Thermo-mechanical vibration analysis of annular and circular graphene sheet embedded in an elastic medium

Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model

Effects of eccentric circular perforation on thermal vibration of circular graphene sheets using translational addition theorem

Because of the production process and constraint conditions, a circular graphene sheet may be opposed to structural defect and pin hole, respectively. Some of the defects and pin hole on a circular graphene sheet can be considered as an eccentric hole. So, analyzing the behavior of a circular graphene sheet with an eccentricholeisimportant.Freevibrationofaneccentricannulargraphenesheet,asthebasisofanydynamical analysis, is analytically studied in this paper. Nonlocal thin plate theory is used to model the problem. The translationaladditiontheoremforcylindricalvectorwavefunctionsisemployedtosolvetheequationofmotion for various boundary conditions. Results are compared with the literature, and their accuracy is approved. Effects of boundary conditions, geometrical properties and nonlocal parameter changes on symmetric and antisymmetric vibrational modes are investigated. It is approved that the eccentricity has a significant effect on the natural frequencies. Also, symmetric and antisymmetric modes of an annular graphene sheet have different behavior when geometrical and nonlocal parameters change.

Possessing the unique and highly valuable properties, graphene sheets (GSs) have attracted increasing attention including that from the building engineer due to the fact that Graphene can be utilized to reinforce concrete and other building materials. In this work, the nonlocal elastic theory and classical plate theory (CLPT) are used to derive the governing equations. The element-free framework for analyzing the buckling behaviors of double layer circular graphene sheets (DLCGSs) relying on an elastic medium is proposed. Pasternak-type model is adopted to describe the elastic medium. Accordingly, the influences of boundary conditions, size of GSs and nonlocal parameters on the buckling behavior of DLCGSs are investigated. The results show that the OP buckling modes are only sensible to the van der Waals forces.

Influence of in-plane pre-load on the vibration frequency of circular graphene sheet via nonlocal continuum theory

Recently, graphene sheets have shown significant potential for environmental engineering applications such as wastewater treatment. Different non-classical theories have been used for modeling of such nano-sized systems to take account of the effect of small length scale. Among all size-dependent theories, the nonlocal elasticity theory has been commonly used to examine the stability of nano-sized structures. Some research works have been reported about the mechanical behavior of rectangular nanoplates with the consideration of thermal effects. However, in comparison with the rectangular graphene sheets, research works about the nanoplates of circular shape are very limited, especially for the buckling properties with thermal effects. Hence, in this paper, an axisymmetric buckling analysis of circular single-layered graphene sheets (SLGS) is presented by decoupling the nonlocal equations of Eringen theory. Constitutive relations are modified to describe the nonlocal effects. The governing equations are derived using equilibrium equations of the circular plate in polar coordinates. Numerical solutions for buckling loads are computed using Galerkin method. 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, radius-to-thickness ratio, temperature change and mode numbers are investigated.

ABSTRACTIn this article, the small-scale effect on the vibration behavior of orthotropic single-layered graphene sheets is studied based on the nonlocal Reddy's plate theory embedded in elastic medium considering initial shear stress. Elastic theory of the graphene sheets is reformulated using the nonlocal differential constitutive relations of Eringen. To simulate the interaction between the graphene sheet and surrounding elastic medium we used both Winkler-type and Pasternak-type foundation models. The effects of initial shear stress and surrounding elastic medium and boundary conditions on the vibration analysis of orthotropic single-layered graphene sheets are studied considering five different boundary conditions. Numerical approach of the obtained equation is derived by differential quadrature method. Effects of shear stress, nonlocal parameter, size of the graphene sheets, stiffness of surrounding elastic medium, and boundary conditions on vibration frequency rate are investigated. The results reveal that as the stiffness of the surrounding elastic medium increases, the nonlocal effect decreases. Further, the nonlocal effect increases as the size of the graphene sheet is decreased. It is also found that the frequency ratios decrease with an increase in vibration modes.

Calibration of Eringen's small length scale coefficient for buckling circular and annular plates via Hencky bar-net model

Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment

As the strongest and toughest material known, graphene has found numerous applications in various types of sensors. Due to the great influences of the graphene sheet’s geometry on resonance frequency, circular defects could effect on expected results of sensors. Circular holes in circular graphene sheets (CGSs) have been modeled with molecular dynamics (MD) simulation in the present work. Then the vibration behavior of intact circular plate and circular sheet with the circular defect has been investigated using frequency-domain analysis (FDD). Furthermore, for validating the used method, the obtained natural frequencies for different graphene sheets have been compared with acquired data in former research. The result of validation showed the accuracy of the used method in this study. The results indicated that by increasing the hole size, the natural frequency of a defected sheet with free edges will be diminished, and with simply-supported interior boundary conditions typically went up. Also, by increasing the hole’s eccentricity, the natural frequency of the defected graphene sheet will be diminished when the hole boundary was subjected to simply-support or free condition.

Vibration analysis of quadrilateral graphene sheets subjected to an in-plane magnetic field based on nonlocal elasticity theory

Multipole Trefftz method implementation in free vibration of a graphene sheet with multiple vacancy defects

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

Analytical investigation on free vibration of circular double-layer graphene sheets including geometrical defect and surface effects

The Eringen's nonlocal elasticity theory is employed to examine the free vibration of a rotating cantilever single-layer graphene sheet (SLGS) under low and high temperature conditions. The governing equations of motion and the related boundary conditions are obtained through Hamilton's principle based on the first-order shear deformation theory (FSDT) of nanoplates. The generalized differential quadrature method (GDQM) is utilized to solve the nondimensional equations of motion. The molecular dynamics (MD) simulation is conducted, and fundamental frequencies of the rotating cantilever square SLGS are computed using the fast Fourier transform (FFT). The comparison of MD and GDQM results leads to finding the appropriate value of the nonlocal parameter for the first time. As an interesting result, this value of the nonlocal parameter is independent of the angular velocity. Results indicate that increases in various parameters, such as the angular velocity, hub radius, nonlocal parameter, and temperature changes in low temperature conditions, leads the first and the second frequencies to increase. In addition, it can be seen that the influence of the hub radius or nonlocal parameters on frequencies cannot be ignored in high angular velocities. Moreover, it is not possible to neglect the angular velocity or nonlocal parameter in high hub radius. The results show that the influence of parameters such as setting angle or nonlocal parameter on the first and the second frequencies increases when some parameters increase, such as the angular velocity, hub radius or temperature change. Graphical abstract (a) A schematic of a rotating cantilever nanoplate. (b) A schematic of cantilever armchair SLGS simulated by MD.