Graphene sheet

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1 - Buckling Analysis of Orthotropic Annular Graphene Sheet with Various Boundary Conditions in an Elastic Medium
Hamed Vahabi Mohammad Esmaeil Golmakani Ismaeil Mobasher

In this study, axisymmetric buckling of annular orthotropic graphene sheet embedded in a Winkler–Pasternak elastic medium is scrutinized for different boundary conditions based on non-local elasticity theory. With the aid of principle of virtual work, the non-loca چکیده کامل

In this study, axisymmetric buckling of annular orthotropic graphene sheet embedded in a Winkler–Pasternak elastic medium is scrutinized for different boundary conditions based on non-local elasticity theory. With the aid of principle of virtual work, the non-local governing equations are derived based on First-order Shear Deformation Theory (FSDT). Differential Quadrature Method (DQM) is also used to solve equilibrium equations. Edges of Nano-plate might be restrained by different combinations of free, simply supported or clamped boundary conditions. To confirm results, comparison of studies is made between results obtained and available solutions in the literature. Finally, a detailed parametric study is conducted to investigate the impact of small scale effects, surrounding elastic medium, boundary conditions and geometrical parameters on critical buckling load. The main goal of this work is to study the effect of various non-local parameters on the buckling load of annular Nano-plate for different boundary conditions, Winkler and shear foundation parameters, annularity and thickness-to-radius ratios. It is seen that for Nano-plates without an elastic foundation, the impact of thickness on buckling load does not depend on values of non-local parameter and annularity. Results also show that impact of elastic basis on the buckling load is independent of small scale effects. پرونده مقاله

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2 - Investigation of the Effect of Pre-Stressed on Vibration Frequency of Rectangular Nanoplate Based on a Visco-Pasternak Foundation
M Goodarzi M Mohammadi A Farajpour M Khooran

In the present work, the free vibration behavior of rectangular graphene sheet under shear in-plane load is studied. Nonlocal elasticity theory has been implemented to study the vibration analysis of orthotropic single-layered graphenesheets (SLGSs) subjected to shear i چکیده کامل

In the present work, the free vibration behavior of rectangular graphene sheet under shear in-plane load is studied. Nonlocal elasticity theory has been implemented to study the vibration analysis of orthotropic single-layered graphenesheets (SLGSs) subjected to shear in-plane load. The SLGSs is embedded on a viscoelastic medium which is simulated as a Visco-Pasternak foundation. Using the principle of virtual work, the governing equations are derived for the rectangular nanoplates. Differential quadrature method (DQM) is employed and numerical solutions for the vibration frequency are obtained. The influence of surrounding elastic medium, material property, aspect ratio, nonlocal parameter, length of nanoplate and effect of boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets (SLGSs) is studied. Six boundary conditions are investigated. Numerical results show that the vibration frequencies of SLGSs are strongly dependent on the small scale coefficient and shear in-plane load. The present analysis results can be used for the design of the next generation of nanodevices that make use of the vibration properties of the graphene. پرونده مقاله

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3 - Levy Type Solution for Nonlocal Thermo-Mechanical Vibration of Orthotropic Mono-Layer Graphene Sheet Embedded in an Elastic Medium
M Mohammadi A Farajpour M Goodarzi R Heydarshenas

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy چکیده کامل

In this paper, the effect of the temperature change on the vibration frequency of mono-layer graphene sheet embedded in an elastic medium is studied. Using the nonlocal elasticity theory, the governing equations are derived for single-layered graphene sheets. Using Levy and Navier solutions, analytical frequency equations for single-layered graphene sheets are obtained. Using Levy solution, the frequency equation and mode shapes orthotropic rectangular nanoplate are considered for three cases of boundary conditions. The obtained results are subsequently compared with valid result reported in the literature. The effects of the small scale, temperature change, different boundary conditions, Winkler and Pasternak foundations, material properties and aspect ratios on natural frequencies are investigated. It has been shown that the non-dimensional frequency decreases with increasing temperature change. It is seen from the figure that the influence of nonlocal effect increases with decreasing of the length of nanoplate and also all results at higher length converge to the local frequency. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration proper ties of the nanoplates. پرونده مقاله

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4 - Temperature Effect on Vibration Analysis of Annular Graphene Sheet Embedded on Visco-Pasternak Foundati
M Mohammadi A Farajpour M Goodarzi H Mohammadi

In this study, the vibration behavior of circular and annular graphene sheet embedded in a Visco-Pasternak foundation and coupled with temperature change and under in-plane pre-load is studied. The single-layered annular graphene sheet is coupled by an enclosing viscoel چکیده کامل

In this study, the vibration behavior of circular and annular graphene sheet embedded in a Visco-Pasternak foundation and coupled with temperature change and under in-plane pre-load is studied. The single-layered annular graphene sheet is coupled by an enclosing viscoelastic medium which is simulated as a Visco- Pasternak foundation. By using the nonlocal elasticity theory and classical plate theory, the governing equation is derived for single-layered graphene sheets (SLGSs). The closed-form solution for frequency vibration of circular graphene sheets has been obtained and nonlocal parameter, in-plane pre-load, the parameters of elastic medium and temperature change appears into arguments of Bessel functions. To verify the accuracy of the present results, the new version differential quadrature method (DQM) is also developed. Closed-form results are successfully veriﬁed with those of the DQM results. The results are subsequently compared with valid result reported in the literature. The effects of the small scale, pre-load, mode number, temperature change, elastic medium and boundary conditions on natural frequencies are investigated. The non-dimensional frequency decreases at high temperature case with increasing the temperature change for all boundary conditions. The effect of temperature change on the non-dimensional frequency vibration becomes the opposite at high temperature case in compression with the low temperature case. The present research work thus reveals that the nonlocal parameter, boundary conditions, temperature change and initial pre-load have significant effects on vibration response of the circular nanoplates. The present analysis results can be used for the design of the next generation of nanodevices that make use of the thermal vibration properties of the graphene. پرونده مقاله

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5 - Closed-form Solution of Dynamic Displacement for SLGS Under Moving the Nanoparticle on Visco-Pasternak Foundation
A Ghorbanpour Arani A Shiravand S Amir

In this paper, forced vibration analysis of a single-layered graphene sheet (SLGS) under moving a nanoparticle is carried out using the non-local elasticity theory of orthotropic plate. The SLGS under moving the nanoparticle is placed in the elastic and viscoelastic fou چکیده کامل

In this paper, forced vibration analysis of a single-layered graphene sheet (SLGS) under moving a nanoparticle is carried out using the non-local elasticity theory of orthotropic plate. The SLGS under moving the nanoparticle is placed in the elastic and viscoelastic foundation which are simulated as a Pasternak and Visco-Pasternak medium, respectively. Movement of the nanoparticle is considered as a linear movement with constant velocity from an edge to another edge of graphene sheet. Using the non-linear Von Kármán strain-displacement relations and Hamilton’s principle, the governing differential equations of motion are derived. The differential equation of motion for all edges simply supported boundary condition is solved by an analytical method and therefore, the dynamic displacement of SLGS is presented as a closed-form solution of that. The influences of medium stiffness (Winkler, Pasternak and damper modulus parameter), nonlocal parameter, aspect ratio, mechanical properties of graphene sheet, time and velocity parameter on dimensionless displacement (dynamic displacement to static displacement of SLGS) are studied. The results indicate that, as the values of stiffness modulus parameter increase, the maximum dynamic displacement of SLGS decreases. Therefore, the results are in good agreement with the previous researches. پرونده مقاله

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6 - Nonlocal Bending Analysis of Bilayer Annular/Circular Nano Plates Based on First Order Shear Deformation Theory
Sh Dastjerdi M Jabbarzadeh

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Sh چکیده کامل

In this paper, nonlinear bending analysis of bilayer orthotropic annular/circular graphene sheets is studied based on the nonlocal elasticity theory. The equilibrium equations are derived in terms of generalized displacements and rotations considering the first-order Shear deformation theory (FSDT). The nonlinear governing equations are solved using the differential quadrature method (DQM) which is a highly accurate numerical method and a new semi-analytical polynomial method (SAPM). The ordinary differential equations (ODE’s) are converted to the nonlinear algebraic equations applying DQM or SAPM. Then, the Newton–Raphson iterative scheme is applied. The obtained results of DQM and SAPM are compared. It is concluded that although, the SAPM’s formulation is considerably simple in comparison with DQM, however, the results of two methods are so close to each other. The results are validated with available researches. The effects of small scale parameter, the value of van der Waals interaction between the layers, different values of elastic foundation and loading, the comparison between the local and nonlocal deflections and linear to nonlinear analysis are investigated. پرونده مقاله

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7 - Non-Local Thermo-Elastic Buckling Analysis of Multi-Layer Annular/Circular Nano-Plates Based on First and Third Order Shear Deformation Theories Using DQ Method
Sh Dastjerdi M Jabbarzadeh

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shea چکیده کامل

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multi-layer sheets. The stability governing equations are obtained according to the adjacent equilibrium estate method. The constitutive equations are solved by applying the differential quadrature method (DQM). Applying the differential quadrature method, the ordinary differential equations are transformed to algebraic equations. Then, the critical temperature is obtained. Since there is not any research in thermo-elastic buckling analysis of multi-layer graphene sheets, the results are validated with available single layer articles. The effects of non-local parameter, the values of van der Waals interaction between the layers, third to first order shear deformation theory analyses, non-local to local analyses, different values of Winkler and Pasternak elastic foundation and analysis of bi-layer and triple layer sheets are investigated. It is concluded that the critical temperature increases and tends to a constant value along the rise of van der Waals interaction between the layers. پرونده مقاله

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8 - Lateral Vibrations of Single-Layered Graphene Sheets Using Doublet Mechanics
A Fatahi-Vajari A. Imam

This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that gove چکیده کامل

This paper investigates the lateral vibration of single-layered graphene sheets based on a new theory called doublet mechanics with a length scale parameter. After a brief reviewing of doublet mechanics fundamentals, a sixth order partial differential equation that governs the lateral vibration of single-layered graphene sheets is derived. Using doublet mechanics, the relation between natural frequency and length scale parameter is obtained in the lateral mode of vibration for single-layered graphene. It is shown that length scale parameter plays a significant role in the lateral vibration behavior of single-layered graphene sheets. Such effect decreases the natural frequency compared to the predictions of the classical continuum mechanics models. However with increasing the length of the plate, the effect of scale parameter on the natural frequency decreases. For validating the results of this method, the results obtained herein are compared with the existing nonlocal and molecular dynamics results and good agreement with the latter is observed. پرونده مقاله

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9 - Investigation of Linear and Nonlinear Buckling of Orthotropic Graphene Sheets with Nonlocal Elasticity Theories
مصطفی صادقیان مهرداد جبارزاده

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of nonlocal elasticity theory, the principle of virtual work, first order shear theo چکیده کامل

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the method of differential quadrature (DQ) with non-uniform distribution points (Chebyshev -Gauss-Lobato) has been used. To check the validity, the obtained results have been compared with other resources, and the effects of nonlocal coefficient, thickness, radius and elastic base on the dimensionless buckling loads were calculated and investigated. Moreover, the results of analysis using nonlocal and local theory were compared together. It can be noticed that the dimensionless buckling loads on graphene sheets increased more with a decrease in flexibility as far boundary condition is concerned. Additionally, with an increase in the sheet radius, the variation between nonlocal and local analysis results will be more. پرونده مقاله

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10 - Bending Sector Graphene Sheet Based on the Elastic Winkler-Pstrnak with the Help of Nonlocal Elasticity Theory Using Developed Kantorovich Method
شهریار دستجردی مهرداد جبارزاده

In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with rega چکیده کامل

In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich method. In this method, the obtained partial differential equations are converted into two categories that can be solved using analytical and numerical methods. Developed Kantorovich method is a method with a high rate of convergence, in which the expected convergence is achieved with just three to four repetitions. With regard to the fact that no research has yet been conducted in this regard, the results, considering the nonlocal coefficient equal to zero, have been compared with other articles in order to check the validity. In the end, the effect of nonlocal coefficient variations on the results in terms of thickness, boundary conditions, hardness of elastic base and difference between nonlocal and local elasticity analysis has been studied. پرونده مقاله

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11 - Vibration and Buckling of Double-Graphene Sheet-Systems with an Attached Nanoparticle Based on Classical and Mindlin Plate Theories Considering Surface Effects
محمد هاشمیان

Vibration of double-graphene sheet-system is considered in this study. Graphene sheets are coupled by Pasternak elastic medium. Classic and Mindlin plate theories are utilized for modeling the coupled system. Upper sheet carries a moving mass. Governing equations are de چکیده کامل

Vibration of double-graphene sheet-system is considered in this study. Graphene sheets are coupled by Pasternak elastic medium. Classic and Mindlin plate theories are utilized for modeling the coupled system. Upper sheet carries a moving mass. Governing equations are derived using energy method and Hamilton’s principle considering surface stress effects and nonlocal parameter. Using Galerkin method, figures of frequency versus nonlocal parameter are drawn and the effects of different parameters such as moving mass, surface effects and etc. are discussed. Results show considering surface effects, the frequency of coupled system increases. Also heavier mass and farther mass away from supports will result in lower frequencies پرونده مقاله

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