Vibration characteristics of two-dimensional FGM nanobeams with couple stress and surface energy under general boundary conditions

Attia, Mohamed A.; Shanab, Rabab A.

doi:10.1016/j.ast.2021.106552

Cited by 27 publications

(9 citation statements)

References 109 publications

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“…Young's modulus, Poisson's ratio, and the bulk mass density of the metallic constituent are, respectively, E m 90 GPa, ν m 0. 3.1688 kg/m 2 , respectively, [70]. Since the value of the material length scale parameter (MLSP) differs from a material to another, it is not reasonable to assume a constant MLSP in FGMs.…”

Section: Resultsmentioning

confidence: 99%

“…Power law was used to express the gradation of the material properties of the bulk continuum in the thickness and length directions, whereas the surface elastic constants were assumed to vary in thickness direction only, and the nonlocal parameter was assumed to be spatially-independent. Shanab and Attia [68][69][70] studied the bending, buckling, and vibration characteristics of uniform and tapered BDFG Euler-Bernoulli and Timoshenko micro/nanobeams in the framework of the MCST and GM-SET. Unlike [67], all the material properties of the bulk and surface continuums were assumed to vary in both the thickness and length directions via power law.…”

Section: Introductionmentioning

confidence: 99%

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On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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This paper presents an investigation of the dynamic behavior of bi-directionally functionally graded (BDFG) micro/nanobeams excited by a moving harmonic load. The formulation is established in the context of the surface elasticity theory and the modified couple stress theory to incorporate the effects of surface energy and microstructure, respectively. Based on the generalized elasticity theory and the parabolic shear deformation beam theory, the nonclassical governing equations of the problem are obtained using Lagrange’s equation accounting for the physical neutral plane concept. The material properties of the beam smoothly change along both the axial and thickness directions according to power-law distribution, accounting for the gradation of the material length scale parameter and the surface parameters, i.e., residual surface stress, two surface elastic constants, and surface mass density. Using trigonometric Ritz method (TRM), the trial functions denoting transverse, axial deflections, and rotation of the cross sections of the beam are expressed in sinusoidal form. Then, with the aid of Lagrange’s equation, the system of equations of motion are derived. Finally, Newmark method is employed to find the dynamic responses of BDFG subjected to a moving harmonic load. To validate the present formulation and solution method, some comparisons of the obtained fundamental frequency and dynamic response with those available in the literature are performed. A parametric study is performed to extensively explore the impact of the key parameters such as the gradient indices in both directions, moving speed, and excitation frequency of the acting load on the dynamic response of BDFG nanobeams. The obtained results can serve as a guideline for assessing the multi-functional and optimal design of micro/nanobeams acted upon by a moving load.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Attia

Shanab

2022

Acta Mech

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“…Karamanli 57 studied unconventional frequencies of geometrical imperfect 3D graded composite plates at microscale. Attia and Shanab 58 anticipated composite nanobeam free oscillations under surface and couple stresses. Sobhani et al 59 modeled a joined conical-spherical-cylindrical shell-type structure made of hybrid porous nanocomposites and analyzed its oscillations.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear three-dimensional oscillations of probabilistic reinforced nanocomposite shells at microscale via modified strain gradient meshfree formulations

Sahmani

Safaei

2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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A numerical solution process based on the moving Kriging meshfree is developed in the current exploration to predict microstructural-dependent three-dimensional nonlinear large-deflection oscillation response of probabilistic nanocomposite microsized shells considering deviatoric stretch, rotation, and dilatation gradient tensors. To do so, the modified strain gradient theory of mechanics is applied within the three-dimensional elasticity framework. Probabilistic composite microshells are prepared from nanocomposites reinforced by graphene nanofillers dispersed in different checkerboard schemes. Material properties are determined using a combination of the Monte-Carlo simulation and probabilistic-based micromechanical scheme. Thereafter, correct meshfree polynomial-based functions associated with a considered nodding system are applied to satisfy the essential boundary conditions correctly. It is described that the strengthening character corresponding to deviatoric stretch, rotation and dilatation, gradient tensors is stronger for probabilistic composite microshells containing nanofillers with larger aspect ratios and higher volume fractions. Also, a peak is observed for a certain three-dimensional frequency ratio at a specific ratio of the length to radius of the microshell. Considering microstructural gradient tensors, frequency ratio peak appears at a lower ratio of the length to radius of the microshell.

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“…Functionally graded material (FGM) is an innovative class of composites with continuous gradation of material through a certain spatial direction, which have enhanced properties rather than traditional composites, such as designability, reduced singular stress interface problems, small stress concentration, lower weight, higher fracture toughness, enhanced thermal properties, high damage resistance, etc. [1]. Due to their unique properties, FGMs are broadly employed in many applications such as electronics, dental implants, and turbines, as well as in aerospace, marine, automotive, military, and nuclear applications [2,3].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution

et al. 2022

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This paper presents for the first time a closed-form solution of the dynamic response of sigmoid bidirectional functionally graded (SBDFG) microbeams under moving harmonic load and thermal environmental conditions. The formulation is established in the context of the modified couple stress theory to integrate the effects of microstructure. On the basis of the elasticity theory, nonclassical governing equations are derived by using Hamilton’s principle in combination with the parabolic higher-order shear deformation theory considering the physical neutral plane concept. Sigmoid distribution functions are used to describe the temperature-dependent thermomechanical material of bulk continuums of the beam in both the axial and thickness directions, and the gradation of the material length scale parameter is also considered. Linear and nonlinear temperature profiles are considered to present the environmental thermal loads. The Laplace transform is exploited for the first time to evaluate the closed-form solution of the proposed model for a simply supported (SS) boundary condition. The solution is verified by comparing the predicted fundamental frequency and dynamic response with the previously published results. A parametric study is conducted to explore the impacts of gradient indices in both directions, graded material length scale parameters, thermal loads, and moving speed of the acted load on the dynamic response of microbeams. The results can serve as a principle for evaluating the multi-functional and optimal design of microbeams acted upon by a moving load.

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Vibration characteristics of two-dimensional FGM nanobeams with couple stress and surface energy under general boundary conditions

Cited by 27 publications

References 109 publications

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

On the dynamic response of bi-directional functionally graded nanobeams under moving harmonic load accounting for surface effect

Nonlinear three-dimensional oscillations of probabilistic reinforced nanocomposite shells at microscale via modified strain gradient meshfree formulations

Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution

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