RETRACTED: Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects

Enayat, Shahzad; Hashemian, Mohammad; Toghraie, Davood; Jaberzadeh, E.

doi:10.1002/zamm.202000231

Cited by 14 publications

(11 citation statements)

References 64 publications

(80 reference statements)

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“…where, T = 0, 0, q, 0, 0 ½ T . Inserting equation ( 13) into equation (19) for e s and then integrating over the top and bottom surfaces for the work due to t 0 give…”

Section: Matrix Representation Of the Energy Functionalmentioning

confidence: 99%

“…Gholami et al 18 suggested a multiscale scheme accounting for the geometric and material nonlinearities to investigate the vibrations behavior of embedded graphene sheets with large-amplitude of oscillations. Enayat et al 19 used the nonlocal and Gurtin-Murdoch’s surface theories to do a mechanical analysis of functionally graded porous nanobeams subjected to thermal environment. Abdelrahman and Eltaher 20 presented a comprehensive study to evaluate the static bending and buckling stability of perforated nanobeams with consideration of the surface free energy based on different beam theories.…”

Section: Introductionmentioning

confidence: 99%

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On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

Shahabodini

Ahmadi

2021

Proceedings of the Institution of Mechanical Engineers, Part N:

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In this research, an elastic model based on the continuum mechanics is developed to study the static behaviors of functionally graded (FG) arbitrary straight-sided quadrilateral nanoplates. The model is constructed in the framework of Gurtin-Murdoch’s surface and Mindlin’s plate theories to account for the surface energy and shear deformation effects, simultaneously. The variational differential quadrature (VDQ) method is used along with a mapping technique to do the discretization process in a variational framework by means of differential and integral operators. Consequently, a weak form of governing equations is obtained from the energy quadratic representation of the problem. The solution method is of a distinguished feature as it involves just the first-order derivative of the field components in the mapping and discretization. After assuring the effectiveness of presented model by doing comparative studies, the critical buckling load and static deflection of the FG nanoplates with different shapes in geometry are investigated considering the surface effects. It is found that the surface energies effect on the static behavior of the rectangular nanoplates is more significant as compared to the non-rectangular nanoplates.

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“…where, T = 0, 0, q, 0, 0 ½ T . Inserting equation ( 13) into equation (19) for e s and then integrating over the top and bottom surfaces for the work due to t 0 give…”

Section: Matrix Representation Of the Energy Functionalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

Shahabodini

Ahmadi

2021

Proceedings of the Institution of Mechanical Engineers, Part N:

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“…Enayat et al. [47] modeled dynamically the bending behavior of a nonlocal strain gradient functionally graded porous nanobeams resting on Pasternak foundation in thermal environment based on Euler‐Bernoulli beam theory, Timoshenko beam theory and Reddy's third‐order shear deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Shear vibration modes of granular structures: Continuous and discrete approaches

et al. 2023

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This work is dedicated to the study of shear vibration modes of one‐dimensional granular microstructured beams using a discrete Cosserat model. The dynamic response of the one‐dimensional granular beam (discrete beam) is investigated for various boundary conditions, through the analytical resolution of an exact discrete eigenvalue problem. For an infinite number of grains, the dynamic behavior of the discrete problem converges towards a Bresse–Timoshenko continuum beam model. First, the effective modeling parameters, the constitutive equations and the governing equations of motion are derived in a difference form. For simply supported granular beams, the appearance of pure shear modes of vibration is highlighted (vibration modes without deflection), a phenomenon which is already known in the free vibration of a continuous Bresse–Timoshenko beam problem. The eigenfrequencies of these pure shear modes for the discrete granular beam coincide with the critical frequencies of the discrete system. These pure shear modes may appear for granular beams composed of few grains, which give a physical support of a phenomenon well studied in the literature from a continuum beam model. The eigenfrequencies of the discrete granular beam are also calculated for various boundary conditions, including clamped, hinge and free end boundary conditions. Based on the discrete element method (DEM), several numerical simulations of dynamic tests in some representative examples have been performed. The responses of the numerical approach are accurately compared against the exact results of the analytical solutions based on the difference eigenvalue problem, which illustrates the relevance of the proposed approach.

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“…The influences of the porosity parameter, viscosity of the pore fluid, the velocity of the moving loads, and stiffness of the foundation on the dynamic response of the beam were examined by them. Enayat et al 28 , 29 studied the mechanical buckling, static bending, and free vibration characteristics of porous nanobeams subjected to thermal loading. It was shown by them that by increasing the porosity parameter, the static deflection increases and the critical buckling load decrease; but the effect of the porosity parameter on the natural frequencies significantly depends on the pore distribution pattern.…”

Section: Introductionmentioning

confidence: 99%

The vibration study of a sandwich conical shell with a saturated FGP core

Esfahani

Hashemian

Aghadavoudi

2022

Sci Rep

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This paper is provided to analyze the free vibration of a sandwich truncated conical shell with a saturated functionally graded porous (FGP) core and two same homogenous isotropic face sheets. The mechanical behavior of the saturated FGP is assumed based on Biot’s theory, the shell is modeled via the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived utilizing Hamilton’s principle. Three different porosity distribution patterns are studied including one homogenous uniform distribution pattern and two non-homogenous symmetric ones. The porosity parameters in mentioned distribution patterns are regulated to make them the same in the shell’s mass. The equations of motion are solved exactly in the circumferential direction via proper sinusoidal and cosinusoidal functions, and a numerical solution is provided in the meridional direction utilizing the differential quadrature method (DQM). The precision of the model is approved and the influences of several parameters such as circumferential wave number, the thickness of the FGP core, porosity parameter, porosity distribution pattern, the compressibility of the pore fluid, and boundary conditions on the shell’s natural frequencies are investigated. It is shown that the highest natural frequencies usually can be achieved when the larger pores are located close to the shell’s middle surface and in each vibrational mode, there is a special value of the porosity parameter which leads to the lowest natural frequencies. It is deduced that in most cases, natural frequencies decrease by increasing the thickness of the FGP core. In addition, reducing the compressibility of the porefluid a small growth in the natural frequencies can be seen.

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RETRACTED: Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects

Cited by 14 publications

References 64 publications

On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

On the buckling and bending analysis of FG straight-sided quadrilateral nanoplates using a continuum mechanics-based surface elastic model

Shear vibration modes of granular structures: Continuous and discrete approaches

The vibration study of a sandwich conical shell with a saturated FGP core

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