free vibration analyses of moderately thick porous FG deep curved and straight beams was investigated by Zhao et al [24].…”

Section: Introductionmentioning

confidence: 99%

Bending and Buckling Analysis of Porous 2D Functionally Graded Beams with Exponential Material Property Variation

Adıyaman,

TURAN

2023

Preprint

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The bending and buckling analysis of porous two-directional (2D) functionally graded (FG) beams was conducted using a higher-order shear deformation theory (HSDT). The introduction of exponential functions to depict changes in material properties is a novel approach in the static analysis of 2D FG beams. Three distinct porosity distribution functions were taken into account. The governing equations were formulated through the application of Lagrange’s principle. During the numerical analysis, a finite element comprising two nodes and eight degrees of freedom (DOFs) was utilized. This choice facilitated accurate and efficient solutions, even for shorter beams, without the need for a shear correction factor. Notably, the obtained shear stresses aligned with actual values, registering as zero at both the top and bottom of the beam. The obtained results of the study were validated against findings reported in the literature. A parametric study was carried out to investigate the effects of porosity, porosity distributions, gradation parameters, slenderness, and boundary conditions on the non-dimensional deflections, stresses, critical buckling loads, and buckling mode shapes. It was found that both porosity and the distribution of porosity have noticeable effects on the static analysis of the beams.

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On the static deformation and frequency analysis of functionally graded porous circular beams

Cited by 30 publications

References 44 publications

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Exact closed-form solutions for the free vibration analysis of multiple cracked FGM nanobeams

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

Bending and Buckling Analysis of Porous 2D Functionally Graded Beams with Exponential Material Property Variation

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