Nonlocal vibration analysis of nanomechanical systems resonators using circular double-layer graphene sheets

Double-layer graphene sheets (DLGSs) have potential applications as nanoelectromechanical systems (NEMS) resonators due to their specific carrier spectrum of electrons. In this study, analysis of the vibration modes of NEMS resonators using simply supported circular DLGSs has been undertaken based on nonlocal thin plate theory. Considering the properties of DLGSs, the vibration mode of circular DLGSs can be divided into an in-phase mode (IPM) and an anti-phase mode (APM). The range of resonance frequencies in the IPM is much larger than in the APM because of the influence of van der Waals forces. Nonlocal effects significantly influence the resonance frequency of circular DLGSs in higher vibration modes and at lower aspect ratios.     

Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model

In this article, the buckling behavior of nanoscale circular plates under uniform radial compression is studied. Small-scale effect is taken into consideration. Using nonlocal elasticity theory the governing equations are derived for the circular single-layered graphene sheets (SLGS). Explicit expressions for the buckling loads are obtained for clamped and simply supported boundary conditions. It is shown that nonlocal effects play an important role in the buckling of circular nanoplates. The effects of the small scale on the buckling loads considering various parameters such as the radius of the plate and mode numbers are investigated.     

Nonlocal vibration of coupled DLGS systems embedded on Visco-Pasternak foundation

In this paper, vibration analysis of the coupled system of double-layered graphene sheets (CS-DLGSs) embedded in a Visco-Pasternak foundation is carried out using the nonlocal elasticity theory of orthotropic plate. The two DLGSs are coupled by an enclosing viscoelastic medium which is simulated as a Visco-Pasternak foundation. Considering the Von Kármán nonlinear strain-displacement-relations, the motion equations are derived using the Hamilton's principle. Differential quadrature method (DQM) is applied to obtain the frequency ratio for various boundary conditions. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, aspect ratio, graphene sheet's size, boundary conditions and the elastic and viscoelastic medium coefficients on the frequency ratio of CS-DLGSs. In this coupled system, two case of DLGSs vibration are investigated and compared with each other: (1) In-phase vibration (2) Out-of-phase vibration. The results indicate that the frequency ratio of the CS-DLGSs is more than the single-layered graphene sheet (SLGS). The results are in good agreement with the previous researches.     

Explicit analytical expressions for the critical buckling stresses in a monolayer graphene sheet based on nonlocal elasticity

Explicit expressions are given to study the biaxial buckling of monolayer graphene sheets. Based upon the continuum mechanics, a plate model is adopted in which the small length scale effect is incorporated into the governing equation through the nonlocal elasticity theory of Eringen. By employing the Galerkin method, analytical expressions are derived which allow quick and accurate calculation of the critical buckling loads of monolayer graphene sheets with various boundary conditions from the static deflection under a uniformly distributed load. The effectiveness of the present study is assessed by molecular dynamics simulations as a benchmark of good accuracy.     

Elastic instability of bilayer graphene using atomistic finite element

In-plane elastic instability of bilayer graphene sheets is investigated using atomistic finite element approaches. The equivalent homogenised properties of graphene sheet are expressed in terms of the thickness, equilibrium lengths and force-field models used to represent the C–C bonds of the graphene lattice. The covalent bonds are represented as structural beams with stretching, bending, torsional and shear deformation, and the strain energies associated to affine deformation mechanisms. The overall mechanical properties and geometric configurations of the nano-structures represented as truss assemblies are then calculated minimising the total potential energy associated to the loading, thickness and average equilibrium lengths of the bonds. Different boundary conditions and aspect ratios are considered for both bilayer and single-layer graphene sheets. The bilayer graphene sheets are found to be offering remarkably higher buckling strengths as compared to single-layer sheets.     

Atomistic finite element model for axial buckling and vibration analysis of single-layered graphene sheets

In this article, an atomistic model is developed to study the buckling and vibration characteristics of single-layered graphene sheets (SLGSs). By treating SLGSs as space-frame structures, in which the discrete nature of graphene sheets is preserved, they are modeled using three-dimensional elastic beam elements for the bonds. The elastic moduli of the beam elements are determined via a linkage between molecular mechanics and structural mechanics. Based on this model, the critical compressive forces and fundamental natural frequencies of single-layered graphene sheets with different boundary conditions and geometries are obtained and then compared. It is indicated that the compressive buckling force decreases when the graphene sheet aspect ratio increases. At low aspect ratios, the increase of aspect ratios will result in a significant decrease in the critical buckling load. It is also indicated that increasing aspect ratio at a given side length results in the convergence of buckling envelops associated with armchair and zigzag graphene sheets. The influence of boundary conditions will be studied for different geometries. It will be shown that the influence of boundary conditions is not significant for sufficiently large SLGSs.     

Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory

Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells.     

Nonlocal elasticity theory for thermal buckling of nanoplates lying on Winkler–Pasternak elastic substrate medium

In the present work, thermal buckling of single-layered graphene sheets lying on an elastic medium is analyzed. For this purpose, the sinusoidal shear deformation plate theory in tandem with the nonlocal continuum theory, which takes the small scale effects into account, is employed. The non-linear stability equations, which contain the reaction of Winkler–Pasternak elastic substrate medium, are derived and then solved analytically for a plate with various boundary conditions and based on various plate theories. Closed form solutions are formulated for three types of thermal loadings as uniform, linear and nonlinear temperature rise through the thickness of the plate. A number of examples are presented to illustrate the numerical results concerned with the buckling temperature response of nanoplates resting on two-parameter elastic foundations. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, nonlocal parameter, and elastic foundation parameters are all investigated.     

Free vibrations and buckling of graphene sheets

The molecular mechanics method is used to determine both eigenfrequencies and modes of vibrations and the critical compressing loads and buckling modes of graphene sheets. To simulate interatomic interactions in graphene, the DREIDING field of potential forces is used. This field includes four types of potential energies of covalent atomic interactions such as central forces, the variations in the angle between the neighboring bonds, the dihedral angle that is responsible for the torsion of the covalent bond, and the inversion angle (the angle corresponding to the retiring of the atom from the plane relative to three neighboring atoms).     

A review on silicene — New candidate for electronics

Silicene-the silicon-based counterpart of graphene-has a two dimensional structure that is responsible for the variety of potentially useful chemical and physical properties. The existence of silicene has been achieved recently owing to experiments involving epitaxial growth of silicon as stripes on Ag(001), ribbons on Ag(110), and sheets on Ag(111). The nano-ribbons observed on Ag(110) were found-by both high definition experimental scanning tunneling microscopy images and density functional theory calculations-to consist of an arched honeycomb structure. Angle resolved photo-emission experiments on these silicene nano-ribbons on Ag(110), along the direction of the ribbons, showed a band structure which is analogous to the Dirac cones of graphene. Unlike silicon surfaces, which are highly reactive to oxygen, the silicene nano-ribbons were found to be resistant to oxygen reactivity.On the theoretical side, recent extensive efforts have been deployed to understand the properties of standalone silicene sheets and nano-ribbons using both tight-binding and density functional theory calculations. Unlike graphene it is demonstrated that silicene sheets are stable only if a small buckling (0.44 Å) is present. The electronic properties of silicene nano-ribbons and silicene sheets were found to resemble those of graphene.Although this is a fairly new avenue, the already obtained outcome from these important first steps in understanding silicene showed promising features that could give a new future to silicon in the electronics industry, thus opening a promising route toward wide-range applications. In this review, we plan to introduce silicene by presenting the available experimental and theoretical studies performed to date, and suggest future directions to be explored to make the synthesis of silicene a viable one.     

热力联合作用弹性薄圆板的弯曲与屈曲

 导出了热力联合作用下弹性薄圆板的弯曲动力响应控制方程,讨论了其弯曲变形特点及影响失效的因素。分析表明在短时热能沉积作用下,热屈曲是弹性薄板失效的主要方式之一;反鼓包或反冲塞是热屈曲的后继行为;增加外载和热能沉积功率水平都将加速热屈曲的发生;材料的温度相关性与热能沉积的时空分布对薄板的力学行为都有重要影响,同为产生和影响热剪切失效(反冲塞)的重要因素。     

Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory

This study presents an analytical approach for buckling analysis and smart control of a single layer graphene sheet (SLGS) using a coupled polyvinylidene fluoride (PVDF) nanoplate. The SLGS and PVDF nanoplate are considered to be coupled by an enclosing elastic medium which is simulated by the Pasternak foundation. The PVDF nanoplate is subjected to an applied voltage in the thickness direction which operates in control of critical load of the SLGS. In order to satisfy the Maxwell equation, electric potential distribution is assumed as a combination of a half-cosine and linear variation. The exact analysis is performed for the case when all four ends are simply supported and free electrical boundary condition. Adopting the nonlocal Mindlin plate theory, the governing equations are derived based on the energy method and Hamilton's principle. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, stiffness of the internal elastic medium, graphene length, mode number and external electric voltage on the buckling smart control of the SLGS. The results depict that the imposed external voltage is an effective controlling parameter for buckling of the SLGS. This study might be useful for the design and smart control of nano-devices.     

Direct observation of nanocrystallite buckling in carbon fibers under bending load

Single carbon fibers are deformed in bending by forming loops with varying radius. Position-resolved x-ray diffraction patterns from the bent fibers are collected from the tension to the compression region with a synchrotron radiation nanobeam of 100 nm size from a waveguide structure. A strain redistribution with a shift of the neutral axis is observed. A significant increase of the misorientation of the graphene sheets in the compression region shows that intense buckling of the nanosized carbon crystallites is the physical origin of different tensile and compressive properties.     

Buckling analysis of variable thickness nanoplates using nonlocal continuum mechanics

This paper presents an investigation on the buckling characteristics of nanoscale rectangular plates under bi-axial compression considering non-uniformity in the thickness. Based on the nonlocal continuum mechanics, governing differential equations are derived. Numerical solutions for the buckling loads are obtained using the Galerkin method. The present study shows that the buckling behaviors of single-layered graphene sheets (SLGSs) are strongly sensitive to the nonlocal and non-uniform parameters. The influence of percentage change of thickness on the stability of SLGSs is more significant in the strip-type nonoplates (nanoribbons) than in the square-type nanoplates.     

单层石墨烯片的非线性板模型

基于实验得到的非线性本构关系和板理论,本文建立了包含三次及五次非线性项的单层石墨烯片的板动力学模型.针对四边简支矩形板,使用Ritz法研究了在板中点作用集中力时的静力弯曲,以及边界均匀受力时的静力屈曲问题.结果显示,基于非线性本构关系的板模型能很好的描述单层石墨烯片的力学行为,而且模型中的五次非线性项对结构的弯曲变形有显著影响.     

Estimation of critical dislocation distances

In this article, graphene is investigated with respect to its electronic properties when introduced into field effect devices (FED). With the exception of manual graphene deposition, conventional top-down CMOS-compatible processes are applied. Few and monolayer graphene sheets are characterized by scanning electron microscopy, atomic force microscopy and Raman spectroscopy. The electrical properties of monolayer graphene sandwiched between two silicon dioxide films are studied. Carrier mobilities in graphene pseudo-MOS structures are compared to those obtained from double-gated Graphene-FEDs and silicon metal-oxide-semiconductor field-effect-transistors (MOSFETs).     

Vibration analysis of defective graphene sheets using nonlocal elasticity theory

Many papers have studied the free vibration of graphene sheets. However, all this papers assumed their atomic structure free of any defects. Nonetheless, they actually contain some defects including single vacancy, double vacancy and Stone-Wales defects. This paper, therefore, investigates the free vibration of defective graphene sheets, rather than pristine graphene sheets, via nonlocal elasticity theory. Governing equations are derived using nonlocal elasticity and the first-order shear deformation theory (FSDT). The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defective graphene sheets. Afterwards, these equations solved using generalized differential quadrature method (GDQ). The small-scale effect is applied in the governing equations of motion by nonlocal parameter. The effects of different defect types are inspected for graphene sheets with clamped or simply-supported boundary conditions on all sides. It is shown that the natural frequencies of graphene sheets decrease by introducing defects to the atomic structure. Furthermore, it is found that the number of missing atoms, shapes and distributions of structural defects play a significant role in the vibrational behavior of graphene. The effect of vacancy defect reconstruction is also discussed in this paper.     

梳状波导结构中石墨烯表面等离子体的传播性质

理论上研究了介质/石墨烯/介质梳状波导结构中表面等离子体的传播性质. 波导中表面等离子体模的有效折射率随着石墨烯费米能级的提高而减小, 随着介质折射率的增加而增加. 分析和仿真结果表明, 基于这种梳状波导可以在中红外波段实现新型的纳米等离子体滤波器, 器件的尺度在几百纳米的范围. 通过改变梳状分支的长度, 石墨烯的费米能级, 介质的折射率和波导中石墨烯的层数, 很容易来调节带隙的位置. 另外, 滤波带隙的宽度随着梳状分支数的增加而增加. 这种滤波性质将在可调的高集成光子滤波器件中具有潜在的应用.     

Topological mode switching in a graphene doublet with exceptional points

We investigate the switching between two surface plasmon polariton modes in a non-Hermitian system composed of a pair of graphene sheets using topological operations. The topological operation is implemented by suitably designing the waveguide geometry and the chemical potential of graphene, which is equivalent to changing the system parameters along a closed loop in the parameter space. Efficient and robust mode switching takes place as the loop encloses an exceptional point and the wave experiences a sufficiently large propagation length. Moreover, we show this mode switching is chiral, in the sense that the output modes are different for choosing different loop directions. The study provides a promising approach to robust mode switching on a deep-subwavelength scale.     

Neutron polarization induced by interfering pseudospins between two graphene sheets inserted into a cavity

We investigate the neutron polarization induced by interfering pseudospins between two graphene sheets inserted into a cavity with a circularly polarized photon field. We find that only when two graphene sheets are located at the coordinate positions of some antinodes of standing photon field, the neutron polarization is most remarkable. This is caused by an interference effect of pseudospins between two graphene sheets induced by photons and neutron. This neutron polarization mechanism has potential application on neutron polarization device.